caa a22 4500 463203135 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00200-006-0031-8 doi (NATIONALLICENCE)springer-10.1007/s00200-006-0031-8 A predictor-corrector-type technique for the approximate parameterization of intersection curves [Elektronische Daten] [Bert Jüttler, Pavel Chalmovianský] 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. Springer-Verlag, 2006 Jüttler Bert Institute of Applied Geometry, Johannes Kepler University, Linz, Austria aut Chalmovianský Pavel Katedra algebry, geometrie a didaktiky matematiky FMFI UK, Bratislava, Slovakia aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 151-168 0938-1279 18:1-2<151 2007 18 200 https://doi.org/10.1007/s00200-006-0031-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-006-0031-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jüttler Bert Institute of Applied Geometry, Johannes Kepler University, Linz, Austria aut NATIONALLICENCE 700 1- Chalmovianský Pavel Katedra algebry, geometrie a didaktiky matematiky FMFI UK, Bratislava, Slovakia aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 151-168 0938-1279 18:1-2<151 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer