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Subject: [Boost-commit] svn:boost r55777 - sandbox/gtl/doc/GTL_boostcon_draft03_files
From: lucanus.j.simonson_at_[hidden]
Date: 2009-08-25 11:55:52


Author: ljsimons
Date: 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
New Revision: 55777
URL: http://svn.boost.org/trac/boost/changeset/55777

Log:
added support files for boostcon presentation
Added:
   sandbox/gtl/doc/GTL_boostcon_draft03_files/
   sandbox/gtl/doc/GTL_boostcon_draft03_files/buttons.gif (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/filelist.xml (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/frame.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/fullscreen.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/master01.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/master03.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/master03.xml (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/master03_stylesheet.css (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/outline.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/pres.xml (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/preview.wmf (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/script.js (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001_image001.png (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001_image002.jpg (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0002.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0002_image003.png (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0002_image004.jpg (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0003.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0003_image005.png (contents, props changed)
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   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006.xml (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006_image032.gif (contents, props changed)
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   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006_image068.gif (contents, props changed)
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   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0007.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0007_image082.gif (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0010.htm (contents, props changed)
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   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0012.htm (contents, props changed)
   sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0012_image093.png (contents, props changed)
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+<table style='position:relative' align=center cellpadding=0 cellspacing=0>
+ <td>
+ <div style='position:absolute;left:-18px;width:24px;height:20px;border-style:
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+
+<table width="100%" style='font-family:Arial;font-size:9pt'>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>1</font></div>
+ </td>
+ <td width="100%">
+ <div id=PPTP1 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0001.htm');" id=PPTL1>GTL<span
+ style='mso-spacerun:yes'>  </span>Geometry Template Library</a></font></div>
+ <div id=PPTC1 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>-for stl-like polygon manipulation</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>2</font></div>
+ </td>
+ <td>
+ <div id=PPTP2 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0073.htm');" id=PPTL2>Overview</a></font></div>
+ <div id=PPTC2 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intel badly needed high performance algorithms for planar polygon
+ manipulation</li>
+ <ul>
+ <li>I implemented them</li>
+ </ul>
+ <li>We have 2D Cartesian geometry</li>
+ <ul>
+ <li>Coordinate, Interval, Point, Rectangle, Polygon, Polygon Set</li>
+ <li>Library of concepts for each</li>
+ </ul>
+ <li>Many generic functions that operate on conceptual types</li>
+ <ul>
+ <li>API strives for symmetry, consistency and simplicity</li>
+ </ul>
+ <li>Some pretty heavy weight algorithms under the hood</li>
+ <li>3 man years and 30kloc</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>3</font></div>
+ </td>
+ <td>
+ <div id=PPTP3 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0068.htm');" id=PPTL3>Introduction</a></font></div>
+ <div id=PPTC3 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Implemented goofy template argument inheritance type system and
+ Manhattan geometry features</li>
+ <li>Request for interest from boost in 2007</li>
+ <ul>
+ <li>Discussed the design on boost dev list</li>
+ <li>Found out the design was bad and needed to be redone the boost way</li>
+ <ul>
+ <li>Thank you Joel Guzman</li>
+ </ul>
+ </ul>
+ <li>Added 45 degree geometry features</li>
+ <li>After six months of work we got permission from Intel to release under
+ boost license</li>
+ <ul>
+ <li>Discussed the code on the boost dev list</li>
+ <li>Got a lot of feedback on specific design considerations</li>
+ </ul>
+ <li>Rewrote the interfaces to be more generic by using tag dispatching</li>
+ <ul>
+ <li>Got more feedback on design considerations from boost, especially
+ refinement</li>
+ </ul>
+ <li>Re-rewrote the interfaces to be more generic still and based on SFINAE</li>
+ <li>Added arbitrary-angle geometry features</li>
+ <ul>
+ <li>Got feedback on arbitrary-angle algorithms and robustness
+ considerations from boost</li>
+ <ul>
+ <li>Thank you Fernando Cacciola</li>
+ </ul>
+ </ul>
+ <li>Ported new SFINAE interfaces to MSVC9</li>
+ <ul>
+ <li>Thank you Steven Watanabe</li>
+ </ul>
+ <li>The library now looks more like Joel said it should back in 2007</li>
+ <ul>
+ <li>We may pursue formal review this year</li>
+ </ul>
+ <li>Deployed library to internal users who are using it now to create the
+ next generation of silicon fabrication process technology and
+ microprocessors</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>4</font></div>
+ </td>
+ <td>
+ <div id=PPTP4 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0002.htm');" id=PPTL4>Agenda</a></font></div>
+ <div id=PPTC4 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL Feature Set</li>
+ <li>Benchmark Comparisons</li>
+ <li>Generic Sweep-line Booleans Algorithm</li>
+ <li>Numerical Robustness</li>
+ <li>Geometry Concepts Type System</li>
+ <li>Booleans Operator Syntax</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>5</font></div>
+ </td>
+ <td>
+ <div id=PPTP5 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0003.htm');" id=PPTL5>Primary GTL Feature</a></font></div>
+ <div id=PPTC5 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Boolean operations on sets of polygons</li>
+ <ul>
+ <li>Manhattan</li>
+ <br>
+ <br>
+ <li>45-degree</li>
+ <br>
+ <br>
+ <br>
+ <li>Arbitrary Angle (XOR)</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>6</font></div>
+ </td>
+ <td>
+ <div id=PPTP6 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0067.htm');" id=PPTL6>Using Booleans</a></font></div>
+ <div id=PPTC6 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Productive operator syntax</li>
+ <li>Clip polygon a against bounding box c, then subtract polygon b, storing
+ the result in polygon set d</li>
+ <li>Takes longer to say than to type</li>
+ <li>No try/catch and no memory management</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>7</font></div>
+ </td>
+ <td>
+ <div id=PPTP7 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0004.htm');" id=PPTL7>Details Of Booleans</a></font></div>
+ <div id=PPTC7 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>?</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>8</font></div>
+ </td>
+ <td>
+ <div id=PPTP8 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0005.htm');" id=PPTL8>Details of 45-degree
+ Booleans</a></font></div>
+ <div id=PPTC8 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Preserve 45-degree nature of geometry at output</li>
+ <li>Handle off-grid intersections by inserting an edge to approximate the
+ output region</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>9</font></div>
+ </td>
+ <td>
+ <div id=PPTP9 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0006.htm');" id=PPTL9>Boolean Operation Output
+ Modes</a></font></div>
+ <div id=PPTC9 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Manhattan Booleans</li>
+ <ul>
+ <li>Polygons with lists of holes</li>
+ <li>Keyhole holes to outer polygon</li>
+ <li>Horizontal and vertical sliced rectangle tiling</li>
+ </ul>
+ <li>45-degree Booleans</li>
+ <ul>
+ <li>Polygon with lists of holes</li>
+ <li>Keyhole holes to outer polygon</li>
+ <li>Vertical sliced trapezoid tiling</li>
+ </ul>
+ <li>Arbitrary-angle Booleans</li>
+ <ul>
+ <li>Polygon with lists of holes</li>
+ <li>Keyhole holes to outer polygon</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>10</font></div>
+ </td>
+ <td>
+ <div id=PPTP10 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0007.htm');" id=PPTL10>Polygon
+ Buffering/Resizing/Offsetting</a></font></div>
+ <div id=PPTC10 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Manhattan</li>
+ <ul>
+ <li>Uniform resizing</li>
+ <li>Resizing by different amount in each of the four directions</li>
+ <li>Optionally leave corners unfilled</li>
+ </ul>
+ <li>45-Degree</li>
+ <ul>
+ <li>Uniform resizing</li>
+ <li>Preserve original topology or cut off acute angled corners at resizing
+ distance</li>
+ <li>Snapping options for moving 45-degree edges</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>11</font></div>
+ </td>
+ <td>
+ <div id=PPTP11 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0010.htm');" id=PPTL11>Many More Features</a></font></div>
+ <div id=PPTC11 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Rectangle query tree</li>
+ <li>Maximum enclosed rectangle in Manhattan polygon</li>
+ <li>Connectivity Extraction</li>
+ <li>Property Merge/Map Overlay</li>
+ <li>Etc.</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>12</font></div>
+ </td>
+ <td>
+ <div id=PPTP12 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0011.htm');" id=PPTL12>Small Arbitrary-angle
+ Input Benchmark Comparison</a></font></div>
+ <div id=PPTC12 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Runtime for intersection operation</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>13</font></div>
+ </td>
+ <td>
+ <div id=PPTP13 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0012.htm');" id=PPTL13>Large Scale
+ Arbitrary-angle Performance Comparison</a></font></div>
+ <div id=PPTC13 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>One to two orders of magnitude larger than previous benchmark</li>
+ <li>Though fastest for small inputs, GPC does not scale well</li>
+ <li>gtlb excludes line segment intersection</li>
+ <li>Core Boolean is n log n, Intel micro-architecture accelerates processing
+ of large vectorss</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>14</font></div>
+ </td>
+ <td>
+ <div id=PPTP14 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0013.htm');" id=PPTL14>Manhattan Benchmarking</a></font></div>
+ <div id=PPTC14 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>100X performance delta between optimal gtl 90-degree algorithm and
+ general algorithms</li>
+ <li>gtl 45-degree Boolean is optimal</li>
+ <li>Core arbitrary angle Boolean (gtlb) is optimal</li>
+ <li>gtl arbitrary angle Boolean is slightly suboptimal due to line segment
+ intersection</li>
+ <li>CGAL is optimal, but has a high constant factor</li>
+ <li>GPC and PolyBoolean both scale sub-optimally</li>
+ <br>
+ <br>
+ <br>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>15</font></div>
+ </td>
+ <td>
+ <div id=PPTP15 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0014.htm');" id=PPTL15>Benchmarking
+ Conclusions about GTL</a></font></div>
+ <div id=PPTC15 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL arbitrary-angle Booleans is near optimal</li>
+ <li>Performance of GTL arbitrary-angle Booleans is middle-of-road for small
+ inputs</li>
+ <li>Performance of GTL arbitrary-angle Booleans is best in class for large
+ inputs</li>
+ <li>Performance of GTL could be improved by up to 10X with further work on
+ the arbitrary-angle Booleans</li>
+ <li>If you have 45-degree or Manhattan polygons gtl provides 50X and 100X
+ performance advantage over cgal</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>16</font></div>
+ </td>
+ <td>
+ <div id=PPTP16 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0016.htm');" id=PPTL16>Observations on GPC,
+ CGAL and PolyBoolean</a></font></div>
+ <div id=PPTC16 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>We found at least two different bugs in PolyBoolean</li>
+ <li>We found one bug in CGAL</li>
+ <li>GPC and PolyBoolean have very difficult to use C-style APIs</li>
+ <li>GPC and PolyBoolean cannot merge multiple overlapping polygons in one
+ step</li>
+ <li>GPC and PolyBoolean both have O(n<sup>1.5</sup>log n) line segment
+ intersection algorithms (sort all edges that intersect sweep-line at
+ every x)</li>
+ <li>PolyBoolean has O(n * m * k) algorithm to determine which polygons
+ contain which holes (n polygons, m holes, k points per polygon), which
+ is O(n^2) in the worst case</li>
+ <li>CGAL requires that overlapping polygons be merged before being an input
+ to a Boolean, but can do that itself</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>17</font></div>
+ </td>
+ <td>
+ <div id=PPTP17 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0018.htm');" id=PPTL17>Observations About
+ Preconditions</a></font></div>
+ <div id=PPTC17 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>CGAL throws an “Precondition Violated” exception if an input polygon is
+ self intersecting/overlapping or has “closed” semantic at last vertex</li>
+ <li>PolyBoolean returns a “bad input polygon” error code if an input polygon
+ is self intersecting/overlapping has zero area or is a hole with no
+ enclosing polygon</li>
+ <li>Both PolyBoolean and CGAL inform the user the input is bad when a bug in
+ their algorithms leads to a fatal error</li>
+ <li>GPC produces garbage output when input polygons are self
+ intersecting/overlapping</li>
+ <li>GTL has no preconditions and produces correct output in all cases</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>18</font></div>
+ </td>
+ <td>
+ <div id=PPTP18 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0015.htm');" id=PPTL18>Generic Sweep-line
+ Algorithm</a></font></div>
+ <div id=PPTC18 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Sweep-line algorithms for polygon clipping is a tradition that goes back
+ to 1979</li>
+ <li>Sweep-line is the best known method for line segment intersection</li>
+ <li>GTL implements different sweep lines for Manhattan, 45-degree and
+ general case</li>
+ <li>GTL Booleans sweep-lines are parameterized to allow them to perform
+ multiple operations</li>
+ <br>
+ <br>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>19</font></div>
+ </td>
+ <td>
+ <div id=PPTP19 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0019.htm');" id=PPTL19>Better Booleans through
+ Calculus</a></font></div>
+ <div id=PPTC19 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>We use the same algorithm for Manhattan, 45-degree and general polygon
+ Booleans</li>
+ <br>
+ <br>
+ <br>
+ <br>
+ <li>We will explain how it works in the Manhattan case first, then how we
+ generalize it</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>20</font></div>
+ </td>
+ <td>
+ <div id=PPTP20 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0020.htm');" id=PPTL20>Boolean Polygon Model</a></font></div>
+ <div id=PPTC20 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>We define a polygon as a two dimensional Boolean function</li>
+ <ul>
+ <li>Function evaluates to true inside the polygon</li>
+ <li>Function evaluates to false outside the polygon</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>21</font></div>
+ </td>
+ <td>
+ <div id=PPTP21 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0021.htm');" id=PPTL21>Math With Polygon Model</a></font></div>
+ <div id=PPTC21 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Because the Polygon is now modeled mathematically…</li>
+ <li>We can manipulate it with calculus</li>
+ <li>The derivative with respect to x of the polygon function is the change
+ in polygon count as we cross its vertical edges</li>
+ <li>In one dimension the polygon looks like a step function at its vertical
+ edges</li>
+ <li>Derivative of a step function is an impulse with area of one</li>
+ <li>Summing changes in polygon count from left to right (scanline) performs
+ an integration over the df/dx to produce the original polygon</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>22</font></div>
+ </td>
+ <td>
+ <div id=PPTP22 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0022.htm');" id=PPTL22>The Great Thing About
+ Math</a></font></div>
+ <div id=PPTC22 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>If it works once, it will work a second time</li>
+ <li>The derivative with respect to y of the d/dx of polygon function f is
+ the change in the change in polygon count with respect to x as we enter
+ and leave its vertical edges in the y dimension</li>
+ <li>In the y dimension d f/dx (vertical edges) looks like a step function</li>
+ <li>Derivative of a step function is an impulse with area of one</li>
+ <li>Summing changes in y of changes in x from low to high y integrates the
+ function and produces changes in x (edges) that can be integrated left
+ to right to produce polygons</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>23</font></div>
+ </td>
+ <td>
+ <div id=PPTP23 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0023.htm');" id=PPTL23>1D Boolean OR Operation
+ Example</a></font></div>
+ <div id=PPTC23 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>We want a data model for polygons that can provide the input for
+ sweep-line and be constructed from n polygon verticies in O(n log n)
+ time</li>
+ <li>If you want to sum two piece-wise linear functions (continuous)</li>
+ <ul>
+ <li>you can take the derivative of each (discreet)</li>
+ <li>combine their derivatives in linear time by merging (sum any
+ overlapping values)</li>
+ <li>and then integrate by summing from low to high (in linear time)</li>
+ </ul>
+ <li>The math is what allows the boolean algorithm to achieve optimal time
+ complexity</li>
+ <ul>
+ <li>All we do is sort vertices, but you have to carry the dxdy values along
+ with them so that the meaning of the vertices is retained</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>24</font></div>
+ </td>
+ <td>
+ <div id=PPTP24 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0027.htm');" id=PPTL24>2D, Two Layer Boolean
+ XOR Example</a></font></div>
+ <div id=PPTC24 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>XOR an L shape with a rectangle</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>25</font></div>
+ </td>
+ <td>
+ <div id=PPTP25 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0028.htm');" id=PPTL25>XOR Example</a></font></div>
+ <div id=PPTC25 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Preprocess input polygons into a merged, sorted sequence of change on y
+ of change on x of polygon intersection count</li>
+ <li>Decomposition is linear, sort is n log n, merge is linear</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>26</font></div>
+ </td>
+ <td>
+ <div id=PPTP26 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0029.htm');" id=PPTL26>XOR Example</a></font></div>
+ <div id=PPTC26 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Sweep-line data structure initialized to a single interval from
+ -infinity to +infinity with intersection count of zero for each input
+ layer</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>27</font></div>
+ </td>
+ <td>
+ <div id=PPTP27 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0030.htm');" id=PPTL27>XOR Example</a></font></div>
+ <div id=PPTC27 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect first input interval of intersection count change on x against
+ sweep-line data structure of intersection count intervals</li>
+ <li>Intersection count changes from zero to one on layer1 on that interval</li>
+ <li>0 xor 0 = false, 1 xor 0 = true, output a left edge because Boolean
+ logic changed from false to true</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>28</font></div>
+ </td>
+ <td>
+ <div id=PPTP28 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0031.htm');" id=PPTL28>XOR Example</a></font></div>
+ <div id=PPTC28 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect second input interval against sweep-line data structure</li>
+ <li>Intersection count changes from zero to one for layer2 on that interval</li>
+ <li>1 xor 0 = true, 1 xor 1 = false, so output a right edge because Boolean
+ logic has changed from true to false</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>29</font></div>
+ </td>
+ <td>
+ <div id=PPTP29 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0032.htm');" id=PPTL29>XOR Example</a></font></div>
+ <div id=PPTC29 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect third input interval against sweep-line data structure</li>
+ <li>Intersection count changes from one to zero for layer1 on that interval</li>
+ <li>1 xor 0 = false, 0 xor 1 = false, so no output</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>30</font></div>
+ </td>
+ <td>
+ <div id=PPTP30 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0033.htm');" id=PPTL30>XOR Example</a></font></div>
