Geometric Properties of Bisector Surfaces |
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| Affiliation: | 1. Université Paris-Saclay, ENS Paris-Saclay, LURPA, 91190 Gif-sur-Yvette, France;2. TOPSOLID, 7 rue du Bois Sauvage, 91055 Evry, France;1. Institute of Mathematics, Poznań University of Technology, Poland;2. Institute of Mathematics, Faculty of Science, P. J. Šafárik University, Košice, Slovakia;3. Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Poland;4. Institute of Plant Genetics, Polish Academy of Sciences, Poznań, Poland;1. Department of Urology, Xiangya Hospital, Central South University, Hunan, PR China;2. Department of Oncology, Xiangya Hospital, Central South University, Hunan, PR China |
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| Abstract: | This paper studies algebraic and geometric properties of curve–curve, curve–surface, and surface–surface bisectors. The computation is in general difficult since the bisector is determined by solving a system of nonlinear equations. Geometric considerations will help us to determine several distinguished curve and surface pairs which possess elementary computable bisectors. Emphasis is on low-degree rational curves and surfaces, since they are of particular interest in surface modeling. |
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