(the policy of Boost lists is to not top-post).
On 12-6-2013 14:28, Tomislav Maric wrote:
I don't think the OGC PolyhedralSurface model will work together
with a multipolygon concept for a polyhedron (surface mesh),
since the connectivity between polygons will be severely
complicated to compute and change during topological operations
if the points are repeated for each polygon.
Note that it is the Concept which repeat points. The implementation
might be different. I mean: the Concept has methods as NumPatch,
Patch(index), or probably an iterator returning polygons. However,
this can be stored internally as the implementator thinks it is
Besides this, I don't understand - if you want to use multipolygons
to store the polyhedron, I always assumed that you wanted to repeat
It is a bit as a collection of polygons, some files (shapefiles)
store all coordinates per polygon, others (ESRI coverages) use
topology, however, retrieving one polygon always returns just that
polygon, regardless how it is stored.
To ensure logical point uniqueness (not involving tolerances to
drop duplicates), the topology of the surface mesh must be
described either as a graph, or using indirect addressing like
Adam described in his previous email/ However, I am 100% certain
that ensuring point uniqueness with indirect addressing will
cause the algorithm complexity to literally explode.
I don't exactly understand why the complexity explodes by just using
indirect addressing. It is IMO just a way to access the coordinates.
If the Concept gives certain methods, the implementations (using
either direct or indirect addresses and either unique or duplicated
points) might vary. The algorithms should use the Concept to support
different types of polyhedrons.
I've tried using indrect addressing and subsequently ensuring
point uniqueness, and that is the reason why I want to switch to
a multipolygon representation and loose the connection between
polygons of the surface mesh, for intersecting smaller
non-planar polyhedra. In the end my goal is to efficiently
intersect and compute volume of the result between a halfspace
and a small polyhedron, two tetrahedral decompositions and two
polyhedrons. Maybe this is too specific for the geometry
library.. I don't know.. this is just my experience..
I don't think it is too specific, but we need a generic concept able
to store polyhedrons described either as triangles, or as polygons.