Developer: C++
Summary: Discusses the calculation of barycentric coordinates.

Are there any solutions for finding the barycentric coordinates of a given point in a quad other than splitting that quad into two triangles?

In general, for four points forming a convex quad and a point P in the quad, there is not a unique solution to the problems:

P = (a * A) + (b * B) + (c * C) + (d * D)

where:

a + b + c + d = 1
a, b, c, d >= 0

So the concept of barycentric coordinates does not make sense when there are more than three corner points.