Title: A tracing method for parametric Bezier triangular surface/plane intersection

Authors: R. Sharma, O.P. Sha

Addresses: Department of Ocean Engineering and Naval Architecture, Design Laboratory, Indian Institute of Technology, Kharagpur – 721 302, India. ' Department of Ocean Engineering and Naval Architecture, Design Laboratory, Indian Institute of Technology, Kharagpur – 721 302, India

Abstract: This paper presents, in the general setting of derivational continuities, a surface/plane intersection algorithm based on a tracing method in which the intersection curves are traced out in the direction of tangent vectors at intersection points for parametric Bezier triangular surface over triangular domain. The intersection curves are given by ordered pairs of surface domain points, and are represented by their piece-wise polynomial approximations. The aim is to obtain the smallest number of structured and ordered points that correctly represent the topology of the true intersection curves without any sorting required. The intersection curve is plotted by fitting an interpolatory cubic spline, and its refinement may include adding or deleting points. The method has been used to compute different planar sections for different derivationally continuous surfaces.

Keywords: Bezier rational triangular patches; rational-triangular parametric surfaces; surface-plane intersection; surface directional tangent vectors; topological sub-division; intersection curves; interpolatory cubic splines.

DOI: 10.1504/IJCAT.2007.014557

International Journal of Computer Applications in Technology, 2007 Vol.28 No.4, pp.240 - 253

Published online: 16 Jul 2007 *

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