+ <div id=PPTC30 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect fourth input interval against sweep-line data structure</li>
+ <li>Intersection count changes from one to zero for layer1 on one interval</li>
+ <li>1 xor 0 = true, 0 xor 0 = false, so output a right edge because Boolean
+ logic has changed from true to false</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>31</font></div>
+ </td>
+ <td>
+ <div id=PPTP31 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0034.htm');" id=PPTL31>XOR Example</a></font></div>
+ <div id=PPTC31 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect fifth input interval against sweep-line data structure</li>
+ <li>Intersection count changes from one to zero for layer1 on two intervals</li>
+ <li>1 xor 0 = true, 0 xor 0 = false, so output a right edge for the first
+ interval</li>
+ <li>1 xor 1 = false, 0 xor 1 = true, so output a left edge for the second
+ interval</li>
+ <br>
+ <br>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>32</font></div>
+ </td>
+ <td>
+ <div id=PPTP32 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0035.htm');" id=PPTL32>XOR Example</a></font></div>
+ <div id=PPTC32 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Intersect sixth input interval against sweep-line data structure</li>
+ <li>Intersection count changes from one to zero for layer2 on one interval</li>
+ <li>0 xor 1 = true, 0 xor 0 = false, so output a right edge</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>33</font></div>
+ </td>
+ <td>
+ <div id=PPTP33 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0036.htm');" id=PPTL33>XOR Example</a></font></div>
+ <div id=PPTC33 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Sweep-line Polygon Formation produces output polygon</li>
+ <li>Could be done in the same pass as the xor</li>
+ <li>Leaving it in the derivative form allows direct input to a subsequent
+ Boolean</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>34</font></div>
+ </td>
+ <td>
+ <div id=PPTP34 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0037.htm');" id=PPTL34>Generalizing The
+ Algorithm</a></font></div>
+ <div id=PPTC34 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>We want the derivative of this vertex:</li>
+ <li>We apply d/dx and d/dy</li>
+ <li>To get a result in terms of &#952;:</li>
+ <li>We sweep the &#952; from low to high:</li>
+ <li>As we integrate wrt. y:</li>
+ <li>And finally integrate wrt. x:</li>
+ <li>To which we assign counter clockwise winding and output partial polygon:</li>
+ <br>
+ <br>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>35</font></div>
+ </td>
+ <td>
+ <div id=PPTP35 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0038.htm');" id=PPTL35>The Algorithm Requires
+ No Preconditions</a></font></div>
+ <div id=PPTC35 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>The great thing about math is that it’s general</li>
+ <li>Every special case is just another instance of the general case</li>
+ <li>Every case that breaks other algorithms is handled implicitly and
+ correctly</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>36</font></div>
+ </td>
+ <td>
+ <div id=PPTP36 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0041.htm');" id=PPTL36>Taking Things One Step
+ Further</a></font></div>
+ <div id=PPTC36 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>The Booleans algorithm is parameterized</li>
+ <li>N layer operations are implemented with a single pass of the same
+ algorithm</li>
+ <li>Is used to provide connectivity extraction / spatial map join and
+ property merge / map overlay</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>37</font></div>
+ </td>
+ <td>
+ <div id=PPTP37 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0039.htm');" id=PPTL37>Robustness</a></font></div>
+ <div id=PPTC37 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Strategies employed by GTL are provably robust for all cases</li>
+ <ul>
+ <li>100% robust--not just “works for all the cases we’ve tried”</li>
+ </ul>
+ <li>A firm guarantee of 100% numerical robustness is a very comforting
+ feature</li>
+ <li>PolyBoolean fails to find polygons that enclose some holes because its
+ point-in-polygon calculation is not numerically robust</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>38</font></div>
+ </td>
+ <td>
+ <div id=PPTP38 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0064.htm');" id=PPTL38>Robust Predicate
+ Primitives</a></font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>39</font></div>
+ </td>
+ <td>
+ <div id=PPTP39 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0040.htm');" id=PPTL39>Robust Comparison of
+ Slope</a></font></div>
+ <div id=PPTC39 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li> Segment 1: (x11,y11) to (x12, y12)</li>
+ <li> Segment 2: (x21,y21) to (x22, y22)</li>
+ <li> Slope1: (y12 - y11) / (x12 - x11)</li>
+ <li> Slope2: (y22 - y21) / (x22 - x21)</li>
+ <li> Slope1 &lt; Slope2 iff (y12 - y11)(x22 - x21) &lt; (x12 - x11)(y22 -
+ y21)</li>
+ <li>Cross multiplication avoids integer truncation of division</li>
+ <li>Requires 65 bits for signed 32 bit integer coordinates</li>
+ <ul>
+ <li>Use long double, multi-precision, SSE quad word, or unsigned 64 bit
+ integer with sign computed separately</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>40</font></div>
+ </td>
+ <td>
+ <div id=PPTP40 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0042.htm');" id=PPTL40>Robust Comparison Of
+ Point and Line Segment</a></font></div>
+ <div id=PPTC40 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Make a 2<sup>nd</sup> segment from one end of the segment to the point</li>
+ <li>Compare slopes</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>41</font></div>
+ </td>
+ <td>
+ <div id=PPTP41 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0045.htm');" id=PPTL41>Robust Line Segment
+ Intersection Check</a></font></div>
+ <div id=PPTC41 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Compute whether the two ends of each segment are on, above or below the
+ other segment</li>
+ <li>Both points of one segment on the same side of the other means no
+ intersection</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>42</font></div>
+ </td>
+ <td>
+ <div id=PPTP42 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0065.htm');" id=PPTL42>Robust Point In Polygon
+ Predicate</a></font></div>
+ <div id=PPTC42 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>For all edges which contain the x value of the point within their x
+ interval</li>
+ <ul>
+ <li>Accumulate the sum of such edges the point is above</li>
+ </ul>
+ <li>The point is inside if the sum is odd</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>43</font></div>
+ </td>
+ <td>
+ <div id=PPTP43 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0044.htm');" id=PPTL43>Robust Calculation of
+ Slope Intercept</a></font></div>
+ <div id=PPTC43 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Apply GMP multi-precision rational and compute exact result</li>
+ <li>To compare two slope intercepts</li>
+ <br>
+ <br>
+ <br>
+ <br>
+ <li> (requires 97 bits of precision)</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>44</font></div>
+ </td>
+ <td>
+ <div id=PPTP44 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0046.htm');" id=PPTL44>Robust Calculation of
+ Line Segment Intersection Point</a></font></div>
+ <div id=PPTC44 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Apply GMP multi-precision rational and compute exact result.</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>45</font></div>
+ </td>
+ <td>
+ <div id=PPTP45 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0047.htm');" id=PPTL45>Robust Snapping of
+ Non-Integer Intersection Points to Grid</a></font></div>
+ <div id=PPTC45 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Truncate down and to left</li>
+ <li>Causes Edges to move slightly</li>
+ <li>Moving edges may introduce artifacts</li>
+ <li>Non overlapping edges may become parallel and overlap</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>46</font></div>
+ </td>
+ <td>
+ <div id=PPTP46 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0049.htm');" id=PPTL46><span
+ style='mso-spacerun:yes'> </span></a></font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>47</font></div>
+ </td>
+ <td>
+ <div id=PPTP47 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0048.htm');" id=PPTL47>Intersections Creating
+ Intersections</a></font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>48</font></div>
+ </td>
+ <td>
+ <div id=PPTP48 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0050.htm');" id=PPTL48>Acceptable vs.
+ Unacceptable Artifacts</a></font></div>
+ <div id=PPTC48 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>An artifact is unacceptable</li>
+ <ul>
+ <li>if it causes any line segments to intersect other than at their end
+ points</li>
+ <li>if it causes a closed cycle in the input to become open at the output</li>
+ </ul>
+ <li>Inserting vertices on line segments and merging vertices are acceptable</li>
+ <li>We insert vertices and merge vertices to snap to integer grid robustly</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>49</font></div>
+ </td>
+ <td>
+ <div id=PPTP49 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0066.htm');" id=PPTL49>What code that uses GTL
+ looks like</a></font></div>
+ <div id=PPTC49 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>Two lines of code in the example invoke five different GTL algorithms</li>
+ <li>Arguments passed into functions are not GTL data types</li>
+ <li>The code is maximally concise, yet easy to read</li>
+ <li>Clip b to the bounding box of a, XOR that with a shrunk by ten then
+ merge into result</li>
+ <li>Details of memory management for intermediate results are abstracted
+ away from the use of algorithms</li>
+ <li>Such code is easy to write and easy to maintain</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>50</font></div>
+ </td>
+ <td>
+ <div id=PPTP50 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0052.htm');" id=PPTL50>C++ Concepts-based Type
+ System</a></font></div>
+ <div id=PPTC50 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL allows application data types to be arguments to its API</li>
+ <li>You can check if your point type lies inside your polygon type with a
+ call to GTL contains() passing in your point and your polygon</li>
+ <li> gtl::contains(my_polygon, my_point);</li>
+ <li>This is accomplished by use of a C++ Concepts-based statically
+ polymorphic type system</li>
+ <li>This is much more convenient than copying your polygon into a GTL
+ polygon data type first</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>51</font></div>
+ </td>
+ <td>
+ <div id=PPTP51 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0054.htm');" id=PPTL51>C++ Traits</a></font></div>
+ <div id=PPTC51 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL accesses your geometry types through type traits that you must
+ provide</li>
+ <li>These traits map your implementation of a geometry object to GTL’s
+ concept of how a such geometry behaves</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>52</font></div>
+ </td>
+ <td>
+ <div id=PPTP52 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0055.htm');" id=PPTL52>C++ Concepts
+ Overloading</a></font></div>
+ <div id=PPTC52 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL functions that expect a polygon check whether the input data type is
+ registered as a polygon and will not instantiate if the check fails</li>
+ <li>A different gtl function with the same name can instantiate if the data
+ type turns out to be registered as a rectangle, or a point</li>
+ <li>The mechanism for doing this is called substitution failure is not an
+ error (SFINAE)</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>53</font></div>
+ </td>
+ <td>
+ <div id=PPTP53 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0058.htm');" id=PPTL53>Concept Refinement</a></font></div>
+ <div id=PPTC53 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>A rectangle is a refinement of the concept of a polygon</li>
+ <ul>
+ <li>A rectangle narrows-down the definition of polygon to four sided,
+ 90-degree angles</li>
+ </ul>
+ <li>A function that requires read only access to a polygon can always work
+ on a rectangle</li>
+ <ul>
+ <li><span style='mso-spacerun:yes'> </span>A polygon is a generalization of
+ a rectangle</li>
+ </ul>
+ <li>A function that requires write-access to a polygon cannot work on a
+ rectangle</li>
+ <ul>
+ <li>A rectangle cannot store a polygon</li>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>54</font></div>
+ </td>
+ <td>
+ <div id=PPTP54 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0059.htm');" id=PPTL54>GTL Refinement
+ Relationships</a></font></div>
+ <div id=PPTC54 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL assign() function</li>
+ <ul>
+ <li>copies data between objects of the same conceptual type</li>
+ <li>copies data from a refinement to a more general conceptual type</li>
+ <li>instantiates for each of the 49 legal combinations</li>
+ <li>requires only one overload definition per concept type</li>
+ <li>each overload protected by SFINAE concept check</li>
+ <br>
+ <br>
+ </ul>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>55</font></div>
+ </td>
+ <td>
+ <div id=PPTP55 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0060.htm');" id=PPTL55>Concept Casting</a></font></div>
+ <div id=PPTC55 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>A Manhattan polygon is a refinement of a general polygon</li>
+ <li>Given a general polygon and the certainly that it contains only
+ Manhattan data</li>
+ <ul>
+ <li>GTL view_as&lt;polygon_90_concept&gt;() can allow that polygon to be
+ legally passed to functions expecting a Manhattan polygon</li>
+ </ul>
+ <li>This is useful when general objects are used by applications to model
+ several specific kinds of data</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>56</font></div>
+ </td>
+ <td>
+ <div id=PPTP56 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0053.htm');" id=PPTL56>Booleans Operator
+ Syntax</a></font></div>
+ <div id=PPTC56 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>GTL overloads the C++ bit-wise logical operators &amp;|^ and the
+ subtraction operator -</li>
+ <li>They perform Boolean AND, OR, XOR and AND-NOT (SUBTRACT)</li>
+ <li>They work with any polygons, rectangles, vectors or lists of polygons or
+ rectangles and the GTL polygon-set data types</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>57</font></div>
+ </td>
+ <td>
+ <div id=PPTP57 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0061.htm');" id=PPTL57>GTL Booleans Operator
+ Templates</a></font></div>
+ <div id=PPTC57 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>C++ requires that operators return their result by value</li>
+ <li>The return value of a GTL Boolean operator function call is an operator
+ template</li>
+ <li>The operator template stores references to the arguments and defers the
+ operation until the result is requested</li>
+ <li>In this way the operation is performed after the operator template is
+ returned by the operator function</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>58</font></div>
+ </td>
+ <td>
+ <div id=PPTP58 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0062.htm');" id=PPTL58>Operator Templates</a></font></div>
+ <div id=PPTC58 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>When chaining operator templates they cache references to each other and
+ build an expression tree</li>
+ <li>When the final result is requested the expression is evaluated and the
+ result is produced</li>
+ <li>This avoids unnecessary copying of intermediate results</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>59</font></div>
+ </td>
+ <td>
+ <div id=PPTP59 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0070.htm');" id=PPTL59>MSVC SFINAE limitation</a></font></div>
+ <div id=PPTC59 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>SFINAE works in MSVC for the simple cases</li>
+ <li>Order of template instantiation in MSVC depends on type of template</li>
+ <ul>
+ <li>compile time constant vs. by type</li>
+ </ul>
+ <li>Substitution failure of a nested template is an error in MSVC</li>
+ <li>The only way to get reliable SFINAE behavior out of MSVC is to use
+ enable_if with compile time logic expressions</li>
+ <li>It took two weeks of work to port the code from EDG/gcc compatibility to
+ MSVC</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>60</font></div>
+ </td>
+ <td>
+ <div id=PPTP60 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0069.htm');" id=PPTL60>EDG SFINAE Bug</a></font></div>
+ <div id=PPTC60 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>An unnamed enum type cannot be referred to in the template definition
+ when instantiating a template on that type</li>
+ <li>STL uses unnamed enum types with arithmetic operators</li>
+ <li>Substituion of my generic operators for the unnamed STL enum types
+ should fail</li>
+ <li>A bug in older versions of EDG frontend produces a syntax error instead
+ of SFINAE if the template references it in the definition</li>
+ <li>Currently fixed in the version of EGD used by the new icc11</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+ <tr onmouseover="Over(this)" onmouseout="Out(this)" onclick="Follow(this)"
+ style='cursor:hand'>
+ <td align=right valign=top>
+ <div class=sldNum><font size=2>61</font></div>
+ </td>
+ <td>
+ <div id=PPTP61 class=PTxt><font size=2><a
+ href="javascript:GoToSld('slide0071.htm');" id=PPTL61>EDG Bug Workaround</a></font></div>
+ <div id=PPTC61 class=CTxt style='display:none'><font size=2>
+ <ul>
+ <li>If substitution of a nested template parameter fails before EDG tries to
+ instantiate the template that would refer to the unnamed enum type no
+ syntax error is generated</li>
+ <li>EDG supports nested SFINAE, of course</li>
+ <li>I provide an intermediate meta-function with preprocessor macros in its
+ definition that results in nested SFINAE except when compiled by MSVC to
+ work around both bugs</li>
+ </ul>
+ </font></div>
+ </td>
+ </tr>
+</table>
+
+
+
+</div>
+
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+function _KPH()
+{
+ if( IsNts() ) return;
+
+ if( !parent.IsFramesMode() && event.keyCode == 27 && !HideMenu() )
+ parent.window.close( self );
+ else if( event.keyCode == 32 ) {
+ if( window.name == "PPTSld" )
+ parent.PPTSld.DocumentOnClick();
+ else
+ parent.GoToNextSld();
+ }
+
+ CatchNumKeys( parent, event );
+}
+
+function CatchNumKeys( win, event ) {
+ if( win.IsFullScrMode() && (48<=event.keyCode) && (event.keyCode<=57) ) {
+ gSldJump = 1;
+ gSldJumpIdx += (event.keyCode-48).toString();
+ }
+ if( win.IsFullScrMode() && gSldJump && event.keyCode == 13 ) {
+ var numSlds = parent.GetSldList().mList.length
+ if ( gSldJumpIdx > numSlds )
+ gSldJumpIdx = numSlds;
+ if ( gSldJumpIdx >= 0 ) {
+ if ( gSldJumpIdx == 0 )
+ gSldJumpIdx = 1;
+ var jumpTo = parseInt(gSldJumpIdx);
+ gSldJump = 0; gSldJumpIdx = "";
+ win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )
+ }
+ }
+}
+
+function _KDH()
+{
+ if( event.keyCode == 8 ) {
+ event.returnValue = 0;
+ parent.GoToPrevSld();
+ }
+}function DocumentOnClick()
+{
+ if( IsNts() || parent.HideMenu() ) return;
+
+ if( ( g_allowAdvOnClick && (window.name=="PPTSld") && !parent.IsFramesMode() ) ||
+ (event && event.keyCode==32) ) {
+
+ if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonext )
+ return;
+
+ parent.GoToNextSld();
+ }
+}
+
+
+var g_supportsPPTHTML = SupportsPPTHTML(), g_scaleInFrame = 1, gId="", g_bgSound="",
+ g_scaleHyperlinks = false, g_allowAdvOnClick = 1, g_showInBrowser = 0, gLoopCont = 0, gUseSldTimings = 1;
+var g_showAnimation = g_supportsPPTHTML && SupportsPPTAnimation() && ( (window.name=="PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );var g_animManager = null;
+var g_animUseRuntime = false;
+var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;
+var g_animMainSequence = null;
+
+var ENDSHOW_MESG="End of slide show, click to exit.", SCREEN_MODE="Frames", gIsEndShow=0, NUM_VIS_SLDS=61, SCRIPT_HREF="script.js", FULLSCR_HREF="fullscreen.htm";
+var gCurSld = gPrevSld = 1, g_offset = 0, gNtsOpen = gHasNts = gOtlTxtExp = 0, gHasNarration = 0, gOtlOpen = true
+window.gPPTHTML=SupportsPPTHTML()
+var g_fBaseHyperlink = false;
+var gMainDoc=new Array(new hrefList("slide0001.htm",1,-1,1),new hrefList("slide0073.htm",1,-1,1),new hrefList("slide0068.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("slide0067.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("slide0012.htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slide0029.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),
new hrefList("slide0031.htm",1,-1,1),new hrefList("slide0032.htm",1,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("slide0035.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0064.htm",1,-1,1),new hrefList("slide0040.htm",1,-1,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0065.htm",1,-1,1),new hrefList("slide0044.htm",1,-1,1),new hrefList("slide0046.htm",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide0048.htm",1,-1,1),new hrefList("slide0050.htm",1,-1,1),new hrefList("slide0066.htm",1,-1,1),new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0055.htm",1,-1,1),new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0059.htm",1,-1,1),new hrefList("slide0060.
