Sampling-Efficient Mesh Parametrization

Texture-mapping is a traditional graphics technique that has several applications in computer graphics rendering. It uses surface signals to achieve a variety of rendering effects, including color mapping, bump mapping (where surface normals are the signal), displacement mapping (geometry), and self-shadowing. While these rendering effects can also be computed in vertex shaders, texturemapping is advantageous because storing and processing texture images is generally more efficient than refining the geometry to represent the detailed signal at the vertices of a dense mesh. To allow texture-mapping, a surface must be parametrized onto a texture domain by assigning texture coordinates to its vertices. This thesis presents newmetrics and algorithms to parametrize a 3D surface onto the 2D domain for the purpose of texture-mapping. The main contributions of this thesis are two ”stretchbased” parametrization algorithms. As opposed to previous methods, our new geometric-stretch metric directly minimizes geometry undersampling in the texture domain. Our novel signal-stretch metric constructs a parametrization that is specialized to store a given surface signal while attempting to minimize a measure of signal approximation error. This latter metric allocates more texture samples to