|M.Sc Student||Ekshtein Ilya|
|Subject||Texture Mapping Using Constrained Parametrization|
|Department||Department of Computer Science||Supervisor||Professor Chaim Craig Gotsman|
Interactive 3D authoring applications frequently involve mapping 2D textures onto a 3D polyhedral mesh. This involves assigning (u,v) coordinates in the texture space to the vertices of the 3D mesh, and defines a mapping of the texture image to the 3D mesh triangles . While many applications do not care about the precise values of the (u,v) coordinates, as long as the result look reasonable, there are applications in which these values are critical. For example, when texture mapping a photograph of a face to a 3D mesh of a head, it is important that the eyes and the nose in the photograph are mapped precisely to the eyes and the nose in the mesh. This means that the (u,v) coordinates associated with these feature points in the 3D mesh are constrained to very specific values, known as hard constraints. The (u,v) coordinates of the rest of the mesh are not as constrained, as long as the resulting mapping is visually appealing. By "visually appealing" we mean that the texture mapped onto the 3D mesh is not too distorted, despite the constraints. We show how to obtain continuous and bijective piecewise-affine mappings of a texture map to a 3D mesh with hard constraints. Our technique always guarantees a solution by introducing extra (Steiner) vertices in the given mesh connectivity, if needed. We also show how to apply our methods to texture mapping in multiresolution scenarios, as well as to image warping and morphing .