Browse > Article

Local Parameterization of Polygonal Models Using Projection Level Set  

Lee, Yeon-Joo (삼성전자 핸드폰사업부)
Cha, Deuk-Hyun (서강대학교 컴퓨터공학과)
Chang, Byung-Joon (서강대학교 컴퓨터공학과)
Ihm, In-Sung (서강대학교 컴퓨터공학과)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.34, no.12, 2007 , pp. 641-655 More about this Journal
Abstract
Parameterization has been one of very important research subjects in several application areas including computer graphics. In the parameterization research, the problem of mapping 3D polygonal model to 2D plane has been studied frequently, but the previous methods often fail to handle complicated shapes of polygonal surfaces effectively as well as entail distortion between the 3D and 2D spaces. Several attempts have been made especially to reduce such distortion, but they often suffer from the problem when an arbitrary rectangular surface region on 3D model is locally parameterized. In this paper, we propose a new local parameterization scheme based on the projection level set method. This technique generates a series of equi-distanced curves on the surface region of interest, which are then used to generate effective local parameterization information. In this paper, we explain the new technique in detail and show its effectiveness by demonstrating experimental results.
Keywords
local parameterization; projection level set; partial differential equation; 3D polygonal model; texture mapping;
Citations & Related Records
연도 인용수 순위
  • Reference
1 E. Bier and K. Sloan, 'Two-part texture mapping,' IEEE Computer Graphics and Applications, pages 40-53, 1986
2 S. Osher and J. A. Sethian, 'Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations,' J. Comput. Phys., Vol. 79(1), pages 12-29, 1988   DOI   ScienceOn
3 C. W. Shu and S. Osher, 'Efficient implementation of essentially non-oscillatory shock capturing schemes,' J. Comput. Phys., Vol.77, pages 439-471, 1988   DOI   ScienceOn
4 S. Osher and C. W. Shu, 'High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations,' J. Numer. Anal., Vol. 28, pages 907-922, 1991   DOI   ScienceOn
5 M. Samek, C. Slean and H. Weghorst, 'Texture mapping and distortions in digital graphics,' The Visual Computer, 2(5):313-320, 1986   DOI
6 D. Peng, B. Merriman, S. Osher, H. K. Zhao and M. Kang, 'A PDE-based fast local level set method,' J. Comput. Phys. Vol. 155, pages 410-438, 1999   DOI   ScienceOn
7 P. Alliez, E. Colin de Verdiere, O. Devillers and M. Isenburg, 'lsotropic surface remeshing,' In Proceedings of Shape Modeling International, pages 49-58, 2003
8 E. Fiume, A. Fournier and V. Canale, 'Conformal texture mapping,' In Proc. of EUROGRAPHICS '87, pages 53-64, 1987
9 P. Snader, S. Gortler, J. Snyder and H. Hoppe, 'Signal specialized parameterization,' In Eurographics Workshop on Rendering '02, 2002
10 G. S. Jiang and D. Peng, 'Weighted ENO schemes for Hamilton-Jacobi equations,' SIAM J. Sci. Comput., Vol. 21, pages 2126-2143, 2000   DOI   ScienceOn
11 M. Desbrun, M. Meyer and P. Alliez, 'Intrinsic parameterizations of surface meshes,' In Proc. of EUROGRAPHICS '02, pages 209-218, 2002
12 E. Catmull, 'A subdivision algorithm for computer display of curved surfaces,' PhD thesis, Dept. of Computer Sciences, University of Utah, December 1974
13 C. Bennis, J. M. Vezien and G. Lglesias, 'Piecewise surface flattening for non-distorted texture mapping,' In Proc. of ACM SIGGRAPH '91, pages 237-246, July 1991
14 X. D. Liu, S. Osher and T. Chan, 'Weighted essentially non-oscillatory schemes,' J. Comput. Phys., Vol. 115, pages 200-212, 1994   DOI   ScienceOn
15 W. E. Lorensen and H. E. Cline, 'Marching cubes: a high resolution 3D surface construction algorithm,' Computer Graphics 21, pages 164-169, 1987
16 F. Lazarus, M. Pocchiola, G. Vegter and A. Verrous, 'Computing a canonical polygonal schema of an orientable triangulated surface,' In Proc. of 17th Annual ACM Symp. Comput. Geom., pages 80-89, 2001
17 L. T. Cheng, P. Burchard, B. Merriman and S. Osher, 'Motion of curves constrained on surfaces using a level set approach,' J. Comput. Phys., Vol. 175, pages 604-644, 2002   DOI   ScienceOn
18 G. S. Jiang and C. W. Shu, 'Efficient implementation of weighted ENO schemes,' J. Comput. Phys., Vol. 126, pages 202-228, 1996   DOI   ScienceOn
19 B. Levy and J. L. Mallet,''Non-distorted texture mapping for sheared triangulated meshes,' In Proc. of ACM SIGGRAPH '98, pages 343-352, 1998
20 B. Levy, 'Constrained texture mapping for polygonal meshes,' In Proc. of ACM SIGGRAPH '01, pages 417-424, 2001
21 B. Levy, S. Petitjean, N. Ra and J. Maillot, 'Least squares conformal maps for automatic texture atlas generation,' In Proc. of ACM SIGGRAPH '02, pages 362-371, 2002
22 V. Krishnamurthy and M. Levoy, 'Fitting smooth surfaces to dense polygon meshes,' In Proc. of ACM SIGGRAPH '96, pages 313-324, August 19960
23 P. Alliez, M. Meyer and M. Desbrun, 'Interactive geometry remeshing,' In Proc. of ACM SIGGRAPH '02, pages 347-354, 2002