htm",1,-1,1),new hrefList("slide0053.htm",1,-1,1),new hrefList("slide0061.htm",1,-1,1),new hrefList("slide0062.htm",1,-1,1),new hrefList("slide0070.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),new hrefList("slide0071.htm",1,-1,1));
+
+/*********************************************
+ Frameset functions
+
+ These functions control slide navigation
+ and state of the frameset.
+**********************************************/
+
+function RemoveFilePrefixFromHref(href)
+{
+ var regExp = /^file:\/\/\//i;
+ return href.replace(regExp, "")
+}
+
+function FullScrInit()
+{
+ g_allowAdvOnClick = GetCurSld().mAdvOnClk
+ document.body.style.backgroundColor="black"
+ document.oncontextmenu=parent._CM;
+ document.onkeydown = _KDH;
+ document.ondragstart=Cancel
+ document.onselectstart=Cancel
+ self.focus()
+}
+
+function Redirect( frmId )
+{
+ var str=document.location.hash,idx=str.indexOf('#'), sId=GetSldId()
+ if(idx>=0) str=str.substr(1);
+ if( window.name != frmId && ( sId != str) ) {
+ obj = GetObj("Main-File")
+ window.location.href=obj.href+"#"+sId
+ return 1
+ }
+ return 0
+}
+
+var MHTMLPrefix = CalculateMHTMLPrefix();
+function CalculateMHTMLPrefix()
+{
+ if ( document.location.protocol == 'mhtml:') {
+ href=new String(document.location.href)
+ Start=href.indexOf('!')+1
+ End=href.lastIndexOf('/')+1
+ if (End < Start)
+ return href.substring(0, Start)
+ else
+ return href.substring(0, End)
+ }
+ return '';
+}
+
+function GetTags(base,tag)
+{
+ if(g_supportsPPTHTML) return base.all.tags(tag);
+ else return base.getElementsByTagName(tag);
+}
+
+
+function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLPrefix+GetHrefObj( gCurSld ).mNtsHref ) }
+
+function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }
+
+function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }
+
+function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }
+
+function SetHasNts( fVal )
+{
+ if( gHasNts != fVal ) {
+ gHasNts=fVal
+ UpdNavPane()
+ }
+}
+
+function ToggleOtlText()
+{
+ gOtlTxtExp=!gOtlTxtExp
+ UpdOtlPane()
+}
+
+function ClearMedia()
+{
+ // Clear any sounds playing before launching another browser window. Otherwise,
+ // in fullscreen mode, you'll continue to hear the sound in the frames mode.
+ if (PPTSld.pptSound) PPTSld.pptSound.loop = 0;
+}
+
+function FullScreen()
+{
+ if ( PPTSld.g_animUseRuntime )
+ PPTSld.document.body.pause();
+ ClearMedia();
+ var href = ( document.location.protocol == 'mhtml:') ? FULLSCR_HREF : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;
+ if (MHTMLPrefix != "")
+ href = RemoveFilePrefixFromHref(href)
+ if(PPTNav.event.ctrlKey) {
+ var w = (window.screen.availWidth * 1.0) / 2.0
+ var h = w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW
+ win = window.open( MHTMLPrefix+href,null,"toolbar=0,resizable=1,top=0,left=0," + "width="+ w + ",height=" + h );
+ if( win.document.body && PPTSld.g_animUseRuntime )
+ win.document.body.PPTSldFrameset=window;
+ }
+ else
+ {
+ win = window.open( MHTMLPrefix+href,null,"fullscreen=yes" );
+ if( win.document.body && PPTSld.g_animUseRuntime )
+ win.document.body.PPTSldFrameset=window;
+ }
+}
+
+function ToggleVNarration()
+{
+ rObj=PPTSld.document.all("NSPlay")
+ if( rObj && !PPTSld.g_animUseRuntime ) {
+ if( (rObj.playState == 1)||(rObj.playState == 0) )
+ rObj.Play()
+ else if( rObj.playState == 2 )
+ rObj.Pause()
+ else
+ return;
+ }
+ else if( PPTSld.g_animUseRuntime )
+ {
+ narObj = PPTSld.document.all("narrationID")
+ if( narObj )
+ narObj.togglePause()
+ }
+}
+
+function GetCurSldNum()
+{
+ obj=GetHrefObj(gCurSld)
+ if( obj.mOrigVis == 1 )
+ return obj.mSldIdx
+ else
+ return gCurSld
+}
+
+function GetNumSlds()
+{
+ if( GetHrefObj(gCurSld).mOrigVis == 1 )
+ return GetSldList().mNumVisSlds;
+ else
+ return GetSldList().mList.length
+}
+
+function GetSldNum( href )
+{
+ for(ii=0; ii<GetSldList().mList.length; ii++) {
+ if ( GetSldList().mList[ii].mSldHref == href )
+ return ii+1
+ }
+ return 1
+}
+
+function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] }
+
+function IsFramesMode(){ return ( SCREEN_MODE == "Frames" ) }
+
+function IsFullScrMode(){ return ( SCREEN_MODE == "FullScreen" ) }
+
+function GoToNextSld()
+{
+ ii=gCurSld + 1
+ if( GetHrefObj( ii-1 ).mOrigVis == 0 ) {
+ if( ii<=GetSldList().mList.length ) {
+ obj=GetHrefObj(ii)
+ obj.mVis=1
+ GoToSldNum(ii)
+ return
+ }
+ }
+ else {
+ obj=GetHrefObj( ii )
+ while ( obj && ( obj.mOrigVis == 0 ) )
+ obj=GetHrefObj(++ii)
+ if( obj && obj.mOrigVis ) {
+ GoToSldNum(ii)
+ return
+ }
+ }
+ if( gSldStack.length > 1 )
+ PopSldList();
+ else if( !IsFramesMode() ) {
+ if( gLoopCont )
+ GoToFirst()
+ else
+ EndShow()
+ }
+}
+
+function GoToPrevSld()
+{
+ ii=gCurSld-1
+ if( ii > 0 ) {
+ obj=GetHrefObj(ii)
+ while ( obj && ( obj.mVis == 0 ) && ( ii>0 ) )
+ obj=GetHrefObj(--ii)
+ if( ii == 0 ) ii=1
+ GoToSldNum(ii)
+ }
+}
+
+function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }
+
+function GoToLast()
+{
+ ii=GetSldList().mList.length
+ if( ii != gCurSld )
+ GoToSld( GetHrefObj(ii).mSldHref )
+}
+
+function GoToSldNum( num )
+{
+ if( PPTSld.event ) PPTSld.event.cancelBubble=true
+ obj = GetHrefObj( num )
+ obj.mVis=1
+ gPrevSld=gCurSld
+ gCurSld = num;
+
+ if (MHTMLPrefix != "")
+ PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref))
+ else
+ PPTSld.location.replace(obj.mSldHref)
+
+ if( IsFramesMode() ) {
+ UpdNavPane(); UpdOtlPane(); UpdNtsPane()
+ }
+}
+
+function GoToSld( href )
+{
+ if( PPTSld.event ) PPTSld.event.cancelBubble=true
+ GetHrefObj( GetSldNum(href) ).mVis=1
+ if (MHTMLPrefix != "")
+ PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href))
+ else
+ PPTSld.location.replace(href)
+}
+
+function SldUpdated( id )
+{
+ if( id == GetHrefObj(gCurSld).mSldHref ) return
+ gPrevSld=gCurSld
+ gCurSld=GetSldNum(id)
+ if( IsFramesMode() ) {
+ UpdNavPane(); UpdOtlPane(); UpdNtsPane()
+ }
+}
+
+function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
+function HasPrevSld() { return ( gIsEndShow || ( gCurSld != 1 && GetHrefObj( gCurSld-1 ).mVis == 1 )||( GetCurSldNum() > 1 ) ) }
+function HasNextSld() { return (GetCurSldNum() != GetNumSlds()) }
+
+function CloseWindow() {
+ if( HideMenu() ) return;
+
+ var event = PPTSld.event;
+ if( !IsFramesMode() && event && (event.keyCode==27 || event.keyCode==32 || event.type=="click" ) )
+ window.close( self );
+ CatchNumKeys( self, event );
+}
+
+function Unload() { gIsEndShow=0; }
+
+function SetupEndShow() {
+ gIsEndShow=1;
+ PPTSld.document.body.scroll="no";
+ PPTSld.document.onkeypress=CloseWindow;
+ PPTSld.document.onclick=CloseWindow;
+ PPTSld.document.oncontextmenu=_CM;
+}
+
+function EndShow()
+{
+ if( IsFramesMode() ) return
+ if( PPTSld.event ) PPTSld.event.cancelBubble=true
+
+ doc=PPTSld.document
+ var dir = doc.body.dir
+ if( dir != "rtl" ) dir = "ltr";
+ doc.open()
+ doc.writeln('<html><body dir=' + dir + ' bgcolor=black onload=parent.SetupEndShow() onunload=parent.Unload()><center><p><font face=Tahoma color=white size=2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></body></html>')
+ doc.close()
+}
+
+function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=true }
+
+function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited }
+
+function hrefList( sldHref, visible, advDelay, advClk )
+{
+ this.mSldHref= this.mNtsHref = sldHref
+ this.mOrigVis= this.mVis = visible
+ this.mVisited= false
+ this.mAdvDelay= advDelay
+ this.mAdvOnClk= advClk
+}
+
+function SldList(arr,curSld,fEnd)
+{
+ this.mCurSld = curSld;
+ this.mList = new Array();
+
+ var idx = 1;
+ for(ii=0;ii<arr.length;ii++) {
+ this.mList[ii] = new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[ii].mAdvDelay, arr[ii].mAdvOnClk );
+ if( arr[ii].mOrigVis )
+ this.mList[ii].mSldIdx = idx++;
+ }
+ this.mNumVisSlds = idx-1;
+ this.fEndShow = fEnd;
+}
+
+function GetSldList() { return gSldStack[gSldStack.length-1] }
+function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1] }
+
+gSldStack = new Array();
+gSldStack[0] = new SldList(gMainDoc,gCurSld,1)
+function ToggleOtlPane()
+{
+ frmset=document.all("PPTHorizAdjust")
+ frm=document.all("PPTOtl")
+
+ if( gOtlOpen )
+ frmset.cols="*,100%"
+ else
+ frmset.cols="25%,*"
+
+ gOtlOpen=!gOtlOpen
+ frm.noResize=!frm.noResize
+ UpdOtNavPane()
+}
+
+function ToggleNtsPane()
+{
+ frmset=document.all("PPTVertAdjust")
+ frm=document.all("PPTNts")
+
+ if( gNtsOpen )
+ frmset.rows="100%,*"
+ else
+ frmset.rows="*,20%"
+
+ gNtsOpen=!gNtsOpen
+ UpdNtsPane()
+}
+
+/*********************************************
+Custom Shows implementation
+
+When ViewCustomShow() is called, we create
+a new array that is a subset of the slides in
+the main doc. This list pushed on a stack so
+we can return after the end of the custom
+show.
