AlSub: Fully Parallel Subdivision for Modeling and Rendering.

Mesh subdivision is a key geometric modeling task which forges smooth, supple, eye-pleasing surfaces out of coarse polygonal outlines. Since its rise to mainstream around the turn of the century, subdivision has become an unavoidable production tool. With industrial demands in sight, there has been a steady effort for developing faster and more efficient subdivision implementations. Despite the tremendous parallelism potential of subdivision algorithms, state-of-the-art implementations are only partially parallel as they are riddled by intermediate serial steps and therefore fail to unleash the compute power of massively parallel devices such as graphics processing units (GPUs). To fully parallelize the subdivision process, we discard traditional linked list data structures in favor of a sparse matrix linear algebra formalism. Subdivision algorithms are written in the language of linear algebra with customized operators which readily demonstrate a performance edge over existing approaches. To further increase performance, we automatically identify critical matrix operations and replace them by specialized, heavily tuned GPU kernels. To substantiate the versatility of our approach we apply it to $sqrt{3}$, Loop and Catmull-Clark subdivision schemes and show support for adaptive subdivision, semi-sharp creases, and a split evaluation scheme that separates topology and topological changes from positional updates. Our results indicate substantial performance gains over the state-of-the-art and current industry standard.