In 3-dimensional computer graphics, texture mapping is a technique for modelling and rendering surface details. In texture mapping, a texture defined in the 2-dimensional space is mapped onto a 3-dimensional surface of a modelled object. There are some unsolved issues in texture mapping such as aliasing, distortion, discontinuity, etc.
In this thesis, an algorithm for mapping 2-D textures onto 3-D surfaces with low distortion is proposed. The proposed algorithm consists of two versions applicable to parametric surfaces and general polyhedra, respectively. Both versions preserve the distance and angle between the points sampled properly on the surface of the object. For parametric surfaces, points are sampled by their parameter, while for general polyhedra, points are sampled on their vertices.
For general polyhedron mapping, an edge belonging to two polygons can be split in texture space with the resultant discontinuity. In such cases, however, distortion becomes low in the interior of the polygons. Therefore, there needs to be some trade-off between distortion and discontinuity in mapping 2-D textures onto 3-D surfaces. This thesis describes a new method to control this trade-off.