+*********************************************/
+function ViewCustomShow(idx,fEnd)
+{
+ if( !IsFullScrMode() ) return;
+ var sldList = new Array();
+ var custShow = custShowList[idx-1];
+ var jj = 0;
+ for( ii=0;ii<custShow.length;ii++ ) {
+ if( custShow[ii] <= gMainDoc.length )
+ sldList[jj++] = gMainDoc[custShow[ii]-1];
+ }
+ if (sldList.length > 0) {
+ PushSldList(sldList,fEnd);
+ gCurSld = 1;
+ }
+ else
+ if( PPTSld.event ) PPTSld.event.cancelBubble=true
+}
+
+function PushSldList(arr,fEnd) {
+ var ii = gSldStack.length;
+ gSldStack[ii] = new SldList(arr,gCurSld,fEnd);
+ GoToSld( gSldStack[ii].mList[0].mSldHref );
+}
+
+function PopSldList() {
+ if (gSldStack[gSldStack.length-1].fEndShow)
+ EndShow()
+ else {
+ gCurSld = gSldStack[gSldStack.length-1].mCurSld;
+ gSldStack[gSldStack.length-1] = null;
+ gSldStack.length--;
+ var sldList = gSldStack[gSldStack.length-1];
+ GoToSld( sldList.mList[gCurSld - 1].mSldHref );
+ }
+}
+var custShowList=new Array();
+
+/*********************************************
+ Navigation button implementation
+
+ There are 2 types of buttons: ImgBtn, TxtBtn
+ implemented as function objects. They share
+ a similiar interface so the event handlers
+ can call SetActive, for example, on a button
+ object without needing to know exactly
+ what type of button it is.
+**********************************************/
+
+//----------------------------------
+function ImgBtn( oId,bId,w,action )
+//----------------------------------
+{
+ var t=this
+ t.Perform = _IBP
+ t.SetActive = _IBSetA
+ t.SetInactive= _IBSetI
+ t.SetPressed = _IBSetP
+ t.SetDisabled= _IBSetD
+ t.Enabled = _IBSetE
+ t.ChangeIcon = null
+ t.UserAction = action
+ t.ChgState = _IBUI
+ t.mObjId = oId
+ t.mBorderId= bId
+ t.mWidth = w
+ t.mIsOn = t.mCurState = 0
+}
+
+function _IBSetA()
+{
+ if( this.mIsOn ) {
+ obj=this.ChgState( gHiliteClr,gShadowClr,2 )
+ obj.style.posTop=0
+ }
+}
+
+function _IBSetI()
+{
+ if( this.mIsOn ) {
+ obj=this.ChgState( gFaceClr,gFaceClr,1 )
+ obj.style.posTop=0
+ }
+}
+
+function _IBSetP()
+{
+ if( this.mIsOn ) {
+ obj=this.ChgState( gShadowClr,gHiliteClr,2 )
+ obj.style.posLeft+=1; obj.style.posTop+=1
+ }
+}
+
+function _IBSetD()
+{
+ obj=this.ChgState( gFaceClr,gFaceClr,0 )
+ obj.style.posTop=0
+}
+
+function _IBSetE( state )
+{
+ var t=this
+ GetObj( t.mBorderId ).style.visibility="visible"
+ if( state != t.mIsOn ) {
+ t.mIsOn=state
+ if( state )
+ t.SetInactive()
+ else
+ t.SetDisabled()
+ }
+}
+
+function _IBP()
+{
+ var t=this
+ if( t.mIsOn ) {
+ if( t.UserAction != null )
+ t.UserAction()
+ if( t.ChangeIcon ) {
+ obj=GetObj(t.mObjId)
+ if( t.ChangeIcon() )
+ obj.style.posLeft=obj.style.posLeft+(t.mCurState-4)*t.mWidth
+ else
+ obj.style.posLeft=obj.style.posLeft+(t.mCurState-0)*t.mWidth
+ }
+ t.SetActive()
+ }
+}
+
+function _IBUI( clr1,clr2,nextState )
+{
+ var t=this
+ SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
+ obj=GetObj( t.mObjId )
+ obj.style.posLeft=obj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj.style.posTop
+ t.mCurState=nextState
+ return obj
+}
+
+//-----------------------------------------
+function TxtBtn( oId,oeId,action,chkState )
+//-----------------------------------------
+{
+ var t=this
+ t.Perform = _TBP
+ t.SetActive = _TBSetA
+ t.SetInactive= _TBSetI
+ t.SetPressed = _TBSetP
+ t.SetDisabled= _TBSetD
+ t.SetEnabled = _TBSetE
+ t.GetState = chkState
+ t.UserAction = action
+ t.ChgState = _TBUI
+ t.mObjId = oId
+ t.m_elementsId= oeId
+ t.mIsOn = 1
+}
+
+function _TBSetA()
+{
+ var t=this
+ if( t.mIsOn && !t.GetState() )
+ t.ChgState( gHiliteClr,gShadowClr,0,0 )
+}
+
+function _TBSetI()
+{
+ var t=this
+ if( t.mIsOn && !t.GetState() )
+ t.ChgState( gFaceClr,gFaceClr,0,0 )
+}
+
+function _TBSetP()
+{
+ if( this.mIsOn )
+ this.ChgState( gShadowClr,gHiliteClr,1,1 )
+}
+
+function _TBSetD()
+{
+ this.ChgState( gFaceClr,gFaceClr,0,0 )
+ this.mIsOn = 0
+}
+
+function _TBSetE()
+{
+ var t=this
+ if( !t.GetState() )
+ t.ChgState( gFaceClr,gFaceClr,0,0 )
+ else
+ t.ChgState( gShadowClr,gHiliteClr,1,1 )
+ t.mIsOn = 1
+}
+
+function _TBP()
+{
+ var t=this
+ if( t.mIsOn ) {
+ if( t.UserAction != null )
+ t.UserAction()
+ if( !t.GetState )
+ return
+ if( t.GetState() )
+ t.SetPressed()
+ else
+ t.SetActive()
+ }
+}
+
+function _TBUI( clr1,clr2,lOffset,tOffset )
+{
+ SetBorder( GetObj( this.mObjId ),clr1,clr2 )
+ Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
+}
+
+function Offset( obj, top, left ){ obj.style.top=top; obj.style.left=left }
+
+function SetBorder( obj, upperLeft, lowerRight )
+{
+ s=obj.style;
+ s.borderStyle = "solid"
+ s.borderWidth = 1
+ s.borderLeftColor = s.borderTopColor = upperLeft
+ s.borderBottomColor= s.borderRightColor = lowerRight
+}
+
+function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }
+
+function BtnOnOver(){ b=GetBtnObj(); if( b != null ) b.SetActive() }
+
+function BtnOnDown(){ b=GetBtnObj(); if( b != null ) b.SetPressed() }
+
+function BtnOnOut(){ b=GetBtnObj(); if( b != null ) b.SetInactive() }
+
+function BtnOnUp()
+{
+ b=GetBtnObj()
+ if( b != null )
+ b.Perform()
+ else
+ Upd()
+}
+function GetNtsState(){ return parent.gNtsOpen }
+
+function GetOtlState(){ return parent.gOtlOpen }
+
+function GetOtlTxtState(){ return parent.gOtlTxtExp }
+
+function NtsBtnSetFlag( fVal )
+{
+ s=document.all.item( this.m_flagId ).style
+ s.display="none"
+ if( fVal )
+ s.display=""
+ else
+ s.display="none"
+}
+
+function _BSetA_Border(){ b = gBtnArr[this.mObjId]; if( b != null ) b.SetActive() }
+
+function _BSetI_Border(){ b = gBtnArr[this.mObjId]; if( b != null ) b.SetInactive() }
+
+function _BSetP_Border(){ b = gBtnArr[this.mObjId]; if( b != null ) b.SetPressed() }
+
+function _BSetA_BorderImg()
+{
+ b = gBtnArr[this.mBorderId]
+ if( b != null && this.mIsOn && !b.GetState() ) {
+ obj=this.ChgState( gHiliteClr,gShadowClr,2 )
+ obj.style.posTop=0
+ }
+}
+
+function _BSetI_BorderImg()
+{
+ b = gBtnArr[this.mBorderId]
+ if( b != null && this.mIsOn && !b.GetState() ) {
+ obj=this.ChgState( gFaceClr,gFaceClr,1 )
+ obj.style.posTop=0
+ }
+}
+
+
+var gHiliteClr="THREEDHIGHLIGHT",gShadowClr="THREEDSHADOW",gFaceClr="THREEDFACE"
+var gBtnArr = new Array()
+gBtnArr["nb_otl"] = new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPane,GetOtlState )
+gBtnArr["nb_otlElem"] = new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPane,GetOtlState )
+gBtnArr["nb_nts"] = new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleNtsPane )
+gBtnArr["nb_nts"].SetActive = _BSetA_BorderImg;
+gBtnArr["nb_nts"].SetInactive = _BSetI_BorderImg;
+gBtnArr["nb_ntsBorder"] = new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.ToggleNtsPane,GetNtsState )
+gBtnArr["nb_ntsElem"] = new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.ToggleNtsPane,GetNtsState )
+gBtnArr["nb_prevBorder"] = gBtnArr["nb_prev"]= new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToPrevSld )
+gBtnArr["nb_nextBorder"] = gBtnArr["nb_next"]= new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToNextSld )
+gBtnArr["nb_sldshw"]= new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent.FullScreen )
+gBtnArr["nb_sldshwBorder"] = new TxtBtn( "nb_sldshw","nb_sldshwBorder",parent.FullScreen,null )
+gBtnArr["nb_sldshwBorder"].SetActive = _BSetA_Border;
+gBtnArr["nb_sldshwBorder"].SetInactive = _BSetI_Border;
+gBtnArr["nb_sldshwText"] = new TxtBtn( "nb_sldshw","nb_sldshwText",parent.FullScreen,null )
+gBtnArr["nb_sldshwText"].SetActive = _BSetA_Border;
+gBtnArr["nb_sldshwText"].SetInactive = _BSetI_Border;
+gBtnArr["nb_voice"] = gBtnArr["nb_voiceBorder"] = new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.ToggleVNarration )
+gBtnArr["nb_otlTxtBorder"] = gBtnArr["nb_otlTxt"]= new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent.ToggleOtlText )
+gBtnArr["nb_ntsBorder"].m_flagId= "nb_nts"
+gBtnArr["nb_ntsBorder"].SetFlag = NtsBtnSetFlag
+gBtnArr["nb_otlTxt"].ChangeIcon= GetOtlTxtState
+
+/*********************************************
+ Context menu implementation
+
+ _CM() is the function that's hooked up to
+ the oncontextmenu event. Once we're asked to
+ show the menu, we first build it by creating
+ DIVs on-the-fly. Then we position it
+ within the screen area so it doesn't get
+ clipped.
+
+ Creating the DIVs using createElement() means
+ we don't have to write out any extra HTML
+ into the slide HTML files.
+**********************************************/
+var sNext="Next",sPrev="Previous",sEnd="End Show",sFont="Arial",sArrow="Arrow",sFreeform="Freeform",sRect="Rectangle",sOval="Oval"
+
+function ShowMenu()
+{
+ BuildMenu();
+ var doc=PPTSld.document.body,x=PPTSld.event.clientX+doc.scrollLeft,y=PPTSld.event.clientY+doc.scrollTop
+ m = PPTSld.document.all.item("ctxtmenu")
+ m.style.pixelLeft=x
+ if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
+ m.style.pixelLeft=x-m.scrollWidth
+
+ m.style.pixelTop=y
+ if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
+ m.style.pixelTop=y-m.scrollHeight
+
+ m.style.display=""
+}
+
+function _CM()
+{
+ if( !parent.IsFullScrMode() ) return;
+ if(!PPTSld.event.ctrlKey) {
+ ShowMenu()
+ return false
+ } else
+ HideMenu()
+}
+
+function BuildMenu()
+{
+ if( PPTSld.document.all.item("ctxtmenu") ) return
+
+ var mObj=CreateItem( PPTSld.document.body )
+ mObj.id="ctxtmenu"
+ mObj.style.visibility="hidden"
+ var s=mObj.style
+ s.position="absolute"
+ s.cursor="default"
+ s.width="120px"
+ SetCMBorder(mObj,"menu","black")
+
+ var iObj=CreateItem( mObj )
+ SetCMBorder( iObj, "threedhighlight","threedshadow" )
+ iObj.style.padding=2
+ CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
+ CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
+
+ CreateSeparator( iObj )
+ CreateMenuItem( iObj,sEnd,M_End,M_True )
+ mObj.style.visibility="visible"
+}
+
+function Cancel() { window.event.cancelBubble=true; window.event.returnValue=false }
+
+function Highlight() { ChangeClr("activecaption","threedhighlight") }
+
+function Deselect() { ChangeClr("threedface","menutext") }
+
+function Perform()
+{
+ e=PPTSld.event.srcElement
+ if( e.type=="menuitem" && e.IsActive() )
+ e.Action()
+ else
+ PPTSld.event.cancelBubble=true
+}
+function ChangeClr( bg,clr )
+{
+ e=PPTSld.event.srcElement
+ if( e.type=="menuitem" && e.IsActive() ) {
+ e.style.backgroundColor=bg
+ e.style.color=clr
+ }
+}
+
+function M_HasPrevSld() { return( parent.HasPrevSld() ) }
+
+function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }
+
+function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=0; history.back(); PPTSld.event.cancelBubble=true; } else GoToPrevSld() }
+
+function M_True() { return true }
+
+function M_End() { window.close( self ) }
+
+function CreateMenuItem( node,text,action,eval )
+{
+ var e=CreateItem( node )
+ e.type="menuitem"
+ e.Action=action
+ e.IsActive=eval
+ e.innerHTML=text
+
+ if( !e.IsActive() )
+ e.style.color="threedshadow"
+
+ e.onclick=Perform
+ e.onmouseover=Highlight
+ e.onmouseout=Deselect
+ s=e.style;
+ s.fontFamily=sFont
+ s.fontSize="9pt"
+ s.paddingLeft=2
+}
+
+function CreateSeparator( node )
+{
+ var sObj=CreateItem( node )
+ SetCMBorder(sObj,"menu","menu")
+ var s=sObj.style
+ s.borderTopColor="threedshadow"
+ s.borderBottomColor="threedhighlight"
+ s.height=1
+ s.fontSize="0px"
+}
+
+function CreateItem( node )
+{
+ var elem=PPTSld.document.createElement("DIV")
+ node.insertBefore( elem )
+ return elem
+}
+
+function SetCMBorder( o,ltClr,rbClr )
+{
+ var s=o.style
+ s.backgroundColor="menu"
+ s.borderStyle="solid"
+ s.borderWidth=1
+ s.borderColor=ltClr+" "+rbClr+" "+rbClr+" "+ltClr
+}
\ No newline at end of file

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001.htm
==============================================================================
--- (empty file)
+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001.htm 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
@@ -0,0 +1,122 @@
+<html xmlns:v="urn:schemas-microsoft-com:vml"
+xmlns:o="urn:schemas-microsoft-com:office:office"
+xmlns:p="urn:schemas-microsoft-com:office:powerpoint"
+xmlns:oa="urn:schemas-microsoft-com:office:activation"
+xmlns="http://www.w3.org/TR/REC-html40">
+
+<head>
+<meta http-equiv=Content-Type content="text/html; charset=windows-1252">
+<meta name=ProgId content=PowerPoint.Slide>
+<meta name=Generator content="Microsoft PowerPoint 11">
+<link id=Main-File rel=Main-File href="../GTL_boostcon_draft03.htm">
+<link rel=Preview href=preview.wmf>
+<!--[if !mso]>
+<style>
+v\:* {behavior:url(#default#VML);}
+o\:* {behavior:url(#default#VML);}
+p\:* {behavior:url(#default#VML);}
+.shape {behavior:url(#default#VML);}
+v\:textbox {display:none;}
+</style>
+<![endif]-->
+<title>GTL Geometry Template Library</title>
+<meta name=Description content="5/15/2009: GTL Geometry Template Library">
+<link rel=Stylesheet href="master03_stylesheet.css">
+<![if !ppt]>
+<style>
+.CB
+ {color:black;}
+.CT
+ {color:black;}
+</style>
+<style media=print>
+<!--.sld
+ {left:0px !important;
+ width:6.0in !important;
+ height:4.5in !important;
+ font-size:107% !important;}
+-->
+</style>
+<script src=script.js></script><script><!--
+if( !IsNts() ) Redirect( "PPTSld" );
+//--></script><!--[if vml]><script>g_vml = 1;
+</script><![endif]--><![endif]><o:shapelayout v:ext="edit">
+ <o:idmap v:ext="edit" data="2"/>
+</o:shapelayout>
+</head>
+
+<body lang=EN-US style='margin:0px;background-color:black'
+onclick="DocumentOnClick()" onresize="_RSW()" onload="LoadSld()"
+onkeypress="_KPH()">
+
+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
+width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%, 101%, 101%, 0%);
+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O style='text-align:right;position:absolute;
+ top:92.0%;left:72.65%;width:21.53%;height:3.25%'><span style='font-size:78%;
+ mso-field-code:meta16'>1</span><span style='font-size:78%;mso-special-format:
+ lastCR;display:none'>&#13;</span></div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s2050"
+ type="#_x0000_m1026" style='position:absolute;left:18pt;top:168pt;width:672pt;
+ height:115.75pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="centerTitle"/></v:shape><p:shaperange
+ href="master03.xml#_x0000_m1027"/><v:shape id="_x0000_s2051" type="#_x0000_m1027"
+ style='position:absolute;left:108pt;top:306pt;width:510pt;height:138pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="subTitle" position="1"/></v:shape><v:rect id="_x0000_s2052"
+ style='position:absolute;left:102pt;top:420pt;width:510pt;height:102pt'
+ filled="f" fillcolor="#bbe0e3 [4]" stroked="f" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:rect>
+ <div v:shape="_x0000_s2050" class=CT style='position:absolute;top:37.5%;
+ left:-4.68%;width:107.86%;height:9.25%'>GTL<span style='mso-spacerun:yes'> 
+ </span>Geometry Template Library</div>
+ <div v:shape="_x0000_s2051" class=CB style='position:absolute;top:57.75%;
+ left:12.17%;width:76.59%;height:6.75%'>-for stl-like polygon manipulation</div>
+ <div v:shape="_x0000_s2052" class=CB>
+ <div style='position:absolute;top:78.75%;left:11.04%;width:77.15%;height:6.75%'><i>Lucanus
+ Simonson, Gyuszi Suto&#13;</i></div>
+ <div style='position:absolute;top:87.25%;left:15.16%;width:68.91%;height:6.75%'>Intel
+ Corporation</div>
+ </div>
+ <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75"
+ o:preferrelative="t" path="m_at_4@5l_at_4@11_at_9@11_at_9@5xe" filled="f" stroked="f">
+ <v:stroke joinstyle="miter"/>
+ <v:formulas>
+ <v:f eqn="if lineDrawn pixelLineWidth 0"/>
+ <v:f eqn="sum @0 1 0"/>
+ <v:f eqn="sum 0 0 @1"/>
+ <v:f eqn="prod @2 1 2"/>
+ <v:f eqn="prod @3 21600 pixelWidth"/>
+ <v:f eqn="prod @3 21600 pixelHeight"/>
+ <v:f eqn="sum @0 0 1"/>
+ <v:f eqn="prod @6 1 2"/>
+ <v:f eqn="prod @7 21600 pixelWidth"/>
+ <v:f eqn="sum @8 21600 0"/>
+ <v:f eqn="prod @7 21600 pixelHeight"/>
+ <v:f eqn="sum @10 21600 0"/>
+ </v:formulas>
+ <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
+ <o:lock v:ext="edit" aspectratio="t"/>
+ </v:shapetype><v:shape id="_x0000_s2053" type="#_x0000_t75" style='position:absolute;
+ left:42pt;top:0;width:636pt;height:189.125pt'>
+ <v:imagedata src="slide0001_image001.png" o:title=""/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s2053"
+ src="slide0001_image002.jpg" style='position:absolute;top:0%;left:5.8%;
+ width:88.38%;height:35.0%'><![endif]></p:slide></div>
+
+</body>
+
+</html>

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001_image001.png
==============================================================================
Binary file. No diff available.

