scholarly journals Concentrated Curvature for Mean Curvature Estimation in Triangulated Surfaces

2012 ◽  
pp. 79-87 ◽  
Author(s):  
Mohammed Mostefa Mesmoudi ◽  
Leila De Floriani ◽  
Paola Magillo
Keyword(s):  
Mean Curvature ◽  
Triangulated Surfaces ◽  
Curvature Estimation

scholarly journals A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces

2019 ◽  
Vol 12 (1) ◽  
pp. 70-78
Author(s):  
Sudip Kumar Das ◽  
Mirza Cenanovic ◽  
Junfeng Zhang
Keyword(s):  
Mean Curvature ◽  
Beltrami Operator ◽  
Force Balance ◽  
Normal Vector ◽  
Triangulated Surface ◽  
Balance Principle ◽  
Alternative Expression ◽  
Triangulated Surfaces ◽  
The Mean ◽  
Mesh Structures

In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.

Contour Representation by Clustering Curvatures of the 3D Objects

2009 ◽  
Vol 147-149 ◽  
pp. 633-638
Author(s):  
Arūnas Lipnickas ◽  
Vidas Raudonis
Keyword(s):  
Free Form ◽  
Distance Measurements ◽  
3D Object ◽  
Human Foot ◽  
3D Objects ◽  
Large Size ◽  
Contour Representation ◽  
Triangulated Surfaces ◽  
Curvature Estimation ◽  
Free Form Surfaces

The purpose of this work is to segment large size triangulated surfaces and the contours extraction of the 3D object by the use of the object curvature value. The curvatures values allow categorizing the type of the local surface of the 3D object. In present work the curvature was estimated for the free-form surfaces obtained by the 3D range scanner. A free-form surface is the surface such that the surface normal is defined and continuous everywhere, except at sharp corners and edges [2, 5]. Two types of distance measurements functions based on Euclidian distance, bounded box and topology of surface were used for the curvature estimation. Clustering technique has been involved to cluster the values of the curvature for 3D object contour representation. The described technique was applied to the 3D objects with free-form surfaces such as the human foot and cube.

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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