Applying Vectorization Techniques for B-Spline Surface Evaluation

Abstract

In this paper we analyze relevance of vectorization for evaluation of Non-Uniform Rational B-Spline (NURBS) surfaces broadly used in Computer Aided Design (CAD) industry to describe free-form surfaces. NURBS evaluation (i.e. computation of surface 3D points and derivatives for the given u, v parameters) is a core component of numerous CAD algorithms and can have a significant performance impact. We achieved up to 5.8x speedup using Intel® Advanced Vector Extensions (Intel® AVX) instructions generated by Intel® C/C++ compiler, and up to 16x speedup including minor algorithmic refactoring, which demonstrates high potential offered by the vectorization technique to NURBS evaluation.

Introduction

Vectorization, or Single Instruction Multiple Data (SIMD), is a parallelization technique available on modern computer processors, which allows to apply the same computational operation (e.g. addition or multiplication) to several data elements at once. For example, on a processor with a 128 bit register a single addition operation can add 4 pairs of integers (each takes 32 bits) or 2 pairs of doubles (64 bits each). With the help of vectorization one can speed up computations due to reduced time required to process the same data sets. SIMD was introduced with Intel® Architecture Processors way back in 1990es, with MMX™ technology as its first generation.

In this paper we analyze relevance of vectorization for evaluation of NURBS surfaces [1]. NURBS is a standard method used in CAD industry to describe free-form surfaces, e.g. car bodies, ship hulls, aircraft wings, consumer products and so on. Examples of 3D models (from [3]) containing NURBS surfaces are given on Fig.1:

NURBS evaluation (i.e. a computation of surface 3D points and derivatives) is a core component of numerous CAD algorithms. For instance...

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