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0001_image002.jpg
==============================================================================
Binary file. No diff available.

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0002.htm
==============================================================================
--- (empty file)
+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0002.htm 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
@@ -0,0 +1,131 @@
+<html xmlns:v="urn:schemas-microsoft-com:vml"
+xmlns:o="urn:schemas-microsoft-com:office:office"
+xmlns:p="urn:schemas-microsoft-com:office:powerpoint"
+xmlns:oa="urn:schemas-microsoft-com:office:activation"
+xmlns="http://www.w3.org/TR/REC-html40">
+
+<head>
+<meta http-equiv=Content-Type content="text/html; charset=windows-1252">
+<meta name=ProgId content=PowerPoint.Slide>
+<meta name=Generator content="Microsoft PowerPoint 11">
+<link id=Main-File rel=Main-File href="../GTL_boostcon_draft03.htm">
+<link rel=Preview href=preview.wmf>
+<!--[if !mso]>
+<style>
+v\:* {behavior:url(#default#VML);}
+o\:* {behavior:url(#default#VML);}
+p\:* {behavior:url(#default#VML);}
+.shape {behavior:url(#default#VML);}
+v\:textbox {display:none;}
+</style>
+<![endif]-->
+<title>GTL Geometry Template Library</title>
+<meta name=Description content="5/15/2009: Agenda">
+<link rel=Stylesheet href="master03_stylesheet.css">
+<![if !ppt]>
+<style media=print>
+<!--.sld
+ {left:0px !important;
+ width:6.0in !important;
+ height:4.5in !important;
+ font-size:107% !important;}
+-->
+</style>
+<script src=script.js></script><script><!--
+if( !IsNts() ) Redirect( "PPTSld" );
+//--></script><!--[if vml]><script>g_vml = 1;
+</script><![endif]--><![endif]><o:shapelayout v:ext="edit">
+ <o:idmap v:ext="edit" data="3"/>
+</o:shapelayout>
+</head>
+
+<body lang=EN-US style='margin:0px;background-color:black'
+onclick="DocumentOnClick()" onresize="_RSW()" onload="LoadSld()"
+onkeypress="_KPH()">
+
+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
+width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%, 101%, 101%, 0%);
+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
+ width:21.53%;height:3.25%'><span style='font-size:78%;mso-field-code:meta16'>4</span><span
+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
+ </div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s3074"
+ type="#_x0000_m1026" style='position:absolute;left:36pt;top:21.625pt;width:9in;
+ height:90pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="title"/></v:shape><p:shaperange
+ href="master03.xml#_x0000_m1027"/><v:shape id="_x0000_s3075" type="#_x0000_m1027"
+ style='position:absolute;left:18pt;top:126pt;width:258pt;height:354pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="body" position="1"/></v:shape>
+ <div v:shape="_x0000_s3074" class=T style='position:absolute;top:8.0%;
+ left:5.99%;width:88.2%;height:9.25%'>Agenda</div>
+ <div v:shape="_x0000_s3075" class=B>
+ <div style='position:absolute;top:24.25%;left:3.55%;width:34.08%;height:5.25%'><span
+ style='position:absolute;top:0%;left:10.98%;width:88.46%;height:100.0%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-12.42%'>•</span></span><span
+ style='font-size:75%'>GTL Feature Set&#13;</span></span></div>
+ <span style='position:absolute;top:30.75%;left:7.3%;width:30.14%;height:5.25%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-12.42%'>•</span></span><span
+ style='font-size:75%'>Benchmark </span></span><span style='position:absolute;
+ top:36.0%;left:7.3%;width:30.14%;height:5.25%'><span style='font-size:75%'>Comparisons&#13;</span></span><span
+ style='position:absolute;top:42.5%;left:7.3%;width:35.2%;height:5.25%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-10.63%'>•</span></span><span
+ style='font-size:75%'>Generic Sweep-line </span></span><span style='position:
+ absolute;top:47.75%;left:7.3%;width:35.01%;height:5.25%'><span
+ style='font-size:75%'>Booleans Algorithm&#13;</span></span><span
+ style='position:absolute;top:54.0%;left:7.3%;width:30.14%;height:5.25%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-12.42%'>•</span></span><span
+ style='font-size:75%'>Numerical </span></span><span style='position:absolute;
+ top:59.5%;left:7.3%;width:30.14%;height:5.25%'><span style='font-size:75%'>Robustness&#13;</span></span><span
+ style='position:absolute;top:65.75%;left:7.3%;width:35.76%;height:5.25%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-10.47%'>•</span></span><span
+ style='font-size:75%'>Geometry Concepts </span></span><span style='position:
+ absolute;top:71.25%;left:7.3%;width:30.14%;height:5.25%'><span
+ style='font-size:75%'>Type System&#13;</span></span><span style='position:
+ absolute;top:77.5%;left:7.3%;width:33.89%;height:5.25%'><span
+ style='font-size:75%'><span class=BB style='position:absolute;left:-11.04%'>•</span></span><span
+ style='font-size:75%'>Booleans Operator </span></span><span style='position:
+ absolute;top:82.75%;left:7.3%;width:30.14%;height:5.25%'><span
+ style='font-size:75%'>Syntax</span></span></div>
+ <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75"
+ o:preferrelative="t" path="m_at_4@5l_at_4@11_at_9@11_at_9@5xe" filled="f" stroked="f">
+ <v:stroke joinstyle="miter"/>
+ <v:formulas>
+ <v:f eqn="if lineDrawn pixelLineWidth 0"/>
+ <v:f eqn="sum @0 1 0"/>
+ <v:f eqn="sum 0 0 @1"/>
+ <v:f eqn="prod @2 1 2"/>
+ <v:f eqn="prod @3 21600 pixelWidth"/>
+ <v:f eqn="prod @3 21600 pixelHeight"/>
+ <v:f eqn="sum @0 0 1"/>
+ <v:f eqn="prod @6 1 2"/>
+ <v:f eqn="prod @7 21600 pixelWidth"/>
+ <v:f eqn="sum @8 21600 0"/>
+ <v:f eqn="prod @7 21600 pixelHeight"/>
+ <v:f eqn="sum @10 21600 0"/>
+ </v:formulas>
+ <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
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+ fillcolor="#bbe0e3 [4]" stroked="f" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="2" delay="0" type="object" effect="zoom" direction="out"
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+ top:0%;left:6.43%;width:83.6%;height:7.74%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.69%'>•</span></span><span
+ style='font-size:75%'>No preconditions placed on </span></span><span
+ style='position:absolute;top:7.01%;left:6.43%;width:81.99%;height:7.74%'><span
+ style='font-size:75%'>input polygons&#13;</span></span></div>
+ <div id="_x0000_s5127_42_79" class=B1 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:15.49%;left:8.68%;width:81.02%;height:12.54%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:6.74%;width:93.25%;
+ height:52.94%'><span style='font-size:71%'><span style='mso-special-format:
+ bullet;position:absolute;left:-7.23%'>–</span></span><span style='font-size:
+ 71%'>Open/closed semantic for last </span></span><span style='position:absolute;
+ top:47.05%;left:6.74%;width:92.06%;height:52.94%'><span style='font-size:71%'>vertex&#13;</span></span></div>
+ <div id="_x0000_s5127_79_122" class=B1 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:28.78%;left:8.68%;width:91.31%;height:12.54%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:5.98%;width:94.01%;
+ height:52.94%'><span style='font-size:71%'><span style='mso-special-format:
+ bullet;position:absolute;left:-6.36%'>–</span></span><span style='font-size:
+ 71%'>Winding direction conventions not </span></span><span style='position:
+ absolute;top:47.05%;left:5.98%;width:81.69%;height:52.94%'><span
+ style='font-size:71%'>enforced&#13;</span></span></div>
+ <div id="_x0000_s5127_122_145" class=B1 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:41.69%;left:8.68%;width:79.74%;height:6.64%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:6.85%;width:93.54%;
+ height:100.0%'><span style='font-size:71%'><span style='mso-special-format:
+ bullet;position:absolute;left:-7.32%'>–</span></span><span style='font-size:
+ 71%'>Input polygons may be &#13;</span></span></div>
+ <div id="_x0000_s5127_145_159" class=B2 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:49.07%;left:17.36%;width:71.38%;height:5.9%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:5.85%;width:93.69%;
+ height:100.0%'><span style='font-size:75%'><span style='mso-special-format:
+ bullet;position:absolute;left:-6.25%'>•</span></span><span style='font-size:
+ 75%'>self touching&#13;</span></span></div>
+ <div id="_x0000_s5127_159_177" class=B2 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:55.35%;left:17.36%;width:71.38%;height:5.9%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:5.85%;width:93.69%;
+ height:100.0%'><span style='font-size:75%'><span style='mso-special-format:
+ bullet;position:absolute;left:-6.25%'>•</span></span><span style='font-size:
+ 75%'>self intersecting&#13;</span></span></div>
+ <div id="_x0000_s5127_177_194" class=B2 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:61.99%;left:17.36%;width:71.38%;height:5.9%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:5.85%;width:93.69%;
+ height:100.0%'><span style='font-size:75%'><span style='mso-special-format:
+ bullet;position:absolute;left:-6.25%'>•</span></span><span style='font-size:
+ 75%'>self overlapping&#13;</span></span></div>
+ <div id="_x0000_s5127_194_239" class=B1 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:68.63%;left:8.68%;width:84.24%;height:12.54%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:6.48%;width:93.51%;
+ height:52.94%'><span style='font-size:71%'><span style='mso-special-format:
+ bullet;position:absolute;left:-6.93%'>–</span></span><span style='font-size:
+ 71%'>Correctly handles duplicate/co-</span></span><span style='position:absolute;
+ top:47.05%;left:6.48%;width:88.54%;height:52.94%'><span style='font-size:71%'>linear
+ points&#13;</span></span></div>
+ <div id="_x0000_s5127_239_325" class=B1 style='mso-line-spacing:"90 20 0";
+ position:absolute;top:81.54%;left:8.68%;width:82.31%;height:18.45%;white-space:
+ nowrap'><span style='position:absolute;top:0%;left:6.64%;width:93.35%;
+ height:36.0%'><span style='font-size:71%'><span style='mso-special-format:
+ bullet;position:absolute;left:-7.11%'>–</span></span><span style='font-size:
+ 71%'>Correctly handles zero degree </span></span><span style='position:absolute;
+ top:32.0%;left:6.64%;width:90.62%;height:36.0%'><span style='font-size:71%'>angles
+ and polygons that </span></span><span style='position:absolute;top:64.0%;
+ left:6.64%;width:93.35%;height:36.0%'><span style='font-size:71%'>degenerate
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+ <v:fill color2="white [0]"/>
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+ strokeweight="1.25pt">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="17" delay="0" type="object" effect="zoom" direction="out"
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+ <v:fill color2="white [0]"/>
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+ left:513.125pt;top:397.375pt;width:10.375pt;height:10.375pt;mso-wrap-style:none;
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+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="14" delay="0" type="object" effect="zoom" direction="out"
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+ left:479.125pt;top:329.875pt;width:75pt;height:75.625pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="red"
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+ left:625.125pt;top:106.5pt;width:78.625pt;height:79.375pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="red"
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+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
+width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%, 101%, 101%, 0%);
+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml" href="slide0006.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
+ width:21.53%;height:3.25%'><span style='font-size:78%;mso-field-code:meta16'>9</span><span
+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
+ </div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><p:shaperange
+ href="master03.xml#_x0000_m1027"/><p:shaperange
+ href="slide0006.xml#_x0000_s7170"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7450,_x0000_s7451,_x0000_s7452,_x0000_s7453,_x0000_s7454,_x0000_s7455,_x0000_s7456,_x0000_s7457,_x0000_s7458,_x0000_s7459,_x0000_s7460,_x0000_s7461,_x0000_s7462"
+ src="slide0006_image032.gif" style='position:absolute;top:81.0%;left:69.1%;
+ width:28.83%;height:17.5%'><![endif]>
+ <div v:shape="_x0000_s7170" class=T style='position:absolute;top:8.0%;
+ left:-3.93%;width:109.55%;height:9.25%'>Boolean Operation Output Modes</div>
+ <div v:shape="_x0000_s7336">
+ <div class=B style='mso-line-spacing:"90 20 0";position:absolute;top:19.25%;
+ left:.93%;width:50.74%;height:5.25%'><span style='position:absolute;
+ top:0%;left:7.38%;width:92.61%;height:100.0%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.96%'>•</span></span><span
+ style='font-size:75%'>Manhattan Booleans&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:25.0%;
+ left:5.99%;width:45.69%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.96%;width:93.03%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.48%'>–</span></span><span
+ style='font-size:71%'>Polygons with lists of holes&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:29.75%;
+ left:5.99%;width:49.06%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.48%;width:93.51%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-6.93%'>–</span></span><span
+ style='font-size:71%'>Keyhole holes to outer polygon&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:34.75%;left:9.17%;width:42.69%;height:4.5%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.45%'>–</span></span><span
+ style='font-size:71%'>Horizontal and vertical sliced </span></span><span
+ style='position:absolute;top:38.75%;left:9.17%;width:42.5%;height:4.5%'><span
+ style='font-size:71%'>rectangle tiling&#13;</span></span></div>
+ <div class=B style='mso-line-spacing:"90 20 0";position:absolute;top:43.75%;
+ left:.93%;width:50.74%;height:5.25%'><span style='position:absolute;
+ top:0%;left:7.38%;width:92.61%;height:100.0%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.96%'>•</span></span><span
+ style='font-size:75%'>45-degree Booleans&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:49.5%;
+ left:5.99%;width:45.69%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.96%;width:93.03%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.48%'>–</span></span><span
+ style='font-size:71%'>Polygon with lists of holes&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:54.25%;
+ left:5.99%;width:49.06%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.48%;width:93.51%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-6.93%'>–</span></span><span
+ style='font-size:71%'>Keyhole holes to outer polygon&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:59.25%;
+ left:5.99%;width:46.25%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.88%;width:93.52%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.35%'>–</span></span><span
+ style='font-size:71%'>Vertical sliced trapezoid tiling&#13;</span></span></div>
+ <div class=B style='mso-line-spacing:"90 20 0";position:absolute;top:64.25%;
+ left:.93%;width:50.74%;height:5.25%'><span style='position:absolute;
+ top:0%;left:7.38%;width:92.61%;height:100.0%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.96%'>•</span></span><span
+ style='font-size:75%'>Arbitrary-angle Booleans&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:70.0%;
+ left:5.99%;width:45.69%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.96%;width:93.03%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-7.48%'>–</span></span><span
+ style='font-size:71%'>Polygon with lists of holes&#13;</span></span></div>
+ <div class=B1 style='mso-line-spacing:"90 20 0";position:absolute;top:74.75%;
+ left:5.99%;width:49.06%;height:4.5%'><span style='position:absolute;
+ top:0%;left:6.48%;width:93.51%;height:100.0%'><span style='font-size:71%'><span
+ style='mso-special-format:bullet;position:absolute;left:-6.93%'>–</span></span><span
+ style='font-size:71%'>Keyhole holes to outer polygon</span></span></div>
+ </div>
+ <div v:shape="_x0000_s7450" class=O>
+ <div style='text-align:center;position:absolute;top:86.0%;left:70.03%;
+ width:10.29%;height:4.0%'>Vertical&#13;</div>
+ <div style='text-align:center;position:absolute;top:90.0%;left:70.22%;
+ width:9.92%;height:4.0%'>Slicing</div>
+ </div>
+ <p:shaperange href="slide0006.xml#_x0000_s7463"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7463" src="slide0006_image033.gif" style='position:absolute;
+ top:23.5%;left:54.3%;width:7.11%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7464"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7464" src="slide0006_image034.gif" style='position:absolute;
+ top:28.99%;left:54.3%;width:8.8%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7465"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7465" src="slide0006_image035.gif" style='position:absolute;
+ top:24.75%;left:61.04%;width:7.11%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7466"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7466" src="slide0006_image036.gif" style='position:absolute;
+ top:24.75%;left:67.79%;width:.37%;height:10.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7467"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7467" src="slide0006_image037.gif" style='position:absolute;
