Improved Rendering on Spherical Coordinate System using Convex Hull

컨벡스 헐을 이용한 개선된 구 좌표계 기반 렌더링 방법

  • 김남중 (중앙대학교 첨단영상대학원 영상학과) ;
  • 홍현기 (중앙대학교 첨단영상대학원 영상학과)
  • Published : 2010.02.20

Abstract

This paper presents a novel real-time rendering algorithm based on spherical coordinate system of the object using convex hull. While OpenGL rendering pipeline touches all vertices of an object, the proposed method takes account the only visible vertices by examining the visible triangles of the object. In order to determine the visible areas of the object in its spherical coordinate representation, the proposed method uses 3D geometric relation of 6 plane equations of the camera frustum and the bounding sphere of the object. In addition, we compute the convex hull of the object and its maximum side factors for hidden surface removal. Simulation results showed that the quality of result image is almost same compared to original image and rendering performance is greatly improved.

본 논문에서는 컨벡스 헐을 이용한 구 좌표계 기반 실시간 렌더링 알고리즘이 제안되었다. OpenGL 렌더링 파이프라인은 물체의 모든 정점들을 고려하지만, 제안된 방법은 물체의 가시 삼각형들을 검사하여 보이는 정점들만을 고려한다. 본 논문에서는 구좌표계 표현에서의 물체의 가시 영역을 결정하기 위하여, 카메라 절두체를 이루는 6개의 평면 방정식과 물체의 경계구와의 기하 관계를 이용한다. 또한 대상 물체의 컨벡스 헐(convex hull)의 최대 측면 성분(maximum side factor)을 고려하여 은면(hidden surface)을 제거하는 효과적인 방법이 구현되었다. 실험결과로부터 결과 영상이 원본 영상과 거의 같고, 렌더링 성능이 크게 개선됐음을 확인하였다.

Keywords

References

  1. J. W. Ratcliff, "Sphere trees for visibility culling, ray tracing, and range searching", Game Programming Gems 2, Charles River Media, pp. 384-387, 2001.
  2. H. Samet, "The design and analysis of spatial data structures", Addison-Wesley, Reading, Massachusetts, 1989.
  3. T. Akenine-Moller, E. Haines, and N. Hoffman, "Real-time rendering", A.K. Peters Ltd., 2002.
  4. D. Cohen-Or, Y. Chrysanthou, C. T. Silva, and F. Durand, "A survey of visibility for walkthrough applications", IEEE Trans on Visualization and Computer Graphics, Vol. 9, No. 3, pp. 412-431, 2003. https://doi.org/10.1109/TVCG.2003.1207447
  5. J. H. Clark, "Hierarchical geometric models for visible surface algorithms," Communications of the ACM, Vol. 19, No. 10, pp. 547-554, 1976. https://doi.org/10.1145/360349.360354
  6. D. Shreiner, M. Woo, J. Neider, and T. Davis, "OpenGL programming guide", 5th Ed., Addison- Wesley Ltd., 2005.
  7. H. Hoppe, "Progressive meshes", Proc. of SIGGRAPH, pp. 99-108, Aug. 1996.
  8. H. Hoppe, "View-dependent refinement of progressive meshes", Proc. of SIGGRAPH, pp. 189-198, Aug. 1997.
  9. J. T. Klosowski and C. T. Silva, "The prioritized-layered projection algorithm for visible set estimation", IEEE Trans. on Visualization and Computer Graphics, Vol. 6, No. 2, pp. 108-123, 2000. https://doi.org/10.1109/2945.856993
  10. J. T. Klosowski and C. T. Silva, "Efficient conservative visibility culling using the prioritized-layered projection algorithm", IEEE Trans. on Visualization and Computer Graphics, Vol. 7, No. 4, pp. 365-379, 2001. https://doi.org/10.1109/2945.965350
  11. S. Katz, A. Tal, and R. Basri, "Direct visibility of point sets", ACM Trans. on Graphics, Vol. 26, No. 3, pp. 24:1-11, July 2007.
  12. 한은호, 홍현기, "물체의 구 좌표계 표현을 이용한 효율적인 렌더링 방법", 한국게임학회 논문지 8권, 3호, pp. 69-76, 2008.
  13. Joseph O'Rourke, "Computational geometry in C", Cambridge University Press, 1998.
  14. M. Berg, O. Cheong, M. Kreveld, and M. Overmars, "Computational geometry: Algorithms and applications", 3rd Ed., Springer, 2000.
  15. Tim Round, "Object occlusion culling," Game Programming Gems 2, Charles River Media, pp. 421-431, 2001.
  16. R. Fernando and M. J. Kilgard, "The Cg tutorial: the definitive guide to programmable real-time graphics", Addison-Wesley Professional, 2003.