טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEkshtein Ilya
SubjectTexture Mapping Using Constrained Parametrization
DepartmentDepartment of Computer Science
Supervisor Professor Chaim Craig Gotsman


Abstract

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 .