Self-Intersection Problems and Approximate Implicitization
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.
KeywordsParameter Plane Implicit Representation NURBS Curve NURBS Surface Algebraic Degree
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