Pyramids That Bound Surface Patches

This paper describes how to construct a pyramid which has the property that if its vertex is translated to any point on a given rational Bézier surface patch with positive weights, the patch will lie completely outside the pyramid. This pyramid can facilitate operations such as loop detection in sur...

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Bibliographic Details
Published inGraphical models and image processing Vol. 58; no. 1; pp. 75 - 81
Main Authors Sederberg, Thomas W., Zundel, Alan K.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.01.1996
Academic Press
Subjects
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Pattern recognition. Digital image processing. Computational geometry
Pyramidal shape
Visibility
Pattern recognition
Bézier curve
Patch
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Summary:This paper describes how to construct a pyramid which has the property that if its vertex is translated to any point on a given rational Bézier surface patch with positive weights, the patch will lie completely outside the pyramid. This pyramid can facilitate operations such as loop detection in surface intersection. Earlier literature asserted that the complement of a normal bounding cone or pyramid is a surface bounding cone or pyramid. This paper proves that the reverse of this statement is always true, but that the statement itself is true only under certain conditions spelled out in the paper.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1077-3169
1090-2481
DOI:10.1006/gmip.1996.0005