scholarly journals Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

2021 ◽  
Vol 11 (3) ◽  
pp. 1321
Author(s):  
De-Yun Zhong ◽  
Li-Guan Wang ◽  
Jin-Miao Wang
Keyword(s):  
Surface Reconstruction ◽  
Experimental Results ◽  
Implicit Surfaces ◽  
Difference Operators ◽  
Implicit Function ◽  
Implicit Surface ◽  
Combination Rules ◽  
Ore Bodies ◽  
Pruning Strategy ◽  
Implicit Modeling

In this paper, we introduce combination constraints for modeling ore bodies based on multiple implicit fields interpolation. The basic idea of the method is to define a multi-labeled implicit function that combines different sub-implicit fields by the combination operations, including intersection, union and difference operators. The contribution of this paper resides in the application of combination of more general implicit fields with combination rules for the implicit modeling of ore bodies, such that the geologist can construct constraints honoring geological relationships more flexibly. To improve the efficiency of implicit surface reconstruction, a pruning strategy is used to avoid unnecessary calculations based on the hierarchical bounding box of the operation tree. Different RBF-based methods are utilized to study the implicit modeling cases of ore bodies. The experimental results of several datasets show that the combination constraints are useful to reconstruct implicit surfaces for ore bodies with mineralization rules involving multiple fields.

A Novel Surface Reconstruction Framework from Point Clouds without Normal

2012 ◽  
Vol 151 ◽  
pp. 711-715
Author(s):  
Yan Ju Liu ◽  
Yong De Zhang ◽  
Ji Xiong Jiang
Keyword(s):  
Surface Reconstruction ◽  
Point Clouds ◽  
Experimental Results ◽  
Implicit Function ◽  
Entire Surface ◽  
Structure Generation ◽  
Lack Of Information

In this paper, we proposed a novel surface reconstruction framework from point clouds without normal. The proposed method involves three processes: partition of unit, which divide the point clouds into sub-domains using octree structure, generation of the sub-surface, which fit the sub-surface by implicit function in each sub-domain, the normal alignment, which compute normal of sub-surface and inference the global normal of surface by iteratively propagate algorithm. During the last process, sub-surfaces are blended to form entire surface reconstruction. The method is suitable to reconstruct surface with lack of information. The experimental results demonstrate that the method is effective in surface reconstruction.

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.

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.

scholarly journals Regularized implicit surface reconstruction from points and normals

2007 ◽  
Vol 13 (4) ◽  
pp. 7-16
Author(s):  
B. Mederos ◽  
M. Lage ◽  
S. Arouca ◽  
F. Petronetto ◽  
L. Velho ◽  
...  
Keyword(s):  
Surface Reconstruction ◽  
Implicit Surface

Implicit surface reconstruction with radial basis functions via PDEs

2020 ◽  
Vol 110 ◽  
pp. 95-103 ◽  
Author(s):  
Xiao-Yan Liu ◽  
Hui Wang ◽  
C.S. Chen ◽  
Qing Wang ◽  
Xiaoshuang Zhou ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Radial Basis

Implicit surface reconstruction for reverse engineering

1998 ◽  
Author(s):  
Y. He ◽  
Peihua Gu ◽  
K. Ferguson ◽  
J. Ronsky ◽  
R. Zernicke
Keyword(s):  
Reverse Engineering ◽  
Surface Reconstruction ◽  
Implicit Surface
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