Pyramids That Bound Surface Patches

✍ Scribed by Thomas W. Sederberg; Alan K. Zundel

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 408 KB
• Volume: 58
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1996.0005

✦ Synopsis

is a curve bounding wedge in the sense that if the wedge vertex is translated to any point on the curve, the curve This paper describes how to construct a pyramid which has the property that if its vertex is translated to any point on a will lie entirely outside of the wedge except for the point given rational Be ´zier surface patch with positive weights, the at the vertex (Fig. 3).

patch will lie completely outside the pyramid. This pyramid

Reference [2] proposes two surface bounding cones, C 1 can facilitate operations such as loop detection in surface interand C 2 . Analogous to the 2-D curve bounding wedge, C 1 section. Earlier literature asserted that the complement of a is defined as having the same central axis as the normal normal bounding cone or pyramid is a surface bounding cone bounding cone and with half angle complementary to that or pyramid. This paper proves that the reverse of this statement of the normal bounding cone. Hohmeyer conceived of an is always true, but that the statement itself is true only under example which points out that C 1 is only valid under certain certain conditions spelled out in the paper.