Massively Parallel Approximation of Irregular Triangular Meshes of Arbitrary Topology with Smooth Parametric Surfaces

Abstract This paper describes a parallel implementation of a previously developed mathematical model intended for the approximation of 3D triangular meshes with smooth surfaces yielding first order geometric continuity G 1 . This represents a novel application of SIMD architectures to the approximation of irregular meshes. Previous related works have focused on the approximation of rectangular meshes using tensor-product approximants, such as B-splines, that suit the regular structure of most parallel architectures. A parallel implementation of the proposed surface model at three degrees of granularity shows that a coarse grain scheme yields maximum performance when each control triangle is approximated by a single processor avoiding inter-processor communication. The data distribution necessary to attain an independent task-farm topology is studied. The different algorithms have been implemented using a data-parallel model and tested on two Connection Machine 200 parallel computers with 4 and 16 K processors, respectively. The algorithms achieve efficiencies close to a 100% and scale linearly in the number of processors.