Results 221 to 230 of about 24,625 (256)
A Natural Programmable Metamaterial Controls 3D Curvature of Compound Eyes
Garrido-García J +7 more
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The Gaussian and mean curvature criteria for curvature continuity between surfaces
Computer Aided Geometric Design, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiuzi Ye
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Journal of Differential Equations, 2021
The authors study the Nirenberg problem on \(S^2\): Given a smooth function \(f:S^2\to\mathbb{R}\) which is positive somewhere, does there exist a metric \(g\) on \(S^2\) conformally equivalent to the standard metric \(g_0\) and having Gaussian curvature \(f\). The main theorem states that a solution exists under the following assumptions. (a) Critical
Xuezhang Chen +3 more
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The authors study the Nirenberg problem on \(S^2\): Given a smooth function \(f:S^2\to\mathbb{R}\) which is positive somewhere, does there exist a metric \(g\) on \(S^2\) conformally equivalent to the standard metric \(g_0\) and having Gaussian curvature \(f\). The main theorem states that a solution exists under the following assumptions. (a) Critical
Xuezhang Chen +3 more
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Mesh segmentation driven by Gaussian curvature
The Visual Computer, 2005Mesh parameterization is a fundamental problem in computer graphics as it allows for texture mapping and facilitates many mesh processing tasks. Although there exists a variety of good parameterization methods for meshes that are topologically equivalent to a disk, the segmentation into nicely parameterizable charts of higher genus meshes has been ...
Yamauchi, H. +3 more
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Gaussian Curvature, Mirrors, and Maps
The American Mathematical Monthly, 2012We present a method to optically measure the Gaussian curvature K of a surface and show how it can be used to establish a link between surfaces with constant K and area preserving maps between a sp...
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Graph Regularisation Using Gaussian Curvature
2009This paper describes a new approach for regularising triangulated graphs. We commence by embedding the graph onto a manifold using the heat-kernel embedding. Under the embedding, each first-order cycle of the graph becomes a triangle. Our aim is to use curvature information associated with the edges of the graph to effect regularisation.
Hewayda ElGhawalby, Edwin R. Hancock
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Gaussian-curvature-derived invariants for isometry
Science China Information Sciences, 2012Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs.
Weiguo Cao +4 more
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The Variational Origin of Motion by Gaussian Curvature
2007A variational formulation of an image analysis problem has the nice feature that it is often easier to predict the effect of minimizing a certain energy functional than to interpret the corresponding Euler-Lagrange equations. For example, the equations of motion for an active contour usually contains a mean curvature term, which we know will ...
Niels Chr. Overgaard, Jan Erik Solem
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Gaussian and mean curvatures of rational maps
Computer Aided Geometric Design, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Gaussian and Geodesic Curvature of Riemannian Manifolds
Canadian Journal of Mathematics, 1974In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:Here, c is a suitable constant depending on the dimension of M and Ω is an n-form (n = dim M) which may be calculated from its curvature tensor. W.
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