TR#: | CIS9908 |

Class: | CIS |

Title: | A Computational Model for the Surface--Surface and Surface--Curve Bisector Surfaces |

Authors: | Gershon Elber and Myung Soo Kim |

CIS9908.pdf | |

Abstract: | The bisector of two rational surfaces in R^3 is nonrational, in general. Moreover, in R^3, the bisector of a rational curve and a rational surface is also nonrational. Thus, the bisector surfaces in these two special cases must be approximated numerically. Unfortunately, these bisector surfaces are algebraic surfaces of very high degree; thus the numerical approximation is a non-trivial task. This paper suggests a new computational model for constructing the curve-surface and surface-surface bisectors. The curve-surface bisector problem is reformulated as a trivariate zero-set finding problem, whereas the surface-surface bisector problem is reduced to that of finding the common zero-set of two four-variate functions. |

Copyright | The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information |

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