Method and system for computing the intersection of a bounding volume and screen-aligned plane

Abstract

Apparatus and methods are provided to perform volume rendering via composited texture-mapped convex polyhedra. This is accomplished by generating a sequence of z polygons defined by the intersection of a sequence of z planes parallel to the view plane with the convex polyhedron. The vertices of the convex polyhedron are numbered sequentially based on z-axis depth and this defines a sequence of slabs that are bounded by z planes intersecting the vertices. The edges of the convex polyhedron are numbered based on viewing the polyhedron along an axis from the closest vertex to the furthest vertex. A data structure maintains a list of active edges for each slab, where an edge is “active” if the edge intersects any z plane in the slab. Each vertex in the z polygon is defined by the intersection of an active edge with the z plane. The z polygon is rendered by connecting adjacent vertices, where the ordering is determined by the order of the active edges in the slab. Each edge of the z polygon can be rendered by performing only three multiplications, two additions, and one subtraction. These computationally efficient methods make volume rendering via texture mapping feasible.