New Torus Bounding for Line-Torus Intersection

Abstract

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 paper a new formulation of the line-torus intersection problem is given and new specification of the bounding volume for a torus is given. The presented approach is based on an idea of a line intersection with an envelope of rotating sphere that forms a torus. Due to this approach new bounding volume can be formulated which is more effective as it enables to detect cases when the line passes the “hole” of a torus.