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Posted 6 Feb 2002

# Tesselation of Mono Connected Non Convex Polygon

, 6 Feb 2002
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Tesselation of mono connected non convex polygon

## 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

• 6th February, 2002: Initial post

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 Re: Found an index range error in code topus10-Apr-03 2:46 topus 10-Apr-03 2:46
 Better tesselation jeckle8-Feb-02 9:00 jeckle 8-Feb-02 9:00
 Re: Better tesselation pepito10-Feb-02 22:05 pepito 10-Feb-02 22:05
 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.
 Re: Better tesselation jeckle11-Feb-02 10:46 jeckle 11-Feb-02 10:46
 Re: Better tesselation Rick York11-Feb-02 10:53 Rick York 11-Feb-02 10:53
 Better tesselation Tim Aidley8-Feb-02 2:45 Tim Aidley 8-Feb-02 2:45
 Re: Better tesselation kilowatt8-Feb-02 8:21 kilowatt 8-Feb-02 8:21
 Re: Better tesselation pepito sbarzeguti10-Feb-02 22:03 pepito sbarzeguti 10-Feb-02 22:03
 Guareschiano anche tu? Anonymous7-Feb-02 21:19 Anonymous 7-Feb-02 21:19
 Re: Guareschiano anche tu? Dieter Hammer8-Feb-02 0:04 Dieter Hammer 8-Feb-02 0:04
 Re: Guareschiano anche tu? pepito8-Feb-02 1:38 pepito 8-Feb-02 1:38
 Re: Guareschiano anche tu? Anonymous10-Feb-02 22:37 Anonymous 10-Feb-02 22:37
 Very poor article on very interesting subject... George7-Feb-02 14:25 George 7-Feb-02 14:25
 Re: Very poor article on very interesting subject... Pepito Sbarzeguti7-Feb-02 21:46 Pepito Sbarzeguti 7-Feb-02 21:46
 Re: Very poor article on very interesting subject... Anonymous7-Feb-02 21:47 Anonymous 7-Feb-02 21:47
 Re: Very poor article on very interesting subject... Andy Metcalfe7-Feb-02 23:14 Andy Metcalfe 7-Feb-02 23:14
 Re: Very poor article on very interesting subject... Anonymous9-Feb-02 23:26 Anonymous 9-Feb-02 23:26
 Re: Very poor article on very interesting subject... George9-Feb-02 23:53 George 9-Feb-02 23:53
 Re: Very poor article on very interesting subject... Nish [BusterBoy]10-Feb-02 0:21 Nish [BusterBoy] 10-Feb-02 0:21
 Re: Very poor article on very interesting subject... Mazdak10-Feb-02 1:02 Mazdak 10-Feb-02 1:02
 Re: Very poor article on very interesting subject... Nish [BusterBoy]10-Feb-02 1:04 Nish [BusterBoy] 10-Feb-02 1:04
 Re: Very poor article on very interesting subject... Anonymous10-Feb-02 15:33 Anonymous 10-Feb-02 15:33
 Re: Very poor article on very interesting subject... Nish [BusterBoy]10-Feb-02 16:32 Nish [BusterBoy] 10-Feb-02 16:32
 Is the artical "fill in the blank"? Jason De Arte7-Feb-02 13:57 Jason De Arte 7-Feb-02 13:57
 Re: Is the artical "fill in the blank"? Nish [BusterBoy]7-Feb-02 23:13 Nish [BusterBoy] 7-Feb-02 23:13
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