고성능 3D 지오메트리 연산을 위한 CORDIC 기반 오프라인 벡터회전 알고리즘 연구

Abstract

Recently, as 3D computer graphics applications are rapidly growing, many works for efficient 3D graphic processor are suggested. Those works are mostly focused on high performance. But, on applications, such as mobile and ubiquitous, we need to consider power and cost problems. COordinate Rotation DIgital Computer (CORDIC) is a well-known algorithm for calculating transcendental functions in a fast and efficient manner. Traditional hardware for calculating transcendental arithmetic operations are complex in nature, large in size and high power requirement. In contrast, CORDIC algorithm can calculate such complex arithmetic operations with hardware that require just adders and shifters. This has made CORDIC the algorithm of choice for Digital Signal Processing(DSP) computing engine. In a similar vein, we can expect better performance by applying CORDIC-type primitives to the main operations of 3D computer graphics. These CORDIC-type primitives are especially useful in Rigid Body Rotations, Interpolation of Orientations, etc. 2D CORDIC algorithm has 'N' elementary angles determined by required accuracy and performs rotations with that number of angles. With a high number of iterations we have a high accuracy and low performance while with a small number of iterations we have low accuracy and high performance. This problems exist in CORDIC-3D that was extended from 2D CORDIC. In this paper, we propose two off-line searching methods named ABS-3D and SCS-3D based on MVR-CORDIC, MSR-CORDIC algorithms to improve operating performance of CORDIC-3D algorithm. ABS-3D and SCS-3D are off-line methods, so we can use them for such applications like graphic movies that are not required dynamic inputs. From this methods, we can get the best sequence for the given inputs and reduce the number of iterations. Using ABS-3D and SCS-3D, we reduced 66.7%, 50% in the amount of operations, respectively.