1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triangulate Concave Shape

  1. Mar 16, 2009 #1
    I am looking for a "good" way to triangulate a closed concave shape of vertices and edges.

    "good" is quite a vague term, but the basic principles I'm interested in are:
    1) Minimize "sliver" triangles that are very thin and contain really small angles.
    2) Must be reasonable to compute. Ideally it would take less than a day to compute the triangulization for a mesh with ~10,000 vertices on a standard computer (so complete brute force is out).

    Here is a diagram (initial shape in black):
    http://img394.imageshack.us/img394/3077/concavetriangle.png [Broken]

    If the mesh was convex, a good strategy would be http://en.wikipedia.org/wiki/Delaunay_trianglulation [Broken] method could work well if I had a fast way of finding the worst possible triangle among a subset of the shape, but I'm having no luck there.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 16, 2009 #2


    User Avatar
    Science Advisor

    Suggestion (it may not be very good): Form the convex hull of the polygon. Use Delaunay, being careful you don't cross any existing lines. Get rid of lines outside original polygon.
  4. Mar 16, 2009 #3
    I think the Delaunay triangulization is unique
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook