Parametric splines on a hyperbolic paraboloid |
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Authors: | Fengfu Peng Xuli Han |
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Affiliation: | 1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China;2. School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410083, China |
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Abstract: | A hyperbolic paraboloid over a tetrahedron, constructed in B–B algebraic reduced form with its barycentric coordinate system, can be conveniently represented by two parameters. An arc on the surface, obtained by determining a type of function relation about the two parameters, has multiformity and consistent endpoint properties. We analyze the equivalence and boundedness of an arc’s curvature, and give a process of the proof. These arcs can be connected into an approximate G2-continuity space curve for fitting to a sequence of points with their advantages, and the curves, connected by this type arcs, are quite different from other algebraic and parametric splines. |
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Keywords: | Algebraic spline Hyperbolic paraboloid Barycentric coordinates Space curve Curve fitting |
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