Texture Mapping with Hard Constraints

We show how to continuously map a texture onto a 3D triangle mesh when some of the mesh vertices are constrained to have given (u, v) coordinates. This problem arises frequently in interactive texture mapping applications and, to the best of our knowledge, a complete and efficient solution is not available. Our techniques always guarantee a solution by introducing extra (Steiner) vertices in the triangulation if needed. We show how to apply our methods to texture mapping in multi-resolution scenarios and image warping and morphing.