+ top:23.5%;left:61.04%;width:.37%;height:1.75%'><![endif]><p:shaperange
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+ top:34.75%;left:62.73%;width:5.43%;height:.5%'><![endif]><p:shaperange
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+ v:shapes="_x0000_s7472" src="slide0006_image042.gif" style='position:absolute;
+ top:24.75%;left:56.92%;width:.37%;height:2.75%'><![endif]><p:shaperange
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+ v:shapes="_x0000_s7474" src="slide0006_image044.gif" style='position:absolute;
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+ v:shapes="_x0000_s7475" src="slide0006_image045.gif" style='position:absolute;
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+ v:shapes="_x0000_s7477" src="slide0006_image047.gif" style='position:absolute;
+ top:47.0%;left:90.63%;width:7.11%;height:.5%'><![endif]><p:shaperange
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+ v:shapes="_x0000_s7480" src="slide0006_image050.gif" style='position:absolute;
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+ top:51.5%;left:92.32%;width:.37%;height:6.0%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7483"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7483" src="slide0006_image053.gif" style='position:absolute;
+ top:47.0%;left:86.51%;width:2.99%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7484"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7484" src="slide0006_image054.gif" style='position:absolute;
+ top:47.0%;left:86.51%;width:.37%;height:2.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7485"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7485" src="slide0006_image055.gif" style='position:absolute;
+ top:45.75%;left:89.13%;width:.37%;height:4.0%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7486"/><![if !vml]><img border=0
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+ style='position:absolute;top:41.5%;left:68.91%;width:20.59%;height:17.5%'><![endif]>
+ <div v:shape="_x0000_s7487" class=O>
+ <div style='text-align:center;position:absolute;top:46.25%;left:70.03%;
+ width:9.92%;height:4.0%'>Hole &#13;</div>
+ <div style='text-align:center;position:absolute;top:50.24%;left:68.16%;
+ width:13.67%;height:4.0%'>Fracturing</div>
+ </div>
+ <p:shaperange href="slide0006.xml#_x0000_s7500"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7500" src="slide0006_image057.gif" style='position:absolute;
+ top:24.75%;left:84.08%;width:7.11%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7501"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7501" src="slide0006_image058.gif" style='position:absolute;
+ top:30.25%;left:84.08%;width:8.8%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7502"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7502" src="slide0006_image059.gif" style='position:absolute;
+ top:26.0%;left:90.82%;width:7.11%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7503"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7503" src="slide0006_image060.gif" style='position:absolute;
+ top:26.0%;left:97.37%;width:.37%;height:10.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7504"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7504" src="slide0006_image061.gif" style='position:absolute;
+ top:24.75%;left:90.82%;width:.37%;height:1.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7505"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7505" src="slide0006_image062.gif" style='position:absolute;
+ top:24.75%;left:84.08%;width:.37%;height:6.0%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7506"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7506" src="slide0006_image063.gif" style='position:absolute;
+ top:36.0%;left:92.5%;width:5.43%;height:.5%'><![endif]><p:shaperange
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+ href="slide0006.xml#_x0000_s7508"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7508" src="slide0006_image065.gif" style='position:absolute;
+ top:26.0%;left:86.51%;width:2.99%;height:.5%'><![endif]><p:shaperange
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+ v:shapes="_x0000_s7509" src="slide0006_image066.gif" style='position:absolute;
+ top:26.0%;left:86.51%;width:.37%;height:2.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7510"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7510" src="slide0006_image067.gif" style='position:absolute;
+ top:26.0%;left:89.13%;width:.37%;height:2.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7511"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7511,_x0000_s7512" src="slide0006_image068.gif"
+ style='position:absolute;top:20.0%;left:69.1%;width:20.41%;height:17.5%'><![endif]>
+ <div v:shape="_x0000_s7512" class=O>
+ <div style='text-align:center;position:absolute;top:25.0%;left:69.66%;
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+ <div style='text-align:center;position:absolute;top:28.99%;left:67.79%;
+ width:14.6%;height:4.0%'>With Holes</div>
+ </div>
+ <p:shaperange href="slide0006.xml#_x0000_s7513"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7513" src="slide0006_image069.gif" style='position:absolute;
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+ href="slide0006.xml#_x0000_s7516"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7516" src="slide0006_image072.gif" style='position:absolute;
+ top:46.5%;left:67.41%;width:.37%;height:10.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7517"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7517" src="slide0006_image073.gif" style='position:absolute;
+ top:45.5%;left:60.86%;width:.37%;height:1.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7518"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7518" src="slide0006_image074.gif" style='position:absolute;
+ top:45.5%;left:54.11%;width:.37%;height:6.0%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7519"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7519" src="slide0006_image075.gif" style='position:absolute;
+ top:56.49%;left:62.54%;width:5.43%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7520"/><![if !vml]><img border=0
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+ top:51.0%;left:62.54%;width:.37%;height:6.0%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7521"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7521" src="slide0006_image077.gif" style='position:absolute;
+ top:46.5%;left:56.74%;width:2.99%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7522"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7522" src="slide0006_image078.gif" style='position:absolute;
+ top:46.5%;left:56.74%;width:.37%;height:2.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7523"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7523" src="slide0006_image079.gif" style='position:absolute;
+ top:46.5%;left:59.17%;width:.37%;height:2.75%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7524"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7524" src="slide0006_image080.gif" style='position:absolute;
+ top:48.75%;left:56.74%;width:2.99%;height:.5%'><![endif]><p:shaperange
+ href="slide0006.xml#_x0000_s7525"/><![if !vml]><img border=0
+ v:shapes="_x0000_s7525,_x0000_s7526,_x0000_s7527,_x0000_s7528,_x0000_s7529,_x0000_s7530,_x0000_s7531,_x0000_s7532,_x0000_s7533,_x0000_s7534,_x0000_s7535,_x0000_s7536,_x0000_s7537,_x0000_s7539,_x0000_s7540,_x0000_s7541,_x0000_s7542,_x0000_s7543,_x0000_s7544,_x0000_s7545,_x0000_s7546,_x0000_s7547,_x0000_s7548,_x0000_s7549,_x0000_s7550,_x0000_s7551,_x0000_s7552,_x0000_s7553,_x0000_s7554,_x0000_s7555,_x0000_s7556,_x0000_s7557,_x0000_s7558,_x0000_s7559,_x0000_s7560,_x0000_s7561,_x0000_s7562,_x0000_s7563"
+ src="slide0006_image081.gif" style='position:absolute;top:62.25%;left:54.3%;
+ width:43.44%;height:34.5%'><![endif]>
+ <div v:shape="_x0000_s7525" class=O>
+ <div style='text-align:center;position:absolute;top:67.25%;left:68.35%;
+ width:13.67%;height:4.0%'>Horizontal&#13;</div>
+ <div style='text-align:center;position:absolute;top:71.25%;left:70.22%;
+ width:9.92%;height:4.0%'>Slicing</div>
+ </div>
+</p:slide>
+</div>
+
+</body>
+
+</html>

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006.xml
==============================================================================
--- (empty file)
+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0006.xml 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
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+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:54.25%;left:9.73%;width:97.0%;height:6.75%'><span style='mso-special-format:
+ bullet;position:absolute;left:-3.86%'>•</span>GTL implements different sweep
+ lines for </span><span style='position:absolute;top:60.5%;left:9.73%;
+ width:94.94%;height:6.75%'>Manhattan, 45-degree and general case&#13;</span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:68.25%;left:9.73%;width:82.77%;height:6.75%'><span style='mso-special-format:
+ bullet;position:absolute;left:-4.52%'>•</span>GTL Booleans sweep-lines are </span><span
+ style='position:absolute;top:74.75%;left:9.73%;width:92.88%;height:6.75%'>parameterized
+ to allow them to perform </span><span style='position:absolute;top:81.0%;
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+ <div style='mso-line-spacing:"90 20 0";position:absolute;top:89.0%;left:5.99%;
+ width:86.51%;height:6.75%'><span style='position:absolute;top:0%;left:4.32%;
+ width:95.67%;height:100.0%'><span style='visibility:hidden'><span
+ style='mso-special-format:bullet;position:absolute;left:-4.52%'>•</span></span><span
+ style='mso-special-format:lastCR;display:none'>&#13;</span></span></div>
+ </div>
+</p:slide></div>
+
+</body>
+
+</html>

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0016.htm
==============================================================================
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+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0016.htm 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
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+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
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+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
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+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
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+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s18434"
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+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="body" position="1"/></v:shape>
+ <div v:shape="_x0000_s18434" class=T><span style='position:absolute;
+ top:4.0%;left:.18%;width:99.81%;height:8.5%'><span style='font-size:91%'>Observations
+ on GPC, CGAL and </span></span><span style='position:absolute;top:12.75%;
+ left:5.99%;width:88.2%;height:8.5%'><span style='font-size:91%'>PolyBoolean</span></span></div>
+ <div v:shape="_x0000_s18435" class=B>
+ <div style='mso-line-spacing:"90 20 0";position:absolute;top:21.75%;
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+ top:0%;left:3.92%;width:96.07%;height:100.0%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-4.08%'>•</span></span><span
+ style='font-size:75%'>We found at least two different bugs in PolyBoolean&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0";position:absolute;top:27.5%;left:3.74%;
+ width:93.07%;height:5.25%'><span style='position:absolute;top:0%;left:4.02%;
+ width:95.97%;height:100.0%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-4.19%'>•</span></span><span
+ style='font-size:75%'>We found one bug in CGAL&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:33.25%;left:7.49%;width:97.94%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.82%'>•</span></span><span
+ style='font-size:75%'>GPC and PolyBoolean have very difficult to use C-style </span></span><span
+ style='position:absolute;top:38.25%;left:7.49%;width:89.32%;height:5.25%'><span
+ style='font-size:75%'>APIs&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:44.0%;left:7.49%;width:102.62%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.64%'>•</span></span><span
+ style='font-size:75%'>GPC and PolyBoolean cannot merge multiple overlapping </span></span><span
+ style='position:absolute;top:48.75%;left:7.49%;width:89.32%;height:5.25%'><span
+ style='font-size:75%'>polygons in one step&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:54.75%;left:7.49%;width:104.3%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.59%'>•</span></span><span
+ style='font-size:75%'>GPC and PolyBoolean both have O(n</span><span
+ style='font-size:50%;position:relative;top:-.45em;mso-text-raise:30%'>1.5</span><span
+ style='font-size:75%'>log n) line segment </span></span><span
+ style='position:absolute;top:59.5%;left:7.49%;width:104.49%;height:5.25%'><span
+ style='font-size:75%'>intersection algorithms (sort all edges that intersect
+ sweep-</span></span><span style='position:absolute;top:64.25%;left:7.49%;
+ width:89.32%;height:5.25%'><span style='font-size:75%'>line at every x)&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:70.0%;left:7.49%;width:104.49%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.58%'>•</span></span><span
+ style='font-size:75%'>PolyBoolean has O(n * m * k) algorithm to determine
+ which </span></span><span style='position:absolute;top:75.0%;left:7.49%;
+ width:106.36%;height:5.25%'><span style='font-size:75%'>polygons contain which
+ holes (n polygons, m holes, k points </span></span><span style='position:absolute;
+ top:79.75%;left:7.49%;width:89.32%;height:5.25%'><span style='font-size:75%'>per
+ polygon), which is O(n^2) in the worst case&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:85.5%;left:7.49%;width:106.17%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.52%'>•</span></span><span
+ style='font-size:75%'>CGAL requires that overlapping polygons be merged before
+ </span></span><span style='position:absolute;top:90.25%;left:7.49%;width:89.32%;
+ height:5.25%'><span style='font-size:75%'>being an input to a Boolean, but can
+ do that itself</span></span></div>
+ </div>
+</p:slide></div>
+
+</body>
+
+</html>

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0018.htm
==============================================================================
--- (empty file)
+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0018.htm 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
@@ -0,0 +1,118 @@
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+<head>
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+<meta name=ProgId content=PowerPoint.Slide>
+<meta name=Generator content="Microsoft PowerPoint 11">
+<link id=Main-File rel=Main-File href="../GTL_boostcon_draft03.htm">
+<link rel=Preview href=preview.wmf>
+<!--[if !mso]>
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+<title>GTL Geometry Template Library</title>
+<meta name=Description content="5/15/2009: Observations About Preconditions">
+<link rel=Stylesheet href="master03_stylesheet.css">
+<![if !ppt]>
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+<script src=script.js></script><script><!--
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+</script><![endif]--><![endif]><o:shapelayout v:ext="edit">
+ <o:idmap v:ext="edit" data="21"/>
+</o:shapelayout>
+</head>
+
+<body lang=EN-US style='margin:0px;background-color:black'
+onclick="DocumentOnClick()" onresize="_RSW()" onload="LoadSld()"
+onkeypress="_KPH()">
+
+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
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+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
+ width:21.53%;height:3.25%'><span style='font-size:78%;mso-field-code:meta16'>17</span><span
+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
+ </div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s21506"
+ type="#_x0000_m1026" style='position:absolute;left:36pt;top:21.625pt;width:9in;
+ height:90pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="title"/></v:shape><p:shaperange
+ href="master03.xml#_x0000_m1027"/><v:shape id="_x0000_s21507" type="#_x0000_m1027"
+ style='position:absolute;left:36pt;top:126pt;width:9in;height:377.25pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="body" position="1"/></v:shape>
+ <div v:shape="_x0000_s21506" class=T style='position:absolute;top:8.5%;
+ left:-.37%;width:100.93%;height:8.5%'><span style='font-size:91%'>Observations
+ About Preconditions</span></div>
+ <div v:shape="_x0000_s21507" class=B>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:23.75%;left:9.73%;width:98.12%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.81%'>•</span></span><span
+ style='font-size:75%'>CGAL throws an “Precondition Violated” exception if an </span></span><span
+ style='position:absolute;top:28.74%;left:9.73%;width:91.01%;height:5.25%'><span
+ style='font-size:75%'>input polygon is self intersecting/overlapping or has </span></span><span
+ style='position:absolute;top:33.5%;left:9.73%;width:84.45%;height:5.25%'><span
+ style='font-size:75%'>“closed” semantic at last vertex&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:39.25%;left:9.73%;width:97.37%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.84%'>•</span></span><span
+ style='font-size:75%'>PolyBoolean returns a “bad input polygon” error code if </span></span><span
+ style='position:absolute;top:44.0%;left:9.73%;width:100.74%;height:5.25%'><span
