The inverse barycentric displacement problem

In this short paper, we analyze the problem of finding the triangular barycentric coordinates of an interpolated ray hitting a given point. This task, which we term the inverse barycentric displacement problem, is general and useful in geometry processing and computer graphics. Concrete applications of the solution include the construction of displacement maps and texture baking. We derive the set of complete, closed-form solutions and discuss the number and existence of solutions. We close with a discussion of implementation-oriented optimizations and a few example applications.