Curvature formulas for implicit curves and surfaces

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 Gaussia...

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Bibliographic Details
Published inComputer aided geometric design Vol. 22; no. 7; pp. 632 - 658
Main Author Goldman, Ron
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 01.10.2005
Elsevier
Subjects
Applied sciences
Computer aided design
Computer science; control theory; systems
Curvature
Exact sciences and technology
Gaussian curvature
Gradient
Hessian
Implicit curves
Implicit surface
Mean curvature
Mechanical engineering. Machine design
Software
Torsion
Implicit surface
Gradient
Gaussian curvature
Curvature
Torsion
Mean curvature
Hessian
Implicit curves
Differential geometry
Gaussian process
Parametric surface
Implicit theory
Hessian matrices
Computer aided design
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2005.06.005