Efficiently parallelised algorithm to find isoptic surface of polyhedral meshes

Abstract

The isoptic surface of a three-dimensional shape is defined in [1] as the generalization of isoptics of curves. The authors of the paper also presented an algorithm to determine isoptic surfaces of convex meshes. In [9] new searching algorithms are provided to find points of the isoptic surface of a triangulated model in E 3 . The new algorithms work for concave shapes as well.In this paper, we present a faster, simpler, and efficiently parallelised version of the algorithm of [9] that can be used to search for the points of the isoptic surface of a given closed polyhedral mesh, taking advantage of the computing capabilities of the high-performance graphics cards and using the benefits of nested parallelism. For the simultaneous computations, the NVIDIA's Compute Unified Device Architecture (CUDA) was used. Our experiments show speedups up to 100 times using the new parallel algorithm.