Mesh Fusion Based on Variational Implicit Surfaces

2005 ◽  
Vol 16 (11) ◽  
pp. 2000 ◽  
Author(s):  
Hua-Gen WAN
Keyword(s):  
Implicit Surfaces ◽  
Mesh Fusion

Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features

2002 ◽  
Vol 2 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Yutaka Ohtake ◽  
Alexander G. Belyaev
Keyword(s):  
Adaptive Mesh ◽  
Implicit Surfaces ◽  
Marching Cubes ◽  
Triangle Mesh ◽  
Implicit Surface ◽  
Weighted Vertex ◽  
Visualization Toolkit ◽  
Object Oriented Approach ◽  
Speed And Accuracy ◽  
Dual Mesh

A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard Marching Cubes mesh [Lorensen, W.E., and Cline, H.E., 1987, Computer Graphics (Proceedings of SIGGRAPH ’87), 21(3), pp. 163–169] (in our experiments we use VTK Marching Cubes [Schroeder, W., Martin, K., and Lorensen, W., 1998, The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics, Prentice Hall]). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that “double dual” mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.

Adaptive Sampling of Implicit Surfaces for Interactive Modelling and Animation

1996 ◽  
Vol 15 (5) ◽  
pp. 319-325 ◽  
Author(s):  
Mathieu Desbrun ◽  
Nicolas Tsingos ◽  
Marie-Paule Gascuel
Keyword(s):  
Adaptive Sampling ◽  
Implicit Surfaces ◽  
Interactive Modelling

A Torus Patch Approximation Approach for Point Projection on Implicit Surfaces

2011 ◽  
Vol 346 ◽  
pp. 259-265
Author(s):  
Xiao Ming Liu ◽  
Lei Yang ◽  
Qiang Hu ◽  
Jun Hai Yong
Keyword(s):  
Iterative Algorithm ◽  
Geometric Modeling ◽  
Second Order ◽  
Implicit Surfaces ◽  
Implicit Surface ◽  
Approximation Approach ◽  
Initial Values ◽  
Point Projection

Point projection on an implicit surface is essential for the geometric modeling and graphics applications of it. This paper presents a method for computing the principle curvatures and principle directions of an implicit surface. Using the principle curvatures and principle directions, we construct a torus patch to approximate the implicit surface locally. The torus patch is second order osculating to the implicit surface. By taking advantage of the approximation torus patch, this paper develops a second order geometric iterative algorithm for point projection on the implicit surface. Experiments illustrate the efficiency and less dependency on initial values of our algorithm.

Lines of curvature and umbilical points for implicit surfaces

2007 ◽  
Vol 24 (7) ◽  
pp. 395-409 ◽  
Author(s):  
Wujun Che ◽  
Jean-Claude Paul ◽  
Xiaopeng Zhang
Keyword(s):  
Implicit Surfaces ◽  
Lines Of Curvature ◽  
Umbilical Points

Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces

2008 ◽  
Vol 24 (1) ◽  
pp. 211-220 ◽  
Author(s):  
Nilanjan Chakraborty ◽  
Jufeng Peng ◽  
Srinivas Akella ◽  
John E. Mitchell
Keyword(s):  
Interior Point ◽  
Implicit Surfaces
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