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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Thomassen, J.B. (2005). Self-Intersection Problems and Approximate Implicitization. In: Computational Methods for Algebraic Spline Surfaces. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27157-0_11
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DOI: https://doi.org/10.1007/3-540-27157-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23274-2
Online ISBN: 978-3-540-27157-4
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