Self-motions of Stewart--Gough platforms
Computer Aided Geometric Design
Parallel manipulators and Borel-Bricard problem
Computer Aided Geometric Design
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Journal of Computational and Applied Mathematics
Journal of Symbolic Computation
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
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We describe a method to approximate a segment of the intersection curve of two implicitly defined surfaces by a rational parametric curve. Starting from an initial solution, the method applies predictor and corrector steps in order to obtain the result. Based on a preconditioning of the two given surfaces, the corrector step is formulated as an optimization problem, where the objective function approximates the integral of the squared Euclidean distance of the curve to the intersection curve. An SQP-type method is used to solve the optimization problem numerically. Two different predictor steps, which are based on simple extrapolation and on a differential equation, are formulated. Error bounds are needed in order to certify the accuracy of the result. In the case of the intersection of two algebraic surfaces, we show how to bound the Hausdorff distance between the intersection curve (an algebraic space curve) and its rational approximation.