Self-Intersection Problems and Approximate Implicitization

Jan B. Thomassen ()
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Jan B. Thomassen: University of Oslo, Centre of Mathematics for Applications

A chapter in Computational Methods for Algebraic Spline Surfaces, 2005, pp 155-170 from Springer

Abstract: Abstract We discuss how approximate implicit representations of parametric curves and surfaces may be used in algorithms for finding self-intersections. We first recall how approximate implicitization can be formulated as a linear algebra problem, which may be solved by an SVD. We then sketch a self-intersection algorithm, and discuss two important problems we are faced with in implementing this algorithm: What algebraic degree to choose for the approximate implicit representation, and — for surfaces — how to find self-intersection curves, as opposed to just points.

Keywords: Parameter Plane; Implicit Representation; NURBS Curve; NURBS Surface; Algebraic Degree (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27157-4_11

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DOI: 10.1007/3-540-27157-0_11

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