Real-time smooth surface construction on the graphics processing unit

Increased realism in interactive graphics and gaming requires complex smooth surfaces to be rendered at ever higher frame rates. In particular, representations used to model surfaces offline, such as spline and subdivision surfaces, have to be modified or reorganized to allow for efficient usage of the graphics processing unit and its SIMD (Single Instruction, Multiple Data) parallelism. This dissertation presents a novel algorithm for converting quad meshes on the GPU to smooth, water-tight surfaces at the highest speed documented so far. The conversion reproduces bi-cubic splines wherever possible and closely mimics the shape of the Catmull-Clark subdivision surface by c-patches where a vertex has a valence different from 4. The smooth surface is piecewise polynomial and has well-defined normals everywhere.