Tesselation of Mono Connected Non Convex Polygon

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Sample Image - PolyTry.jpg

Introduction

A simple alternative to OpenGL polygon tesselation callback. You can focus on file triangle.h that contain the class to evaluate convexity of polygon and tesselate the polygon. No extra points are inserted. You can work only with planar polygon also in 3D.

Every suggestion in order to speed up the class and create better tesselation ('better' triangles) is appreciated.

History

6^th February, 2002: Initial post

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

About the Author

Peppino Sbargzeguti

United States

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A more little explanation about my article. In order to tesselate the polygon i use this tecnique:
First compute the normal of polygon (i use the newell method see Graphic Gems..)
For each sequence of three vertex ( i, j, k ) in the polygon compute the vector area (alias normal of triangle).
If the normal go in the opposite direction of polygon normal the triangle is 'concave' and go ahead.
If the area il 0.0 the point j is alligned from i to k and eliminated from the list of vertex.
If the normal of triangle is in the same direction of polygon normal the triangle is convex. In the last case check if any other point is inside the triangle (the IsPointInside function). This function test if the point is on solid angle ik ^ jk. if this is true compute distance of intersection k->point to line ij and test distance. If all is good emit triangle, remove vertex j from list and go to the next triplet....
The reason for wich i posted this article is that i don't find this tecnique in any book or article and ave a doubt about the mathematical basic of my algoritm In other words is true that it work in any case ? (my experience ask yes but is very far from a theorem...)
The Delauney algortim work fine but is 'computational' more expensive than my algortim (using my Delauney implementation) for this reason i try this way. At the end my apologize for my poor english but my sincerly idea is to contribute to codeproject and suggest a way to resolv a problem that i found. Thanks pepito.

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Tesselation of mono connected non convex polygon

Type	Article
Licence	CPOL
First Posted	6 Feb 2002
Views	149,688
Downloads	1,113
Bookmarked	20 times

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