Linear perturbation methods for topologically consistent representations of free-form surface intersections

Authors:
Xiaowen Song;Thomas W. Sederberg;Jianmin Zheng;Rida T. Farouki;Joel Hass
Affiliations:
Department of Computer Science, Brigham Young University, Provo, UT;Department of Computer Science, Brigham Young University, Provo, UT;Department of Computer Science, Brigham Young University, Provo, UT;Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA;Department of Mathematics, University of California, Davis, CA
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

By applying displacement maps to slightly perturb two free-form surfaces, one can ensure exact agreement between the images in R3 of parameter-domain approximations to their curve of intersection. Thus, at the expense of slightly altering the surfaces in the vicinity of their intersection, a perfect matching of the surface trimming curves is guaranteed. This exact agreement of contiguous trimmed surfaces is essential to achieving topologically consistent solid model constructions through Boolean operations, and has a profound impact on the efficiency and reliability of applications such as meshing, rendering, and computing volumetric properties. Moreover, the control point perturbations require only the solution of a linear system for their determination. The basic principles of this approach to topologically consistent surface trimming curves are described, and example results from the implementation of a simple instance of the method are presented.