Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

Si, Hang; Shewchuk, Jonathan Richard

doi:10.1007/s00366-013-0331-0

Cited by 22 publications

(7 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Triangulate the step line of the stope 38 – 40 to get the triangle set . Therein is the j-th triangle of stope step, , is the total number of triangles for stope steps; use the stope triangle set to cut the 3D entity set of rock mass within the blasting range, and retains the 3D rock mass entity below the step triangle of the stope, namely the three-dimensional solid model of rock mass in blasting area, recorded as .…”

Section: The Three-dimensional Solid Model Of the Blast Hole Chargementioning

confidence: 99%

Calculation of blast hole charge amount based on three-dimensional solid model of blasting rock mass

Chen

Wang

Chen

et al. 2022

Sci Rep

View full text Add to dashboard Cite

The development and use of intelligent drilling rigs make it available to obtain accurate lithology data of blast drilling. In order to make full use of drilling data to improve blasting efficiency, the following research was carried out. First, a database is established to manage and store the blast hole data recognized by the intelligent drill. Secondly, the blast hole lithology data is taken as a sample, and the inverse distance square method is used to interpolate the blasting range's solid elements to generate a three-dimensional solid model of the blasting rock mass. Afterward, the blasting range polygon and stope triangle grid are used successively in the solid model to obtain the cut 3D solid model of the blasting rock mass; finally, the blast hole charge is calculated based on the cut 3D solid model of the blasting rock. The C++ programming language is used to realize all the blast hole charge amount processes based on the three-dimensional solid model of the blasting rock mass. With the application example of No. 918 bench blasting of Shengli Open-pit Coal Mine in Xilinhot, Inner Mongolia, the blast hole charge amount in the blasting area is calculated and compared with the results of single hole rock property calculation, the results show that the blast hole charge calculated by three-dimensional rock mass model can be effectively reduced.

show abstract

Section: The Three-dimensional Solid Model Of the Blast Hole Chargementioning

confidence: 99%

Calculation of blast hole charge amount based on three-dimensional solid model of blasting rock mass

Chen

Wang

Chen

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Delaunay Meshing. The most studied and most widely used algorithms to generate tetrahedral meshes are based on the Delaunay condition [Alliez et al 2005a;Aurenhammer 1991;Aurenhammer et al 2013;Bishop 2016;Boissonnat et al 2002;Boissonnat and Oudot 2005;Busaryev et al 2009;Chen and Xu 2004;Cheng et al 2008Cheng et al , 2012Chew 1989Chew , 1993Cohen-Steiner et al 2002;Du and Wang 2003;Jamin et al 2015;Murphy et al 2001;Remacle 2017;Ruppert 1995;Sheehy 2012;Shewchuk 1996Shewchuk , 1998Shewchuk , 1999Shewchuk , 2002Si 2015;Si and Gartner 2005;Si and Shewchuk 2014;Tournois et al 2009]. These methods are efficient and are widely used in commercial software.…”

Section: Tetrahedral Meshingmentioning

confidence: 99%

Tetrahedral meshing in the wild

et al. 2018

View full text Add to dashboard Cite

5.0% 2.6% 1.2% 0.6% 0.4% 0.2% 9.6% 6.8% 4.8% 3.7% 2.7% 1.5% 54.5% 26.9% 8.1% 1.9% 0.5% 0.1% 8.7% 2.1% 0.6% 0.2% 0.1% >1m >2m >4m >8m >16m >32m 0% 10% 20% 30% 40% 50% TetGen CGAL TetWild Ours CGAL #T = 1 362 980 444s TetGen #T = 8 221 130 1705s TetWild #T = 459 626 1588s Ours #T = 278 997 291s Input #F = 392 040 Fig. 1. A mouse skull model (from micro-CT) tetrahedralized by fTetWild (right) compared with other popular tetrahedral meshing algorithms. The plot shows the percentage of models requiring more than a certain time for the different approaches over 4540 inputs (the subset of Thingi10k where all 4 algorithms succeed). Our algorithm successfully meshes 99.4% of the input models in less than 2 minutes, and processes all models within 32 minutes. The comparison has been done using the experimental setup of TetWild ] and selecting a similar target resolution for all methods. The CGAL surface approximation parameter has been selected to be comparable to the envelope size used for TetWild and for our method.We propose a new tetrahedral meshing technique, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds upon the TetWild algorithm, inheriting its unconditional robustness, but dramatically reducing its computation cost and guaranteeing the generation of a valid tetrahedral mesh with floating point coordinates. This is achieved by introducing a new problem formulation, which is well suited for a pure floating point implementation and naturally leads to a parallel implementation. Our algorithm produces results qualitatively and quantitatively similar to TetWild, but at a fraction of the computational cost, with a running time comparable to Delaunay-based tetrahedralization algorithms. ACM Reference format:

show abstract

“…The advantage in this case is a better control of dimensions and classification of the elements in a tetrahedral mesh, but at the same time the algorithm complexity is increased, due to the verification tests for optimal point insertions (Lo, 1985;Nguyen-Van-Phai, 1982). The Delaunay algorithm is related to a geometric structure introduced in 1934 by Delaunay (Si and Shewchuk, 2014;Ray and Adviser-Dey, 2006;Marcum and Weatherill, 1995;Weatherill and Hassam, 1994), which is the Delaunay triangulation of a vertex set. The Delaunay algorithm brings many advantages for the automatic mesh generation, since it needs only the coordinates of the vertex set to work properly, not requiring orientations or detailed information about the solid structure.…”

Section: Mesh Generation Techniques: An Overviewmentioning

confidence: 99%