Analysis of validated error bounds of surface-to-surface intersection

Authors:
K. H. Ko;N. M. Patrikalakis
Affiliations:
Modeling and Simulation Laboratory, Room 202, Department of Mechatronics, Gwangju Institute of Science and Technology, Gwangju, 500-712, Republic of Korea;Design Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Computer-Aided Design
Year:
2008

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Abstract

In this paper, we address the problem of computing the error bounds of surface-to-surface intersection and propose a novel procedure to reduce them. We formulate the surface-to-surface intersection problem as solving a system of ordinary differential equations and using the validated ODE solver we compute the validated a priori enclosures of an intersection curve, in which the existence and the uniqueness of a solution are guaranteed. Then we use straight line enclosures to reduce the size of the a priori enclosures. These reduced enclosures are again enclosed by bounding curves, which can be used as the reduced error bounds of the intersection curve. We demonstrate our method with tangential and transversal intersections.