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A Geometric Algorithm for Ray/Bézier Surfaces Intersection Using Quasi-Interpolating Control Net

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4 Author(s)
Fougerolle, Y.D. ; Le2i Lab., Univ. of Burgundy, France ; Lanquetin, S. ; Neveu, M. ; Lauthelier, T.

In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bezier patch. The novelty of our approach resides in the use of bounds of the difference between a Bezier patch and its quasi-interpolating control net. The quasi-interpolating polygon of a Bezier surface of arbitrary degree approximates the limit surface within a precision that is function of the second order difference of the control points, which allows for very simple projections and 2D intersection tests to determine sub-patches containing a potential intersection. Our algorithm is simple, because it only determines a 2D parametric interval containing the solution, and efficient because the quasi-interpolating polygon is directly computed, which avoids both minimum or maximum evaluations of the basis functions or complex envelops construction.

Published in:

Signal Image Technology and Internet Based Systems, 2008. SITIS '08. IEEE International Conference on

Date of Conference:

Nov. 30 2008-Dec. 3 2008

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