source: downloads/ogre/Tools/Wings3DExporter/pgon.py @ 56

# ear-clipping polygon triangulation
#
# written in 2003 by Attila Tajti

from vector import Vector

def sum(a, b):
        return a + b

# get the average normal of a 3d polygon
def pgon_normal(verts):
        normal = Vector(0,0,0)
        for i in range(len(verts)):
                x1, y1, z1 = verts[i - 1]
                x2, y2, z2 = verts[i]
                nx = (y1 - y2) * (z1 + z2)
                ny = (z1 - z2) * (x1 + x2)
                nz = (x1 - x2) * (y1 + y2)
                normal += Vector(nx, ny, nz)
        return normal.unit()

class Triangulator:

        def dump(self, what):
                if __name__ == "__main__":
                        print what

        def __init__(self, pgon):
                self.pgon = pgon

                self.dump("pgon: %s" % repr(self.pgon))

                # normal used for direction calculation
                self.normal = pgon_normal(pgon)
                self.dump("normal: %s" % repr(self.normal))

                # original indices
                self.indices = range(len(self.pgon))

                # result triangles
                self.tris = []
        
        def process(self):

                while len(self.indices) > 3:
                        self.find_and_clip_ear()
                
                self.tris.append(self.indices)

                self.dump("triangles: %s\n" % repr(self.tris))

                return self.tris

        def this_v(self, vert):
                "return position of given vertex"
                return self.pgon[vert]

        def pred_i(self, vert):
                cur = self.indices.index(vert)
                return self.indices[cur - 1]

        def pred_v(self, vert):
                "return position of predecessor vertex"
                pred = self.pred_i(vert)
                return self.pgon[pred]

        def succ_i(self, vert):
                cur = self.indices.index(vert)
                return self.indices[cur + 1 - len(self.indices)]

        def succ_v(self, vert):
                "return position of successor vertex"
                succ = self.succ_i(vert)
                return self.pgon[succ]

        def tri_i_at(self, vert):
                Ai = self.pred_i(vert)
                Bi = vert
                Ci = self.succ_i(vert)
                #self.dump("   tri %d,%d,%d" % (Ai,Bi,Ci))
                return Ai, Bi, Ci

        def tri_at(self, vert):
                Ai, Bi, Ci = self.tri_i_at(vert)
                A = self.pgon[Ai]
                B = self.pgon[Bi]
                C = self.pgon[Ci]
                return A, B, C

        def reflex_factor(self, eartip):
                A, B, C = self.tri_at(eartip)
                AB = B - A
                BC = C - B
                # vector pointing outside
                AB_out = Vector.cross(AB, self.normal).unit()
                return Vector.dot(AB_out, BC.unit())

        def is_convex(self, eartip):
                return self.reflex_factor(eartip) < 0

        def all_outside(self, eartip, verts):
                tri = self.tri_at(eartip)
                A, B, C = tri
                sides = B - A, C - B, A - C
                # vector pointing outside
                normals = map(lambda x: Vector.cross(x, self.normal), sides)
                for vert in map(lambda x: self.pgon[x], verts):
                        out = 0
                        for i in range(3):
                                outside_edge = Vector.dot(vert - tri[i], normals[i])
                                if outside_edge:
                                        out = 1
                        # vertex inside triangle
                        if not out: return 0
                return 1

        def is_ear(self, eartip):

                # create array of other vertices 
                others = self.indices[:]

                # remove current triangle
                A, B, C = self.tri_i_at(eartip)
                others.remove(A)
                others.remove(B)
                others.remove(C)

                # check if all is outside
                return self.all_outside(eartip, others)

        def clip_ear(self, vert):
                self.tris.append(list(self.tri_i_at(vert)))
                self.indices.remove(vert)

        def find_and_clip_ear(self):
                "find clip one ear"

                # try to cut at the tightest angles first
                # TODO: check if this is good for us

                # vertices we are working with
                work = self.indices[:]

                # factors for all vertices
                factors = map(self.reflex_factor, work)

                while len(factors):
                        f = min(factors)
                        eartip = work[factors.index(f)]

                        if self.is_ear(eartip):

                                self.clip_ear(eartip)
                                return
                        else:
                                # remove this from our work list
                                factors.remove(f)
                                work.remove(eartip)

                print self.pgon
                print self.indices
                raise ValueError("failed!")

        def find_and_clip_earx(self):
                "find clip one ear"

                print self.indices
                for vert in self.indices:
                        # check if point is convex
                        if self.is_convex(vert):
                                self.dump("%s is convex" % repr(vert))

                                # check if this vertex is an ear
                                if self.is_ear(vert):

                                        self.dump("%s is an ear" % repr(vert))

                                        # found an eartip, remove it
                                        self.clip_ear(vert)
                                        return
                        else:
                                self.dump("%s is reflex" % repr(vert))
                raise ValueError("failed!")


def triangulate(pgon):
        "triangulate a polygon defined by its vertices"

        t = Triangulator(pgon)

        return t.process()

if __name__ == "__main__":

        print "* normal polygon"
        pgon = []
        pgon.append(Vector(0,0,0))
        pgon.append(Vector(1,0,0))
        pgon.append(Vector(1,1,0))
        pgon.append(Vector(0,1,0))
        triangulate(pgon)
        
        print "* concave polygon"
        pgon = []
        pgon.append(Vector(0,0,0))
        pgon.append(Vector(1,1,0))
        pgon.append(Vector(3,0,0))
        pgon.append(Vector(3,1,0))
        pgon.append(Vector(0,1,0))
        triangulate(pgon)
        
        print "* poly with straight edges"
        pgon = []
        pgon.append(Vector(0,0,0))
        pgon.append(Vector(0.5,0,0))
        pgon.append(Vector(1,0,0))
        pgon.append(Vector(2,0,0))
        pgon.append(Vector(2,2,0))
        pgon.append(Vector(0,2,0))
        triangulate(pgon)