期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 22, 期 7, 页码 632-658出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cagd.2005.06.005
关键词
curvature; torsion; Gaussian curvature; mean curvature; gradient; Hessian; implicit curves; implicit surface
Curvature formulas for implicit curves and surfaces are derived from the classical curvature formulas in Differential Geometry for parametric curves and surfaces. These closed formulas include curvature for implicit planar curves, curvature and torsion for implicit space curves, and mean and Gaussian curvature for implicit surfaces. Some extensions of these curvature formulas to higher dimensions are also provided. (c) 2005 Elsevier B.V. All rights reserved.
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