GPU-Parallel Constant-Time Limit Evaluation of Catmull-Clark Solids

Abstract

Subdivision solids, such as Catmull-Clark (CC) solids, are versatile volumetric representation schemes that can be employed for geometric modeling, physically based simulation, and multi-material additive manufacturing. With volumetric limit evaluation still being the performance bottleneck for these applications, we present a massively parallel approach to Altenhofen et al.'s constant-time limit evaluation method for CC solids. Our algorithm exploits the computational power of modern GPUs, while maintaining the mathematical concepts of Altenhofen et al.'s method. Distributing the computations for a single cell across multiple streaming multiprocessors (SMs) increases the utilization of the GPU's resources compared to straightforward parallelization. Specialized compute kernels for different topological configurations optimize shared memory usage and memory access. Our hybrid approach dynamically chooses the best kernel based on the topology and the evaluation parameters, resulting in speedups of between 5.75x and 61.58x compared to a CPU-parallel implementation of Altenhofen et al.'s method.