B. Joe, "Tetrahedral Mesh Generation in Polyhedral Regions Based on Convex Polyhedron Decompositions," International Journal for Numerical Methods in Engineering, vol 37, pp693-713, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....operator digs a tetrahedron from a convex object edge. This can always be done as a polyhedron should have at least one convex edge. The final one is t 2 which cuts open holes to deal with multiply connected polyhedra. The operators are applied repeatedly until only one tetrahedron is left. Joe [39] has published a technique which is also capable of generating a tetrahedral mesh. He assumes that the curved surfaces of the object have been approximated by planar polygons. His algorithm is to place cutting surfaces along reflex edges that have interior dihedral angles greater than 180 o . In ....

B. Joe, "Tetrahedral Mesh Generation in Polyhedral Regions Based on Convex Polyhedron Decompositions," International Journal for Numerical Methods in Engineering, vol 37, pp693-713, 1994.

....four kinds of elements are shown in Figure 1. A B C D A B C D E A B C D E F A B C D E F G H Figure 1. Mixed elements (from left to right) tetrahedron, pyramid, wedge and hexahedron The scheme first decomposes a 3D geometry into a set of convex polyhedra by using the method described in the paper [5]. Then the boundary quadrilateral meshes of these convex polyhedra are formed by using the method described in Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada, T6G 2H1, weidong cs.ualberta.ca the paper [6] For every convex polyhedron, the algorithm proposed ....

B. Joe. Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions. Int. J. Numer. Methods. Eng., 37:693--713, 1994.

....hand, this freedom largely contributes to the complexity of the remaining shape. This problem does not apply to the advancing by a layer approach of Johnston and Sullivan [16] The complex remaining shape leads to the main criticism of AFT: there is no proof that two fronts will join correctly [13, 15]. In other words, the remaining part of Step 6 may be irregularly shaped or even untetrahedralizable. This problem has been acknowledged by [7, 14, 22] The solution of Moller and Hansbo is to save the current state at regular intervals. Thus when AFT fails, this technique can recover the last ....

B. Joe. Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions. International Journal for Numerical Methods in Engineering, 37:693-- 713, 1994.

.... Omega Gamma nr r 7=3 ) Section 3.2 establishes this as an upper bound as well. We view this as the main contribution of our paper. Section 3.3 describes an algorithm to compute the decompostion in O(nr r 3 ) time and space. This improves on Chazelle s and Dey s time bounds. Joe [19] has done interesting work on chosing notch planes in practical examples to obtain few or well shaped convex pieces. 1.2 2 d problems in notch cutting We prove our combinatorial bounds by looking at two planar problems that are of independent interest. Problem 1.2 What is the total complexity ....

....algorithm one whose running time was proportional to the size of the decomposition. Reducing the time to O(nr r 7=3 ) also remains open. There also remain several open questions on how best to choose notch planes in practical examples to obtain few or well shaped convex pieces [19]. ....

Barry Joe. Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions. Int. J. Numer. Methods Eng., 37:693--713, 1994.

.... of refined tetrahedra in a refined mesh (see details in [Liu94] We report our experimental results for four single tetrahedra (Tables I IV in [RiL92] and two tetrahedral meshes of polyhedral regions (one is a convex polyhedron, Figure 1a in [Joe91] the other is a U shaped region, Figure 10 in [Joe94]) For a single tetrahedron, we refine all tetrahedra in the mesh at each step of refinement as in [RiL92, LiJ94c] For the two tetrahedral meshes, a fixed point on the object is chosen as the center of a sphere; at each step of refinement, we refine any tetrahedron with at least one of its ....

....are listed in Table 1 in terms of the coordinates of the four vertices. P1 and P2 are well shaped tetrahedra; P3 is a poorly shaped tetrahedron; P4 is the regular tetrahedron, where p 3 and p 2 are rounded to 16 decimal places. For the two polyhedral regions, by using the methods described in [Joe91, Joe94], the convex polyhedron is subdivided into 273 tetrahedra, and has minimum mean ratio 0.6230 after local transformations are used to obtain an improved quality mesh with respect to radius ratio ae; the U shaped object is subdivided into 466 tetrahedra with minimum mean ratio 0.5580 after local ....

B. Joe (1994), Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions, Intern. J. Num. Meth. Eng., 37, pp. 693-713.

....described. In Section 3, the input format and data structures are briefly described for the method of [JoS86] which generates convex polygon decompositions and triangular meshes in 2 D polygonal regions. In Section 4, the input format and data structures are briefly described for the method of [Joe93b] which generates convex polyhedron decompositions and tetrahedral meshes in 3 D polyhedral regions. 2 Directories of routines Currently, the routines of GEOMPACK are organized into the 15 directories listed below. Each directory contains a Makefile and one or more main driver programs (in files ....

....of a convex polyhedron, shrink a convex polyhedron. Routines which a user may wish to call include DIAM3, DSCPH, RMCLED, RMCPFC, SHRNK3, VOLCPH, WIDTH3. 12) dechol3d: This directory contains routines for resolving holes on faces of a polyhedral region and interior polyhedron holes as described in [Joe93b], i.e. the polyhedral region is decomposed into simple faces and polyhedra. Routines which a user may wish to call include DSPHFH, DSPHIH. 13) decomp3d: This directory contains routines for decomposing a polyhedral region into convex polyhedra using the algorithm in [Joe93b] Routines which a ....

[Article contains additional citation context not shown here]

B. Joe (1993), Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions, revised version, to appear in Intern. J. Num. Meth. Eng.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC