Acceleration of Delaunay Refinement Algorithm by Geometric Hashing

2017 ◽  
Vol 22 (2) ◽  
pp. 110-117 ◽  
Author(s):  
Donguk Kim
Keyword(s):  
Delaunay Refinement ◽  
Geometric Hashing ◽  
Refinement Algorithm

scholarly journals PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES

2007 ◽  
Vol 17 (01) ◽  
pp. 1-30 ◽  
Author(s):  
DANIEL A. SPIELMAN ◽  
SHANG-HUA TENG ◽  
ALPER ÜNGÖR
Keyword(s):  
Mesh Size ◽  
Constant Factor ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Delaunay Refinement ◽  
Steiner Points ◽  
Input Domain ◽  
Set Of Points ◽  
Refinement Algorithm

We present a parallel Delaunay refinement algorithm for generating well-shaped meshes in both two and three dimensions. Like its sequential counterparts, the parallel algorithm iteratively improves the quality of a mesh by inserting new points, the Steiner points, into the input domain while maintaining the Delaunay triangulation. The Steiner points are carefully chosen from a set of candidates that includes the circumcenters of poorly-shaped triangular elements. We introduce a notion of independence among possible Steiner points that can be inserted simultaneously during Delaunay refinements and show that such a set of independent points can be constructed efficiently and that the number of parallel iterations is O( log 2Δ), where Δ is the spread of the input — the ratio of the longest to the shortest pairwise distances among input features. In addition, we show that the parallel insertion of these set of points can be realized by sequential Delaunay refinement algorithms such as by Ruppert's algorithm in two dimensions and Shewchuk's algorithm in three dimensions. Therefore, our parallel Delaunay refinement algorithm provides the same shape quality and mesh-size guarantees as these sequential algorithms. For generating quasi-uniform meshes, such as those produced by Chew's algorithms, the number of parallel iterations is in fact O( log Δ). To the best of our knowledge, our algorithm is the first provably polylog(Δ) time parallel Delaunay-refinement algorithm that generates well-shaped meshes of size within a constant factor of the best possible.

A 2-D Delaunay Refinement Algorithm Using an Initial Prerefinement From the Boundary Mesh

2008 ◽  
Vol 44 (6) ◽  
pp. 1418-1421 ◽  
Author(s):  
M.M. Sakamoto ◽  
J.R. Cardoso ◽  
J.M. Machado ◽  
M. Salles
Keyword(s):  
Delaunay Refinement ◽  
Refinement Algorithm

A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation

1995 ◽  
Vol 18 (3) ◽  
pp. 548-585 ◽  
Author(s):  
J. Ruppert
Keyword(s):  
Mesh Generation ◽  
Delaunay Refinement ◽  
Refinement Algorithm

CONSTRUCTING CONSTRAINED DELAUNAY TETRAHEDRALIZATIONS OF VOLUMES BOUNDED BY PIECEWISE SMOOTH SURFACES

2011 ◽  
Vol 21 (05) ◽  
pp. 571-594 ◽  
Author(s):  
SERGE GOSSELIN ◽  
CARL OLLIVIER-GOOCH
Keyword(s):  
Poor Quality ◽  
Sampling Procedure ◽  
Piecewise Smooth ◽  
Surface Patch ◽  
Smooth Surfaces ◽  
Delaunay Refinement ◽  
Protection Scheme ◽  
Delaunay Tetrahedralization ◽  
Boundary Curves ◽  
Refinement Algorithm

This article presents an algorithm to construct constrained Delaunay tetrahedralizations of geometric domains bounded by piecewise smooth surfaces. Meshes are built from the bottom-up by first discretizing the boundary curves and then by sampling the smooth surfaces. The sampling procedure refines the Delaunay triangulation restricted to these surfaces, targeting topological violations and poor quality triangles. Unlike previously published algorithms adopting a similar approach, we propose to sample each smooth surface patch independently. This obviates the need for a boundary protection scheme around small dihedral angles in the input and can also lead to coarser constraining triangulations. Starting from a Delaunay tetrahedralization of the point samples, a combination of mesh reconfigurations and vertex insertions is then used to obtain a tetrahedralization constrained to the boundary surfaces. The algorithm is designed to produce tetrahedralizations that can be used in conjunction with a Delaunay refinement algorithm implemented on a Bowyer-Watson framework.

Grid-Based Local Refinement Algorithm of Three-Dimensional Hexahedral Meshes

2010 ◽  
Vol 22 (4) ◽  
pp. 612-618
Author(s):  
Lili Huang ◽  
Guoqun Zhao ◽  
Zhonglei Wang
Keyword(s):  
Three Dimensional ◽  
Local Refinement ◽  
Hexahedral Meshes ◽  
Refinement Algorithm ◽  
Grid Based

scholarly journals A Disparity Refinement Algorithm for Satellite Remote Sensing Images Based on Mean-Shift Plane Segmentation

2021 ◽  
Vol 13 (10) ◽  
pp. 1903
Author(s):  
Zhihui Li ◽  
Jiaxin Liu ◽  
Yang Yang ◽  
Jing Zhang
Keyword(s):  
Remote Sensing ◽  
Satellite Remote Sensing ◽  
Stereo Matching ◽  
Mean Shift ◽  
Segmentation Method ◽  
Remote Sensing Images ◽  
Edge Matching ◽  
Refinement Method ◽  
Initial Segmentation ◽  
Refinement Algorithm

Objects in satellite remote sensing image sequences often have large deformations, and the stereo matching of this kind of image is so difficult that the matching rate generally drops. A disparity refinement method is needed to correct and fill the disparity. A method for disparity refinement based on the results of plane segmentation is proposed in this paper. The plane segmentation algorithm includes two steps: Initial segmentation based on mean-shift and alpha-expansion-based energy minimization. According to the results of plane segmentation and fitting, the disparity is refined by filling missed matching regions and removing outliers. The experimental results showed that the proposed plane segmentation method could not only accurately fit the plane in the presence of noise but also approximate the surface by plane combination. After the proposed plane segmentation method was applied to the disparity refinement of remote sensing images, many missed matches were filled, and the elevation errors were reduced. This proved that the proposed algorithm was effective. For difficult evaluations resulting from significant variations in remote sensing images of different satellites, the edge matching rate and the edge matching map are proposed as new stereo matching evaluation and analysis tools. Experiment results showed that they were easy to use, intuitive, and effective.

Scalable Data-Parallel Implementations of Object Recognition Using Geometric Hashing

1994 ◽  
Vol 21 (1) ◽  
pp. 96-109 ◽  
Author(s):  
C.L. Wang ◽  
V.K. Prasanna ◽  
H.J. Kim ◽  
A.A. Khokhar
Keyword(s):  
Object Recognition ◽  
Geometric Hashing ◽  
Data Parallel ◽  
Parallel Implementations
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