+ style='font-size:75%'>an input polygon is self intersecting/overlapping has
+ zero </span></span><span style='position:absolute;top:48.75%;left:9.73%;
+ width:84.45%;height:5.25%'><span style='font-size:75%'>area or is a hole with
+ no enclosing polygon&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:54.75%;left:9.73%;width:100.0%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.74%'>•</span></span><span
+ style='font-size:75%'>Both PolyBoolean and CGAL inform the user the input is </span></span><span
+ style='position:absolute;top:59.5%;left:9.73%;width:98.12%;height:5.25%'><span
+ style='font-size:75%'>bad when a bug in their algorithms leads to a fatal
+ error&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:65.25%;left:9.73%;width:99.06%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.78%'>•</span></span><span
+ style='font-size:75%'>GPC produces garbage output when input polygons are </span></span><span
+ style='position:absolute;top:70.25%;left:9.73%;width:84.45%;height:5.25%'><span
+ style='font-size:75%'>self intersecting/overlapping&#13;</span></span></div>
+ <div style='mso-line-spacing:"90 20 0"'><span style='position:absolute;
+ top:76.0%;left:9.73%;width:101.12%;height:5.25%'><span style='font-size:75%'><span
+ style='mso-special-format:bullet;position:absolute;left:-3.7%'>•</span></span><span
+ style='font-size:75%'>GTL has no preconditions and produces correct output in </span></span><span
+ style='position:absolute;top:80.75%;left:9.73%;width:84.45%;height:5.25%'><span
+ style='font-size:75%'>all cases</span></span></div>
+ </div>
+</p:slide></div>
+
+</body>
+
+</html>

Added: sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0019.htm
==============================================================================
--- (empty file)
+++ sandbox/gtl/doc/GTL_boostcon_draft03_files/slide0019.htm 2009-08-25 11:55:42 EDT (Tue, 25 Aug 2009)
@@ -0,0 +1,126 @@
+<html xmlns:v="urn:schemas-microsoft-com:vml"
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+xmlns:p="urn:schemas-microsoft-com:office:powerpoint"
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+xmlns="http://www.w3.org/TR/REC-html40">
+
+<head>
+<meta http-equiv=Content-Type content="text/html; charset=windows-1252">
+<meta name=ProgId content=PowerPoint.Slide>
+<meta name=Generator content="Microsoft PowerPoint 11">
+<link id=Main-File rel=Main-File href="../GTL_boostcon_draft03.htm">
+<link rel=Preview href=preview.wmf>
+<!--[if !mso]>
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+v\:textbox {display:none;}
+</style>
+<![endif]-->
+<title>GTL Geometry Template Library</title>
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+<link rel=Stylesheet href="master03_stylesheet.css">
+<![if !ppt]>
+<style media=print>
+<!--.sld
+ {left:0px !important;
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+<script src=script.js></script><script><!--
+if( !IsNts() ) Redirect( "PPTSld" );
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+ <o:idmap v:ext="edit" data="22"/>
+</o:shapelayout>
+</head>
+
+<body lang=EN-US style='margin:0px;background-color:black'
+onclick="DocumentOnClick()" onresize="_RSW()" onload="LoadSld()"
+onkeypress="_KPH()">
+
+<div id=SlideObj class=sld style='position:absolute;top:0px;left:0px;
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+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
+ width:21.53%;height:3.25%'><span style='font-size:78%;mso-field-code:meta16'>19</span><span
+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
+ </div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s22530"
+ type="#_x0000_m1026" style='position:absolute;left:23.5pt;top:0;width:675.375pt;
+ height:90pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="title"/></v:shape><p:shaperange
+ href="master03.xml#_x0000_m1027"/><v:shape id="_x0000_s22531" type="#_x0000_m1027"
+ style='position:absolute;left:12.25pt;top:74pt;width:707.75pt;height:444.5pt'>
+ <v:fill o:detectmouseclick="f"/>
+ <v:stroke o:forcedash="f"/>
+ <o:lock v:ext="edit" text="f"/>
+ <p:placeholder type="body" position="1"/></v:shape>
+ <div v:shape="_x0000_s22530" class=T style='position:absolute;top:4.0%;
+ left:-4.49%;width:109.55%;height:9.25%'>Better Booleans through Calculus</div>
+ <div v:shape="_x0000_s22531" class=B><span style='position:absolute;
+ top:14.75%;left:6.36%;width:109.92%;height:6.75%'><span class=BB
+ style='position:absolute;left:-3.4%'>•</span>We use the same algorithm for
+ Manhattan, 45-</span><span style='position:absolute;top:22.0%;left:6.36%;
+ width:92.69%;height:6.75%'>degree and general polygon Booleans&#13;</span>
+ <div style='position:absolute;top:30.5%;left:2.62%;width:96.44%;height:6.75%'><span
+ style='position:absolute;top:0%;left:3.88%;width:96.11%;height:100.0%'><span
+ style='visibility:hidden'><span class=BB style='position:absolute;left:-4.04%'>•</span></span>&#13;</span></div>
+ <div style='position:absolute;top:39.0%;left:2.62%;width:96.44%;height:6.75%'><span
+ style='position:absolute;top:0%;left:3.88%;width:96.11%;height:100.0%'><span
+ style='visibility:hidden'><span class=BB style='position:absolute;left:-4.04%'>•</span></span>&#13;</span></div>
+ <div style='position:absolute;top:47.5%;left:2.62%;width:96.44%;height:6.75%'><span
+ style='position:absolute;top:0%;left:3.88%;width:96.11%;height:100.0%'><span
+ style='visibility:hidden'><span class=BB style='position:absolute;left:-4.04%'>•</span></span>&#13;</span></div>
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+visibility:hidden'><p:slide coordsize="720,540"
+ colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"
+ masterhref="master03.xml">
+ <p:shaperange href="master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange
+ href="master03.xml#_x0000_s1028"/><p:shaperange
+ href="master03.xml#_x0000_s1029"/><p:shaperange
+ href="master03.xml#_x0000_s1030"/>
+ <div v:shape="_x0000_s1030" class=O>
+ <div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
+ width:21.53%;height:3.25%'><span style='font-size:78%;mso-field-code:meta16'>21</span><span
+ style='font-size:78%;mso-special-format:lastCR;display:none'>&#13;</span></div>
+ </div>
+ <![endif]><p:shaperange href="master03.xml#_x0000_m1026"/><v:shape id="_x0000_s24578"
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+ <v:stroke o:forcedash="f"/>
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+ <div v:shape="_x0000_s24578" class=T style='position:absolute;top:8.0%;
+ left:5.99%;width:88.2%;height:9.25%'>Math With Polygon Model</div>
+ <p:shaperange href="master03.xml#_x0000_m1027"/><v:shape id="_x0000_s24579"
+ type="#_x0000_m1027" style='position:absolute;left:36pt;top:96pt;width:660pt;
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+ <div v:shape="_x0000_s24579" class=B style='position:absolute;top:18.0%;
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+ <div style='mso-line-spacing:"80 20 0";position:absolute;top:0%;left:0%;
+ width:86.64%;height:13.22%'><span style='position:absolute;top:0%;left:4.16%;
+ width:95.83%;height:100.0%'><span style='font-size:56%'><span
+ style='mso-special-format:bullet;position:absolute;left:-4.34%'>•</span></span><span
+ style='font-size:56%'>Because the Polygon is now modeled mathematically…&#13;</span></span></div>
+ <div id="_x0000_s24579_51_86" style='mso-line-spacing:"80 20 0";position:absolute;
+ top:13.22%;left:0%;width:86.64%;height:13.22%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:4.16%;width:95.83%;height:100.0%'><span
+ style='font-size:56%'><span style='mso-special-format:bullet;position:absolute;
+ left:-4.34%'>•</span></span><span style='font-size:56%'>We can manipulate it
+ with calculus&#13;</span></span></div>
+ <div id="_x0000_s24579_86_205" style='mso-line-spacing:"80 20 0";position:
+ absolute;top:26.44%;left:0%;width:94.58%;height:23.96%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:3.81%;width:96.18%;height:55.17%'><span
+ style='font-size:56%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.96%'>•</span></span><span style='font-size:56%'>The derivative with
+ respect to x of the polygon function is the change in </span></span><span
+ style='position:absolute;top:44.82%;left:3.81%;width:87.78%;height:55.17%'><span
+ style='font-size:56%'>polygon count as we cross its vertical edges&#13;</span></span></div>
+ <div id="_x0000_s24579_205_283" style='mso-line-spacing:"80 20 0";position:
+ absolute;top:50.41%;left:0%;width:99.45%;height:13.22%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:3.62%;width:96.37%;height:100.0%'><span
+ style='font-size:56%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.76%'>•</span></span><span style='font-size:56%'>In one dimension the
+ polygon looks like a step function at its vertical edges&#13;</span></span></div>
+ <div id="_x0000_s24579_283_344" style='mso-line-spacing:"80 20 0";position:
+ absolute;top:63.63%;left:0%;width:86.64%;height:13.22%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:4.16%;width:95.83%;height:100.0%'><span
+ style='font-size:56%'><span style='mso-special-format:bullet;position:absolute;
+ left:-4.34%'>•</span></span><span style='font-size:56%'>Derivative of a step
+ function is an impulse with area of one&#13;</span></span></div>
+ <div id="_x0000_s24579_344_478" style='mso-line-spacing:"80 20 0";position:
+ absolute;top:76.85%;left:0%;width:100.0%;height:23.96%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:3.61%;width:96.38%;height:55.17%'><span
+ style='font-size:56%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.74%'>•</span></span><span style='font-size:56%'>Summing changes in
+ polygon count from left to right (scanline) performs an </span></span><span
+ style='position:absolute;top:44.82%;left:3.61%;width:83.03%;height:55.17%'><span
+ style='font-size:56%'>integration over the df/dx to produce the original
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+ <p:animation number="7" delay="0" type="object" effect="zoom" direction="out"
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+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="4" delay="0" type="object" effect="zoom" direction="out"
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+ <div id="_x0000_s24583_AllText" v:shape="_x0000_s24583" class=B
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span>changing_polygon_count
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
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+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
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+ <div id="_x0000_s24590_AllText" v:shape="_x0000_s24590" class=B
+ style='position:absolute;top:56.49%;left:35.2%;width:8.23%;height:6.75%;
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
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+ height:48pt' filled="f" fillcolor="#bbe0e3 [4]" stroked="f" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="19" delay="0" type="object" effect="zoom" direction="out"
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+ <div id="_x0000_s24591_AllText" v:shape="_x0000_s24591" class=B
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+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span><span
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+ </div>
+ <v:rect id="_x0000_s24592" style='position:absolute;left:90pt;top:300pt;
+ width:1in;height:48pt' filled="f" fillcolor="#bbe0e3 [4]" stroked="f"
+ strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="20" delay="0" type="object" effect="zoom" direction="out"
+ flag="1028"/></v:rect>
+ <div id="_x0000_s24592_AllText" v:shape="_x0000_s24592" class=B
+ style='position:absolute;top:56.49%;left:13.48%;width:8.23%;height:6.75%;
+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span>0</div>
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+ <v:line id="_x0000_s24593" style='position:absolute' from="84pt,414pt" to="156pt,414pt"
+ strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ <p:animation number="22" delay="0" type="object" effect="zoom" direction="out"
+ flag="16388"/></v:line><![if !vml]><img border=0 v:shapes="_x0000_s24593"
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+ <v:shadow color="gray [2]"/>
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+ flag="16388"/></v:line><![if !vml]><img border=0 v:shapes="_x0000_s24595"
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+ <p:animation number="25" delay="0" type="object" effect="zoom" direction="out"
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+ <p:animation number="26" delay="0" type="object" effect="zoom" direction="out"
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+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
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+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
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+ <v:fill color2="white [0]"/>
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+ <div id="_x0000_s24599_AllText" v:shape="_x0000_s24599" class=B
+ style='position:absolute;top:71.0%;left:.93%;width:16.66%;height:4.5%;
+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span><span
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+ <v:rect id="_x0000_s24600" style='position:absolute;left:192pt;top:420pt;
+ width:1in;height:48pt' filled="f" fillcolor="#bbe0e3 [4]" stroked="f"
+ strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
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+ <div id="_x0000_s24600_AllText" v:shape="_x0000_s24600" class=B
+ style='position:absolute;top:78.75%;left:27.71%;width:8.23%;height:6.75%;
+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span>-1</div>
+ </div>
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+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
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+ width:42pt;height:48pt' filled="f" fillcolor="#bbe0e3 [4]" stroked="f"
+ strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ <p:animation number="9" delay="0" type="object" effect="zoom" direction="out"
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+ <div id="_x0000_s24602_AllText" v:shape="_x0000_s24602" class=B
+ style='position:absolute;top:62.0%;left:65.16%;width:3.93%;height:4.5%;
+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span><span
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+ strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
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+ white-space:nowrap'>
+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span><span
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+ left:3.55%;width:93.25%;height:9.25%'>The Great Thing About Math</div>
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+ style='position:absolute;top:0%;left:4.13%;width:95.86%;height:100.0%'><span
+ style='font-size:63%'><span style='mso-special-format:bullet;position:absolute;
+ left:-4.31%'>•</span></span><span style='font-size:63%'>If it works once, it
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+ style='position:absolute;top:0%;left:3.53%;width:96.46%;height:39.13%'><span
+ style='font-size:63%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.66%'>•</span></span><span style='font-size:63%'>The derivative with
+ respect to y of the d/dx of polygon function f is the </span></span><span
+ style='position:absolute;top:30.43%;left:3.53%;width:94.86%;height:39.13%'><span
+ style='font-size:63%'>change in the change in polygon count with respect to x
+ as we enter </span></span><span style='position:absolute;top:60.86%;
+ left:3.53%;width:82.12%;height:39.13%'><span style='font-size:63%'>and leave
+ its vertical edges in the y dimension&#13;</span></span></div>
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+ style='position:absolute;top:0%;left:3.71%;width:96.28%;height:100.0%'><span
+ style='font-size:63%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.85%'>•</span></span><span style='font-size:63%'>In the y dimension d
+ f/dx (vertical edges) looks like a step function&#13;</span></span></div>
+ <div id="_x0000_s25603_305_366" style='mso-line-spacing:"80 20 0";position:
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+ style='position:absolute;top:0%;left:4.13%;width:95.86%;height:100.0%'><span
+ style='font-size:63%'><span style='mso-special-format:bullet;position:absolute;
+ left:-4.31%'>•</span></span><span style='font-size:63%'>Derivative of a step
+ function is an impulse with area of one&#13;</span></span></div>
+ <div id="_x0000_s25603_366_537" style='mso-line-spacing:"80 20 0";position:
+ absolute;top:67.8%;left:0%;width:100.0%;height:31.5%;white-space:nowrap'><span
+ style='position:absolute;top:0%;left:3.49%;width:93.18%;height:39.13%'><span
+ style='font-size:63%'><span style='mso-special-format:bullet;position:absolute;
+ left:-3.75%'>•</span></span><span style='font-size:63%'>Summing changes in y
+ of changes in x from low to high y integrates </span></span><span
+ style='position:absolute;top:32.6%;left:3.49%;width:96.5%;height:39.13%'><span
+ style='font-size:63%'>the function and produces changes in x (edges) that can
+ be integrated </span></span><span style='position:absolute;top:63.04%;
+ left:3.49%;width:81.11%;height:39.13%'><span style='font-size:63%'>left to
+ right to produce polygons</span></span></div>
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+ height:100.0%'><b><span style='mso-spacerun:yes'>   </span></b><span
