While I am learning some concepts from (discrete)differential geometry, I find it intuitive to visualize them on the mesh as various hues. For this job I need to locate the corresponding position on the mesh for each given UV coordinate.

I write an operator to illustrate how this can be done using barycentric_transform and intersect_point_tri_2d functions. Almost all of this implementation is learned from CoDEmanX’s answer in this BlenderArtists post.

Later I will rewrite this in C for optimal performance.