Study On GPU Accelerated Affine Arithmetic In Geometric Design

Affine arithmetic is a self-validated model in numerical computation, which has been widely applied in computer graphics and computer aided geometric design. For example, polygonization and rendering of implicit surfaces, and surface-surface intersection can be solved by affine arithmetic. However, because the serial algorithm of affine arithmetic should be performed recursively, the computation of affine arithmetic is inefficient, costing lots of time. For this reason, this thesis presents a GPU-based parallel algorithm for affine arithmetic, and applies it in polygonization and rendering of implicit surfaces, and surface-surface intersection. The main contribution of this thesis is as follows:1. We present an implicit surface polygonization and rendering algorithm based on GPU and affine arithmetic, resulting in smooth surface mesh..2. We propose a GPU accelerated B-spline surface-surface intersection algorithm with affine arithmetic, and an ordered intersection point extraction algorithm, to generate a B-spline intersection curve.The algorithms presented in this thesis are reliable and efficient, which greatly enhance the speed and reach the real-time response.