+ style='font-size:44%'><b>-1</b></span><span style='mso-special-format:lastCR;
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+ </div>
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+ <v:fill color2="white [0]"/>
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+ width:1.31%;height:1.75%'><![endif]>
+ <div id="_x0000_s25606_AllText" v:shape="_x0000_s25606" class=O
+ style='position:absolute;top:71.0%;left:67.97%;width:5.05%;height:4.0%;
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+ <div style='text-align:center;position:absolute;top:0%;left:0%;width:100.0%;
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+ style='font-size:44%'><b>+1</b></span><span style='mso-special-format:lastCR;
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+ height:100.0%'><b><span style='mso-spacerun:yes'>     </span></b><span
+ style='font-size:44%'><b>-1</b></span><span style='mso-special-format:lastCR;
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+ </div>
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+ style='font-size:44%'><b>-1</b></span><span style='mso-special-format:lastCR;
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+ </div>
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
+ style='mso-special-format:nobullet;display:none'>•</span><span
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+ <div style='position:absolute;top:0%;left:0%;width:100.0%;height:100.0%'><span
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+ left:7.67%;width:88.2%;height:9.25%'>XOR Example</div>
+ <div v:shape="_x0000_s31747" class=B><span style='position:absolute;
+ top:51.0%;left:8.98%;width:98.5%;height:6.75%'><span class=BB
+ style='position:absolute;left:-3.8%'>•</span>Preprocess input polygons into a
+ merged, </span><span style='position:absolute;top:58.25%;left:8.98%;
+ width:100.74%;height:6.75%'>sorted sequence of change on y of change </span><span
+ style='position:absolute;top:65.25%;left:8.98%;width:84.45%;height:6.75%'>on x
+ of polygon intersection count&#13;</span><span style='position:absolute;
+ top:73.75%;left:8.98%;width:91.38%;height:6.75%'><span class=BB
+ style='position:absolute;left:-4.09%'>•</span>Decomposition is linear, sort is
+ n log n, </span><span style='position:absolute;top:81.0%;left:8.98%;
+ width:84.45%;height:6.75%'>merge is linear</span></div>
+ <v:line id="_x0000_s31749" style='position:absolute' from="150pt,186pt" to="174pt,186pt"
+ strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ </v:line><![if !vml]><img border=0 v:shapes="_x0000_s31749"
+ src="slide0028_image233.gif" style='position:absolute;top:34.5%;left:20.78%;
+ width:3.74%;height:.5%'><![endif]><v:line id="_x0000_s31750" style='position:absolute'
+ from="174pt,2in" to="174pt,186pt" strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ </v:line><![if !vml]><img border=0 v:shapes="_x0000_s31750"
+ src="slide0028_image234.gif" style='position:absolute;top:26.5%;left:24.15%;
+ width:.37%;height:8.25%'><![endif]><v:line id="_x0000_s31751" style='position:absolute;
+ flip:x' from="162pt,2in" to="174pt,2in" strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ </v:line><![if !vml]><img border=0 v:shapes="_x0000_s31751"
+ src="slide0028_image235.gif" style='position:absolute;top:26.5%;left:22.47%;
+ width:2.05%;height:.5%'><![endif]><v:line id="_x0000_s31752" style='position:absolute'
+ from="162pt,114pt" to="162pt,2in" strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ </v:line><![if !vml]><img border=0 v:shapes="_x0000_s31752"
+ src="slide0028_image236.gif" style='position:absolute;top:21.0%;left:22.47%;
+ width:.37%;height:6.0%'><![endif]><v:line id="_x0000_s31753" style='position:absolute;
+ flip:x' from="150pt,114pt" to="162pt,114pt" strokecolor="black [1]">
+ <v:shadow color="gray [2]"/>
+ </v:line><![if !vml]><img border=0 v:shapes="_x0000_s31753"
+ src="slide0028_image237.gif" style='position:absolute;top:21.0%;left:20.78%;
+ width:2.05%;height:.5%'><![endif]><v:rect id="_x0000_s31754" style='position:absolute;
+ left:138pt;top:222pt;width:36pt;height:42pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:rect><![if !vml]><img border=0 v:shapes="_x0000_s31754"
+ src="slide0028_image238.gif" style='position:absolute;top:41.0%;left:19.1%;
+ width:5.43%;height:8.25%'><![endif]><v:shapetype id="_x0000_t13" coordsize="21600,21600"
+ o:spt="13" adj="16200,5400" path="m_at_0,l_at_0@1,0_at_1,0_at_2@0_at_2@0,21600,21600,10800xe">
+ <v:stroke joinstyle="miter"/>
+ <v:formulas>
+ <v:f eqn="val #0"/>
+ <v:f eqn="val #1"/>
+ <v:f eqn="sum height 0 #1"/>
+ <v:f eqn="sum 10800 0 #1"/>
+ <v:f eqn="sum width 0 #0"/>
+ <v:f eqn="prod @4 @3 10800"/>
+ <v:f eqn="sum width 0 @5"/>
+ </v:formulas>
+ <v:path o:connecttype="custom" o:connectlocs="@0,0;0,10800;@0,21600;21600,10800"
+ o:connectangles="270,180,90,0" textboxrect="0,@1,@6,@2"/>
+ <v:handles>
+ <v:h position="#0,#1" xrange="0,21600" yrange="0,10800"/>
+ </v:handles>
+ </v:shapetype><v:shape id="_x0000_s31755" type="#_x0000_t13" style='position:absolute;
+ left:198pt;top:120pt;width:84pt;height:66pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31755"
+ src="slide0028_image239.gif" style='position:absolute;top:22.0%;left:27.52%;
+ width:12.17%;height:13.0%'><![endif]>
+ <div v:shape="_x0000_s31755" class=O>
+ <div style='text-align:center;position:absolute;top:26.25%;left:27.71%;
+ width:10.11%;height:2.25%'><span style='font-size:56%'><b>Decompose &#13;</b></span></div>
+ <div style='text-align:center;position:absolute;top:28.49%;left:28.65%;
+ width:8.42%;height:2.25%'><span style='font-size:56%;mso-special-format:lastCR;
+ display:none'><b>&#13;</b></span></div>
+ </div>
+ <v:shapetype id="_x0000_t32" coordsize="21600,21600" o:spt="32" o:oned="t"
+ path="m,l21600,21600e" filled="f">
+ <v:path arrowok="t" fillok="f" o:connecttype="none"/>
+ <o:lock v:ext="edit" shapetype="t"/>
+ </v:shapetype><v:shape id="_x0000_s31756" type="#_x0000_t32" style='position:absolute;
+ left:186pt;top:153pt;width:12pt;height:3pt;flip:y' o:connectortype="straight"
+ strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31756"
+ src="slide0028_image240.gif" style='position:absolute;top:27.75%;left:25.84%;
+ width:2.24%;height:1.75%'><![endif]><v:shape id="_x0000_s31757" type="#_x0000_t32"
+ style='position:absolute;left:282pt;top:153pt;width:12pt;height:3pt'
+ o:connectortype="straight" strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><v:shape id="_x0000_s31758" type="#_x0000_t13" style='position:absolute;
+ left:198pt;top:204pt;width:84pt;height:66pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31757,_x0000_s31758"
+ src="slide0028_image241.gif" style='position:absolute;top:28.24%;left:27.52%;
+ width:13.85%;height:22.25%'><![endif]>
+ <div v:shape="_x0000_s31758" class=O>
+ <div style='text-align:center;position:absolute;top:41.75%;left:27.71%;
+ width:10.11%;height:2.25%'><span style='font-size:56%'><b>Decompose &#13;</b></span></div>
+ <div style='text-align:center;position:absolute;top:44.0%;left:28.65%;
+ width:8.42%;height:2.25%'><span style='font-size:56%;mso-special-format:lastCR;
+ display:none'><b>&#13;</b></span></div>
+ </div>
+ <v:shape id="_x0000_s31759" type="#_x0000_t32" style='position:absolute;
+ left:186pt;top:237pt;width:12pt;height:3pt;flip:y' o:connectortype="straight"
+ strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31759"
+ src="slide0028_image242.gif" style='position:absolute;top:43.25%;left:25.84%;
+ width:2.24%;height:1.75%'><![endif]><v:shape id="_x0000_s31760" type="#_x0000_t32"
+ style='position:absolute;left:282pt;top:237pt;width:12pt;height:3pt'
+ o:connectortype="straight" strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31760"
+ src="slide0028_image243.gif" style='position:absolute;top:43.75%;left:39.13%;
+ width:2.24%;height:1.75%'><![endif]><v:shape id="_x0000_s31761" type="#_x0000_t13"
+ style='position:absolute;left:366pt;top:162pt;width:84pt;height:66pt;
+ mso-wrap-style:none;v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]"
+ strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31761"
+ src="slide0028_image244.gif" style='position:absolute;top:29.75%;left:50.74%;
+ width:12.17%;height:13.0%'><![endif]>
+ <div v:shape="_x0000_s31761" class=O>
+ <div style='text-align:center;position:absolute;top:34.0%;left:51.12%;
+ width:10.11%;height:2.25%'><span style='font-size:56%'><b>Merge Input &#13;</b></span></div>
+ <div style='text-align:center;position:absolute;top:36.25%;left:51.87%;
+ width:8.61%;height:2.25%'><span style='font-size:56%'><b>Vertices</b></span></div>
+ </div>
+ <v:shape id="_x0000_s31762" type="#_x0000_t32" style='position:absolute;
+ left:354pt;top:195pt;width:12pt;height:3pt;flip:y' o:connectortype="straight"
+ strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31762"
+ src="slide0028_image245.gif" style='position:absolute;top:35.5%;left:49.06%;
+ width:2.24%;height:1.75%'><![endif]><v:shape id="_x0000_s31763" type="#_x0000_t32"
+ style='position:absolute;left:450pt;top:195pt;width:12pt;height:3pt'
+ o:connectortype="straight" strokecolor="black [1]">
+ <v:stroke endarrow="block"/>
+ <v:shadow color="gray [2]"/>
+ </v:shape><![if !vml]><img border=0 v:shapes="_x0000_s31763"
+ src="slide0028_image246.gif" style='position:absolute;top:36.0%;left:62.35%;
+ width:2.24%;height:1.75%'><![endif]><v:oval id="_x0000_s31764" style='position:absolute;
+ left:300pt;top:114pt;width:6pt;height:6pt;mso-wrap-style:none;
+ v-text-anchor:middle' filled="f" fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31764"
+ src="slide0028_image247.gif" style='position:absolute;top:21.0%;left:41.57%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31764" class=O style='text-align:center;position:absolute;
+ top:20.0%;left:39.32%;width:5.61%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31765" style='position:absolute;left:318pt;top:114pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31765"
+ src="slide0028_image248.gif" style='position:absolute;top:21.0%;left:44.19%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31765" class=O style='text-align:center;position:absolute;
+ top:20.0%;left:41.94%;width:5.61%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31766" style='position:absolute;left:318pt;top:2in;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31766"
+ src="slide0028_image249.gif" style='position:absolute;top:26.5%;left:44.19%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31766" class=O style='text-align:center;position:absolute;
+ top:25.5%;left:41.76%;width:5.8%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31767" style='position:absolute;left:336pt;top:2in;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31767"
+ src="slide0028_image250.gif" style='position:absolute;top:26.5%;left:46.62%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31767" class=O style='text-align:center;position:absolute;
+ top:25.5%;left:44.19%;width:5.8%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31768" style='position:absolute;left:300pt;top:174pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31768"
+ src="slide0028_image251.gif" style='position:absolute;top:32.25%;left:41.57%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31768" class=O style='text-align:center;position:absolute;
+ top:31.0%;left:39.32%;width:5.8%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31769" style='position:absolute;left:336pt;top:174pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31769"
+ src="slide0028_image252.gif" style='position:absolute;top:32.25%;left:46.62%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31769" class=O style='text-align:center;position:absolute;
+ top:31.0%;left:44.38%;width:5.61%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31770" style='position:absolute;left:516pt;top:162pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31770"
+ src="slide0028_image253.gif" style='position:absolute;top:30.0%;left:71.53%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31770" class=O style='text-align:center;position:absolute;
+ top:28.74%;left:68.91%;width:6.74%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>0,-1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31771" style='position:absolute;left:516pt;top:3in;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31771"
+ src="slide0028_image254.gif" style='position:absolute;top:40.0%;left:71.53%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31771" class=O style='text-align:center;position:absolute;
+ top:38.75%;left:68.72%;width:6.92%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>0,+1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31772" style='position:absolute;left:570pt;top:3in;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31772"
+ src="slide0028_image255.gif" style='position:absolute;top:40.0%;left:79.02%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31772" class=O style='text-align:center;position:absolute;
+ top:38.75%;left:76.4%;width:6.74%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>0,-1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31773" style='position:absolute;left:570pt;top:162pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31773"
+ src="slide0028_image256.gif" style='position:absolute;top:30.0%;left:79.02%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31773" class=O style='text-align:center;position:absolute;
+ top:28.74%;left:76.21%;width:6.92%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>0,+1</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31774" style='position:absolute;left:474pt;top:132pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31774"
+ src="slide0028_image257.gif" style='position:absolute;top:24.5%;left:65.73%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31774" class=O style='text-align:center;position:absolute;
+ top:23.25%;left:62.92%;width:6.74%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31775" style='position:absolute;left:516pt;top:132pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31775"
+ src="slide0028_image258.gif" style='position:absolute;top:24.5%;left:71.53%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31775" class=O style='text-align:center;position:absolute;
+ top:23.25%;left:68.72%;width:6.92%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s31776" style='position:absolute;left:516pt;top:192pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
+ <v:shadow color="gray [2]"/>
+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s31776"
+ src="slide0028_image259.gif" style='position:absolute;top:35.5%;left:71.53%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s31776" class=O style='text-align:center;position:absolute;
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+ <div v:shape="_x0000_s33804" class=O style='text-align:center;position:absolute;
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+ <div v:shape="_x0000_s33806" class=O style='text-align:center;position:absolute;
+ top:23.25%;left:43.82%;width:6.74%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s33807" style='position:absolute;left:402pt;top:192pt;
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+ </v:oval><![if !vml]><img border=0 v:shapes="_x0000_s33807"
+ src="slide0030_image284.gif" style='position:absolute;top:35.5%;left:55.8%;
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+ <div v:shape="_x0000_s33807" class=O style='text-align:center;position:absolute;
+ top:34.25%;left:52.8%;width:6.92%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s33808" style='position:absolute;left:336pt;top:228pt;
+ width:6pt;height:6pt;mso-wrap-style:none;v-text-anchor:middle' filled="f"
+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
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+ src="slide0030_image285.gif" style='position:absolute;top:42.25%;left:46.62%;
+ width:1.31%;height:1.75%'><![endif]>
+ <div v:shape="_x0000_s33808" class=O style='text-align:center;position:absolute;
+ top:41.0%;left:43.63%;width:6.92%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>+1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s33809" style='position:absolute;left:402pt;top:228pt;
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+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
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+ <div v:shape="_x0000_s33809" class=O style='text-align:center;position:absolute;
+ top:41.0%;left:52.99%;width:6.74%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1,0</b></span><span
+ style='mso-special-format:lastCR;display:none'><b>&#13;</b></span></div>
+ <v:oval id="_x0000_s33810" style='position:absolute;left:558pt;top:150pt;
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+ fillcolor="#bbe0e3 [4]" strokecolor="black [1]">
+ <v:fill color2="white [0]"/>
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+ src="slide0030_image287.gif" style='position:absolute;top:27.75%;left:77.52%;
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+ <div v:shape="_x0000_s33810" class=O style='text-align:center;position:absolute;
+ top:26.5%;left:75.28%;width:5.61%;height:4.0%'><b><span
+ style='mso-spacerun:yes'>     </span></b><span style='font-size:44%'><b>-1</b></span><span
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+ width:1.31%;height:1.75%'><![endif]>
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