gGMED: Towards GPU Accelerated Geometric Modeling Evaluation and Derivative Processes

Geometric modeling algorithms serve as the fundamental computation of CAD/CAM software in the field of computer graphics. The evaluation and derivative processes, being an essential component of geometric modeling algorithms, significantly impact their overall performance. However, when dealing with scenarios involving high-precision models or large-scale datasets, the lack of parallel acceleration for geometric modeling computation results in prolonged computation time and low computation efficiency, hindering the satisfactory experience of user interaction. Although the massive parallelism of GPUs has been proved with successful performance acceleration in various application fields, it has not been effectively utilized for accelerating geometric modeling algorithms. In this paper, we propose gGMED, a GPU-based approach specifically designed for accelerating the evaluation and derivative processes in geometric modeling. To leverage the massive parallel capability of GPU, our approach provides several optimizations such as data reuse, bank conflict avoidance, and pipeline execution, for effectively improving the performance of evaluation and derivative processes. The experiment results on representative GPUs and various NURBS models demonstrate that our approach can achieve up to 10.18 \(\times \) and 34.56 \(\times \) performance speedup in end-to-end process and kernel computation respectively, compared to the state-of-the-art geometric modeling libraries.