simplex_points.py

def simplex_points(n):
    """
    Generates subtriangles of the 3d 0-1 simplex (tripples of tripples).
    `n` is the number of triangles along an edge (so it total it generates a
    number of subtriangles equal to the n'th triangular number)
    """

    def down(x,y,z):
        return (x+1, y, z-1)
    def left(x,y,z):
        return (x-1, y+1, z)
    def triangle(fst,snd,trd):
        def point(x,y,z):
            return (x/n, y/n, z/n)
        return (point(*fst),point(*snd),point(*trd))

    for i in range(1, n+1):

        fst = ((n-i),0,i)
        snd = down(*fst)
        trd = left(*snd)
        yield triangle(fst,snd,trd) 

        last_left = True
        while not trd == ((n-i),i,0):
            fst = snd
            snd = trd
            trd = down(*trd) if last_left else left(*trd)
            last_left = not last_left
            yield triangle(fst,snd,trd)