The more I think about it, the more confused I get. What are the exact pre-conditions and post-conditions of your algorithms?

On
http://www.boost.org/doc/libs/1_56_0/libs/geometry/doc/html/geometry/reference/algorithms/difference.html it says: “Check the Polygon Concept for the rules that polygon input for this algorithm should fulfill”.

On
http://www.boost.org/doc/libs/1_56_0/libs/geometry/doc/html/geometry/reference/concepts/concept_polygon.html it says “There should be no cut lines, spikes or punctures”. It also says “If the input is invalid, the output might be invalid too”. Fair enough.

What it doesn’t say is that a polygon without area is invalid. Let’s take that at face value, though: It is trivial to imagine, e.g., the difference
of two non-empty, valid polygons that results in empty polygon. Does this mean that, e.g., the difference algorithm can take valid input and return invalid output?

If I a have a computation that consists of multiple steps, I would like to make sure that the input is valid, and then run my computation as a sequence
of calls to geometry algorithms. Given the above – do I have to verify every intermediate result, and make sure that if I find an invalid polygon, the algorithm returns half way? What is your recommended best practice to deal with this? I am sure that calling
correct, unique, remove_spikes (in which order?) and is_valid all over the place cannot be the answer…

Thanks again for your help.

Volker

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Volker Schöch | vschoech@think-cell.com

Senior Software Engineer

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**From:** Geometry [mailto:geometry-bounces@lists.boost.org]
**On Behalf Of **Adam Wulkiewicz

**Sent:** Montag, 13. Oktober 2014 17:35

**To:** Boost.Geometry library mailing list

**Subject:** Re: [geometry] single-point polygons

Adam Wulkiewicz wrote:

Hi,

Volker Schöch wrote:It is now my understanding that WKT demands closing points for polygons. The following should be a well-formed polygon:

POLYGON((2079 1968,2301 1968,2079 1968))

No, it should be invalid. A valid Polygon should have a non-0 area. This means that it should at least be a triangle - contain 3 points for open, 4 points for closed.

You may now call bg::is_valid() to check it however it is as computionally expensive as set or relation operation, e.g. intersects().

Calling remove_spikes on the resulting polygon, and outputting it as WKT, results in the following (boost 1.56.0):

POLYGON((2079 1968))

My questions:

- Is this expected (no closing point)?

- I presume that for some algorithms (which?) the position of the single point makes a difference while for others, like difference, any empty polygon should create the same result. Is this correct?

- A year ago I made a note in my code that some algorithms cannot deal with input polygons that contain spikes (Boost.Geometry Overlay invalid input exception results). Therefore I established an invariant for my own polygons, that requires all polygons to be free of spikes. Is this still necessary?

- How is a single-point polygon different from a spike?

- If spikes are not allowed, how should single-point polygons be dealt with? Should they be considered empty, and have their last remaining point removed before passing them to, e.g., the difference algorithm? Or is some wrapper code required that avoids calling certain algorithms with single-point polygons?

My internal representation is oriented counter-clockwise and not closed, my point type is based on int.

I'd say that remove_spikes() assume that the Polygon is valid and since an invalid one is passed it treats it as a one spike which is removed.

This is not precise enough, sorry. A Polygon containing spikes is of course invalid so remove_spikes() can't assume that it is. It just naiively remove spikes which in some cases may result in a Polygon containing to small number of Points.

I guess at the end we could check the number of Points and throw an exception if the result contained too small number of Points.

In some cases numbers of Points are checked at the beginning of a function, maybe for "mutable" functions we should also check this at the end?

Another possible solution would be to generate invalid Polygon but, containing the "correct" number of Points, e.g.:

POLYGON((2079 1968,2079 1968,2079 1968,2079 1968)) for closed

Btw, this is related to convex_hull() for a 1- or 2-Point geometry (https://github.com/boostorg/geometry/pull/152).

Regards,

Adam