Publication Detail

Surface-to-surface intersections for geometric modeling.

P V. Prakash, Nicholas M. Patrikalakis
85 pp.
MITSG 88-8

This work addresses the problem of intersecting algebraic surfaces with piecewise continuous rational polynomial parametric surface patches, such as B-splines. Such problems can be reduced to tracing a planar algebraic curve within a rectangular domain. The method proposed combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable solution procedure. This representation transforms the problem of intersection of two curved polynomial surfaces to the intersection of a Bezier surface with a plane. The method has been successfully tested in tracing complex algebraic curves and in solving actual intersection problems with diverse features.

type: Technical reports

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