Bounding volume for 3d graphic primitives

Abstract

A method of and system for testing a graphic primitive for trivial acceptance or rejection. An initial bounding volume, such as a rectangular parallelepiped, is defined by the graphic primitive's maximum and minimum x, y, and z coordinates in an initial coordinate system. A first bounding volume is then defined by the graphic primitive's maximum and minimum x′, y′, and z′ coordinates in a first coordinate system, where the first coordinate system is transformed with respect to the initial coordinate system. Preferably this transformation comprises a 45° rotation about a common axis such as the z-axis. The initial bounding volume and the first bounding volume are then intersected to form a modified bounding volume. The vertices of the modified bounding volume are then available for use in determining whether the graphic primitive may be trivially rejected or accepted within a specified viewing volume. In one embodiment, the method further includes defining and using a second modified bounding volume by intersecting the initial bounding volume with a second bounding volume defined by the graphic primitive's maximum and minimum x″, y″, and z″ values in a second coordinate system. The second coordinate system is determined by applying a second transformation, such as a 45° rotation about a common y-axis, with respect to the initial coordinate system. Still further, the invention may include defining and using a third modified bounding volume by intersecting the initial bounding volume with a third bounding volume defined by the graphic primitive's maximum and minimum x′″, y′″, and z′″ values in a third coordinate system determined by applying a third transformation, such as a 45° rotation about a common x-axis with respect to the initial coordinates system.