Publication
A projectively invariant intersection test for polyhedra
Journal Article (2002)
Journal
The Visual Computer
Pages
405-414
Volume
18
Number
7
Doc link
http://dx.doi.org/10.1007/s003710100158
File
Authors
Projects associated
Abstract
Although intersection relations are projectively invariant, most existing intersection detection tests for arbitrary polyhedra can give different results before and after a nonsingular arbitrary projective transformation of the polyhedra under test. This paper presents a projectively invariant intersection test for general polyhedra whose only numerical part is the computation of 4×4 determinants of homogeneous vertex coordinates. Degeneracies are resolved using a technique of symbolic infinitesimals which also reduces to the computation of 4×4 determinants. This greatly simplifies the implementation of the test in hardware. Moreover, its projective invariance permits applying it at any point in the graphics pipeline. Since no auxiliary geometric entities need to be computed, the presented test can be concisely expressed as a Boolean formula, instead of a procedure.
Categories
robots.
Author keywords
intersection detection, projective invariance, degenerate configurations, 4×4 determinant method
Scientific reference
F. Thomas and C. Torras. A projectively invariant intersection test for polyhedra. The Visual Computer, 18(7): 405-414, 2002.
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