Preserving computational topology by subdivision of quadratic and cubic Bézier curves

Authors:
E. L. F. Moore;T. J. Peters;J. A. Roulier
Affiliations:
University of Connecticut, Department of Computer Science and Engineering, 06269-2155, Storrs, CT, USA;University of Connecticut, Department of Computer Science and Engineering, 06269-2155, Storrs, CT, USA;University of Connecticut, Department of Computer Science and Engineering, 06269-2155, Storrs, CT, USA
Venue:
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Year:
2007

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Abstract

Non-self-intersection is both a topological and a geometric property. It is known that non-self-intersecting regular Bézier curves have non-self-intersecting control polygons, after sufficiently many uniform subdivisions. Here a sufficient condition is given within ℝ3 for a non-self-intersecting, regular C 2 cubic Bézier curve to be ambient isotopic to its control polygon formed after sufficiently many subdivisions. The benefit of using the control polygon as an approximant for scientific visualization is presented in this paper.