Geometry processing : intersections, contours, and cubatures
R. E. Barnhill (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Displaying similar documents to “Curvature computations on surfaces in -space”
Geometry processing : intersections, contours, and cubatures
The PDE describing constant mean curvature surfaces
Hongyou Wu (2001)
Mathematica Bohemica
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We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.
On the Lines of Equidistance of a Family of Surfaces
C. E. Weatherburn (1930)
Journal de Mathématiques Pures et Appliquées
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Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...
Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature
Rafael López, Esma Demir (2014)
Open Mathematics
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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
A common characterization of the curvature axis for ruled surfaces and curves. (Eine gemeinsame Kennzeichnung der Krümmungsachse bei Regelflächen und Kurven.)
Benz, Walter (2000)
Beiträge zur Algebra und Geometrie
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Metric minimizing surfaces.
Petrunin, Anton (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Minimizing the squared mean curvature integral for surfaces in space forms.
Hsu, Lucas, Kusner, Rob, Sullivan, John (1992)
Experimental Mathematics
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Polynomial translation surfaces of Weingarten types in Euclidean 3-space
Dae Yoon (2010)
Open Mathematics
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In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.