On the curvature of curves and surfaces defined by normalforms
Computer Aided Geometric Design
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Shape Interrogation for Computer Aided Design and Manufacturing
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Ridges and Ravines on Implicit Surfaces
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Curve interpolation based on the canonical arc length parametrization
Computer-Aided Design
Curvature of singular Bézier curves and surfaces
Computer Aided Geometric Design
Intersection curves of hypersurfaces in R4
Computer Aided Geometric Design
Affine-invariant curvature estimators for implicit surfaces
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GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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Graphical Models
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MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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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.