Geometry Processing Problems Using the Total Variation of the Normal Vector Field

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Ronny Bergmann ◽  
Marc Herrmann ◽  
Roland Herzog ◽  
Stephan Schmidt ◽  
José Vidal-Núñez
Keyword(s):  
Vector Field ◽  
Total Variation ◽  
Normal Vector ◽  
Geometry Processing ◽  
Normal Vector Field

scholarly journals Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems

2020 ◽  
Vol 36 (5) ◽  
pp. 054003 ◽  
Author(s):  
Ronny Bergmann ◽  
Marc Herrmann ◽  
Roland Herzog ◽  
Stephan Schmidt ◽  
José Vidal-Núñez
Keyword(s):  
Vector Field ◽  
Inverse Problems ◽  
Total Variation ◽  
Normal Vector ◽  
Shape Prior ◽  
Normal Vector Field ◽  
Geometric Inverse Problems

scholarly journals Total variation of the normal vector field as shape prior

2020 ◽  
Vol 36 (5) ◽  
pp. 054004
Author(s):  
Ronny Bergmann ◽  
Marc Herrmann ◽  
Roland Herzog ◽  
Stephan Schmidt ◽  
José Vidal-Núñez
Keyword(s):  
Vector Field ◽  
Total Variation ◽  
Normal Vector ◽  
Shape Prior ◽  
Normal Vector Field

scholarly journals Constant angle spacelike surface in de Sitter space S₁³

2017 ◽  
Vol 35 (3) ◽  
pp. 79-93
Author(s):  
Tugba Mert ◽  
Baki Karlıga
Keyword(s):  
Vector Field ◽  
De Sitter Space ◽  
Normal Vector ◽  
Spacelike Surface ◽  
De Sitter ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Constant Angle ◽  
Unit Normal Vector Field ◽  
Unit Normal

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

scholarly journals Extension of the unit normal vector field from a hypersurface

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Roland Duduchava ◽  
Eugene Shargorodsky ◽  
George Tephnadze
Keyword(s):  
Vector Field ◽  
Existence And Uniqueness ◽  
Elementary Proof ◽  
Gradient Field ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Unit Normal Vector Field ◽  
Outer Unit ◽  
Unit Normal

AbstractIn many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

scholarly journals An integral formula for compact hypersurfaces in a Euclidean space and its applications

1992 ◽  
Vol 34 (3) ◽  
pp. 309-311 ◽  
Author(s):  
Sharief Deshmukh
Keyword(s):  
Vector Field ◽  
Euclidean Space ◽  
Smooth Function ◽  
Support Function ◽  
Integral Formula ◽  
Position Vector ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Unit Normal Vector Field

Let M be a compact hypersurface in a Euclidena space ℝn+1. The support function p of M is the component of the position vector field of Min ℝn+1 along the unit normal vector field to M, which is a smooth function defined on M. Let S be the scalar curvature of M. The object of the present paper is to prove the following theorems.

scholarly journals On compact minimal hypersurfaces in a sphere with constant scalar curvature

1980 ◽  
Vol 78 ◽  
pp. 177-188 ◽  
Author(s):  
Naoya Doi
Keyword(s):  
Vector Field ◽  
Constant Scalar Curvature ◽  
Arbitrary Point ◽  
Second Fundamental Form ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Covariant Differentiation ◽  
Normal Vector Field ◽  
Unit Normal Vector Field ◽  
Unit Normal

Let M be an n-dimensional hypersurface immersed in the (n + 1)-dimensional unit sphere Sn+1 with the standard metric by an immersion f. We denote by A the second fundamental form of the immersion / which is considered as a symmetric linear transformation of each tangent space TXM, i.e. for an arbitrary point x of M and the unit normal vector field ξ defined in a neighborhood of x, A is given by where is the covariant differentiation in Sn+i and Thus, A depends on the orientation of the unit normal vector field ξ and, in general, it is locally defined on M.

scholarly journals Piecewise smooth reconstruction of normal vector field on digital data

2016 ◽  
Vol 35 (7) ◽  
pp. 157-167 ◽  
Author(s):  
David Coeurjolly ◽  
Marion Foare ◽  
Pierre Gueth ◽  
Jacques-Olivier Lachaud
Keyword(s):  
Vector Field ◽  
Piecewise Smooth ◽  
Digital Data ◽  
Normal Vector ◽  
Normal Vector Field
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