Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
권호 표지

Octree Generation and Clipping Algorithm using Section Curves for Three Dimensional Cartesian Grid Generation

삼차원 직교 격자 생성을 위한 단면 커브를 이용한 옥트리 생성과 셀 절단 알고리듬

  • Published : 2008.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Recently, Cartesian grid approach has been popular to generate grid meshes for complex geometries in CFD (Computational Fluid Dynamics) because it is based on the non-body-fitted technique. This paper presents a method of an octree generation and boundary cell clipping using section curves for fast octree generation and elimination of redundant intersections between boundary cells and triangles from 3D triangular mesh. The proposed octree generation method uses 2D Scan-Converting line algorithm, and the clipping is done by parameterization of vertices from section curves. Experimental results provide octree generation time as well as Cut-cell clipping time of several models. The result shows that the proposed octree generation is fast and has linear relationship between grid generation time and the number of cut-cells.

Keywords

References

  1. M. J. Aftosmis, "Solution adaptive Cartesian grid methods for aerodynamic flows with complex geometries," Computational Fluid Dynamics VKI Lecture Series, Belgium, 1997
  2. C. Andujar, P. Brunet, and D. Ayala, "Topology-Reducing Surface Simplification Using a Discrete Solid Representation," ACM Transactions on Graphics, Vol. 21, No. 2, pp. 88-105, 2002 https://doi.org/10.1145/508357.508359
  3. D. Ayala, P. Brunet, P. Juan, and I. Navazo, "Object Representation by Means of Nonminimal Division Quadtrees and Octrees," ACM Transactions on Graphics, Vol. 4, No.1, pp. 41-59, 1985 https://doi.org/10.1145/3973.3975
  4. M. J. Berger and M. J. Aftosmis, "Aspects (and aspect ratios) of Cartesian Mesh Methods," Proceedings of the 16th International Conf. on Num. Meth. in Fluid Dynamics, Jul 1998
  5. J. Bonet and J. Peraire, "An alternating digital tree (ADT) Algorithm for Geometric Searching and Intersection Problems," Int. J. Num. Meth. Eng, Vol. 31, pp. 1-17, 1991 https://doi.org/10.1002/nme.1620310102
  6. J. E. Bresenham, "Algorithm for computer control of a digital plotter," IBM Systems journal, Vol. 4, No. 1, pp. 25-30, 1965 https://doi.org/10.1147/sj.41.0025
  7. E. F. Charlton, "An octree solution to conservationlaws over arbitrary regions (OSCAR) with applications to aircraft aerodynamics," Ph.D. Thesis, Univ. of Mich., Dept. of Aero. and Astro. Engr., 1997
  8. J. D. Foley, A. van Dam, S. K. Feiner, and H. F. Hughes, "Computer Graphics: Principles and Practice," Addison Wesley, 1996
  9. H. C. Homer and S. H. Thomas, "A Survey of Construction and Manipulation of Octrees," Computer Vision, Graphics, and Image Processing, Vol. 43, pp. 409-431, 1988 https://doi.org/10.1016/0734-189X(88)90092-8
  10. J. D. Hunt, "An Adaptive 3D Cartesian Approach for the Parallel Computation of Inviscid Flow About Static and Dynamic Configurations," Ph.D. Thesis, Univ. of Mich., Dept. of Aero Eng and Sci Comp., 2004
  11. T. Ju, "Robust repair of polygonal models," ACM Transactions on Graphics, Vol. 23, No. 3, pp. 888-895, 2004 https://doi.org/10.1145/1015706.1015815
  12. A. Kaufman, "Efficient Algorithms for Scan-Converting 3D Polygons," Comput. & Graphics, Vol. 12, No. 2, pp. 213-219, 1988 https://doi.org/10.1016/0097-8493(88)90032-5
  13. I. Navazo, D. Ayala, and P. Brunet, "A geometric modeller based on the exact octree representation of polyhedra," Comp. Graphics Forum, Vol. 5, No. 2, pp. 91-104, 1986
  14. I. E. Sutherland and G. W. Hodgman, "Reentrant polygon clipping," Communications of the ACM, Vol. 17, No. 1, pp. 32-42, 1974 https://doi.org/10.1145/360767.360802
  15. J. Thompson, B. Soni, and N. Weatherill, Eds, "Handbook of Grid Generation", CRC Press, 1998
  16. Z. J. Wang, et al., "A $2^N$ Tree Based Automated Viscous Cartesian Grid Methodology for Feature Capturing," AIAA Paper, No. 99-3300, 1999