Matchmaker: Constructing constrained texture maps

Texture mapping enhances the visual realism of 3D models by adding fine details. To achieve the best results, it is often necessary to force a correspondence between some of the details of the texture and the features of the model. The most common method for mapping texture onto 3D meshes is to use a planar parameterization of the mesh. This, however, does not reflect any special correspondence between the mesh geometry and the texture. The Matchmaker algorithm presented here forces user-defined feature correspondence for planar parameterization of meshes. This is achieved by adding positional constraints to the planar parameterization. Matchmaker allows users to introduce scores of constraints while maintaining a valid one-to-one mapping between the embedding and the 3D surface. Matchmaker's constraint mechanism can be used for other applications requiring parameterization besides texture mapping, such as morphing and remeshing. Matchmaker begins with an unconstrained planar embedding of the 3D mesh generated by conventional methods. It moves the constrained vertices to the required positions by matching a triangulation of these positions to a triangulation of the planar mesh formed by paths between constrained vertices. The matching triangulations are used to generate a new parameterization that satisfies the constraints while minimizing the deviation from the original 3D geometry.