Torus/Sphere Intersection Based on a Configuration Space Approach

Torus/Sphere Intersection Based on a Configuration Space Approach1

This paper presents an efficient and robust geometric algorithm that classifies and detects all possible types of torus/sphere intersections, including all degenerate conic sections (circles) and singular intersections. Given a torus and a sphere, we treat one surface as an obstacle and the other surface as the envelope surface of a moving ball. In this case, the Configuration space (C-space) o...

A Simple Algorithm for Torus/sphere Intersection

Based on a Connguration space approach, the authors recently suggested an eecient and robust algorithm that computes the intersection curve of a torus and a sphere 3]. This paper presents a simpler algorithm, while utilizing the symmetry in the relative connguration of a torus and a sphere.

A New Torus Bounding for Line-Torus Intersection

Intersection algorithms are very important in computation of geometrical problems. An intersection of a line with linear or quadratic surfaces is well done, however a line intersection with other surfaces is more complex and time consuming. In this case the object is usually closed into a simple bounding volume to speed up the cases when the given line cannot intersect the given object. In this...

Line-Torus Intersection for Ray Tracing: Alternative Formulations

Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are more complex and time consuming. In this case the object is usually closed into a simple bounding volume to speed up the cases when the given line cannot in...

Crime Prevention in Urban Design: towards Space Syntax Approach as a Quantitative Analytic Modeling of Qualitative Issue of Security (Based on Spatial Configuration)