Automatic Generation of Tetrahedral Meshes from General Sections

일반 단면으로부터 사면체 요소망의 자동생성

  • Published : 2000.01.01


Computed Tomography (CT), Nuclear Magnetic Resonance Imaging (MR1) and some ultrasound techniques make it possible to obtain cross sections of human body or mechanical parts. In CAD system, a series of sectional surfaces can also be obtained from solid models of 3D objects. In this paper we introduce a tetrahedral meshing algorithm from these series of general sections using basic operators. In this scheme. general sections of three-dimensional object are triangulated first and side surfaces between two sections are triangulated by the use of tiling process. Finally tetrahedral meshing process is performed on each layer of 3D objects, which is composed of two general sections and one side surface.


Tetrahedral Meshs;General Sections;Tiling;Side Meshing;Warping Criterion;Zig-zag Pattern;Splitting Operator


  1. Dey, S., Shephard, M. S. and Georges, M. K., 1997, 'Elimination of the Adverse Effects of Small Model Features by the Local Modification of Automatically Generater Meshes,' Engng. Comput., Vol. 13, pp.134-152
  2. Ekoule, A. B., Peyrin, F. C. and Odet, C. L., 1991, 'A Triangulation Algorithm from Arbitrary Shaped Multiple Planar Contours,' ACM trans. Graphics, 10(2), pp. 182-199
  3. Keppel, E., 1975, 'Approximating Complex Surfaces by Triangulation of Contour Lines,' IBM J. Res. Develop., (19), pp. 2-11
  4. Fuchs, H., Kedem, Z. M. and Uselton, S. P., 1997, 'Optimal Surface Reconstrution from Planar Contours, ' Commum. ACM20, 10, pp. 693-702
  5. Mayers, D., Skiner, S. and Sloan, K., 1992, 'Surfaces from Contours,' ACM trans. Graphics, 11(3), pp.228-258
  6. Jin, H. and Tanner, R. I., 'Generation of Unstructured Tetrahedral Meshes by Advancing Front Technique,' Int. J. Num. Meth. Engng., Vol. 36, pp. 1805-1823
  7. Moller, P., 1985, 'On Advancing Front Mesh Generation in Three Dimensions,' Int. J. Num. Meth. Engng., Vol. 38 ,pp. 3551-3519
  8. Chae, S. W. and Kim, J. S., 1995, 'Tetrahedral Meshing Algorithm Using Basic Operators,' Proc. of the 4th International Meshing Roundtable, pp. 305-317
  9. 손창현, 채수원, 1996, '3차원 곡면에서 삼각형 유한요소망의 자동생성,' 한국 CAD/CAM학회 논문집 제 1 권 제 3 호, pp. 224-233
  10. Bajaj, C. L., Coyle, E. J. and Lin, K. N., 1996, 'Surface and 3D Triangular Meshes from planar Cross Sections,' Proc. of the 5th International Meshing Roundtable, pp. 169-178
  11. Weatherill, N. P. and Hassan, 0., 1992, 'Efficent Three-Dimensional Delaunay Triangulation with Automatic Point Creation and Imoised Boundary Conditions,' Int. J. Num. Meth. Engng., Vol. 34, pp. 1035-1050
  12. Chae, S. W. and Bathe, K. J., 1989, 'On Automatic Mesh Refinement In Finite Element Analysis,' Computers & Structures, Vol.32, No.3/4, pp. 911-936
  13. Yerry, M. A. and Shephard, M. S., 1984, 'Automatic Three-Dimensional Mesh Generation by the Modified-Octree Technique,' Int. J. Num. Meth. Engng., Vol. 20, pp.1965-1990
  14. 정융호, 이건우, 1995, '삼차원 유한요소의 자동생성(2)-사면체 octree로 부터 유한요소의 생성,' 대한기계학회 논문집,제 19 권 제 3 호, pp.647-660