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• W2003805315 abstract "Two numerical algorithms for computing starting points on the curve of intersection between two parametric surfaces are presented. The problem of determining intersection curves between two surfaces is analytically formulated by parametrizing inequality constraints into equality constraints and augmenting the constraint function. The first method uses an iterative optimization formulation and an iterative conjugate gradient algorithm to minimize a function comprising the vector of coordinates and a weighted constraint term. The second method uses the Moore-Penrose pseudo inverse of the constraint function to determine a starting point. Numerical examples are presented to validate both methods. Both methods require an initial point on one of the surfaces. Numerical examples illustrating the validity of the presented methods are discussed. The local versus the global views of the intersection problem in terms of iterative and recursive subdivision methods are addressed. Difficulties in determining more than one point are also illustrated using examples. The two algorithms are compared by studying their computational complexity. The Moore-Penrose inverse method has showed superior efficiency in the computational complexity, number of iterations needed, and time for conversion to a starting point. It is also shown that the Moore-Penrose inverse converges to a starting point in cases where the iterative optimization method does not." @default.
• W2003805315 created "2016-06-24" @default.
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• W2003805315 date "1997-01-01" @default.
• W2003805315 modified "2023-09-26" @default.
• W2003805315 title "On the determination of starting points for parametric surface intersections" @default.
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• W2003805315 doi "https://doi.org/10.1016/s0010-4485(96)00046-2" @default.
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