Point-Based Rendering of Non-Manifold Surfaces
We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a point‐based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that...
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| Veröffentlicht in: | Computer graphics forum Jg. 27; H. 1; S. 63 - 72 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Oxford, UK
Blackwell Publishing Ltd
01.03.2008
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a point‐based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non‐manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point‐based method allows for hidden surface elimination using a z‐buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages. |
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| AbstractList | We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a point‐based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non‐manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point‐based method allows for hidden surface elimination using a z‐buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages. We are concerned with producing high-quality images of parametric and implicit surfaces, in particular those with non-manifold features. We present a point-based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non-manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point-based method allows for hidden surface elimination using a z-buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages. [PUBLICATION ABSTRACT] |
| Author | Suffern, K. G. Jones, Huw Balsys, Ron J. |
| Author_xml | – sequence: 1 givenname: Ron J. surname: Balsys fullname: Balsys, Ron J. organization: Faculty of Business & Informatics, Central Queensland University, Rockhampton M. C., Qld. 4702, Australia balsys@cqu.edu.au – sequence: 2 givenname: K. G. surname: Suffern fullname: Suffern, K. G. organization: Faculty of Business & Informatics, Central Queensland University, Rockhampton M. C., Qld. 4702, Australia balsys@cqu.edu.au – sequence: 3 givenname: Huw surname: Jones fullname: Jones, Huw organization: Retired |
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| References | Balsys, R. J., Suffern, K. G.: Visualisation of implicit surfaces, Computers and Graphics, 25,:89-107. 2001. Suffern, K. G., Fackerell E. D.: Interval methods in computer graphics. Computers and Graphics, 15,:331-40. 1991. Schmidt M. F. W.: Cutting cubes - visualizing implicit surfaces by adaptive polygonization. The Visual Computer, 10,:101-115. 1990. Tanaka, S., Shibata, A., Yamamoto, H., Kotsuru H.: Generalized Stochastic Sampling Method for Visualization and Investigating of Implicit Surfaces, Proc. Eurographics 2001, Computer Graphics Forum, 20,:3:359-367. 2001. Wyvill, C. G., Mcpheeters, C., Wyvill B.: Data structures for soft objects. The Visual Computer, 2,:227-234. 1986. Witkin A. P., Heckbird P. S.: Using Particles to Sample and Control Implicit Surfaces. Proceedings of SIGGRAPH 94. In Computer Graphics Proceedings, Annual Conference Series, 269-277. 1994. Suffern, K. G. Balsys R. J.: Rendering the Intersections of implicit surfaces, IEEE Computer Graphics and Applications, 23,:5:70-77. 2003. Tanaka S., Morisaki A., Nakata S, Fukuda Y., Yamamoto H.: Sampling implicit surfaces based on stochastic differential equations with converging constraint, Computers & Graphics, 24,:419-431. 2000. Apery F.: The Boy Surface. Advances in Mathematics, 61,: 185-266. 1996. Kalaiah, A., Varshney A.: Statistical Point Geometry Eurographics Symposium on Geometrical Processing, 371-378. 2003. Lorenson, W. E., Cline.H. E.: Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics, 21,:163-170. 1987. Taubin G.: Rasterizing algebraic curves and surfaces. IEEE Computer Graphics and Applications, 14,:14-23. 1994. De figueiredo L. H. Gomes J.: Sampling implicit surfaces with physically-based particle systems, Computers and Graphics, 20,:3:365-375. 1996. Moore R. E.: Interval analysis. Prentice-Hall, Englewood Cliffs , NJ .1996. Rockwood A.: A Generalised Scanning Technique for Display of Parametrically Defined Surfaces, IEEE Computer Graphics and Applications, 7,:8:15-26. 1987. Synder J. M.: Generative modelling for computer graphics and CAD, Boston , Academic Press, 1992. Foley, J. D., Van dam, A., Feiner, S. K., Hughes J. F.: Computer graphics: principles and practice (2 ed.), Addison-Wesley, Reading , MA . 1990. Hansen E. R.: Global optimisation using interval analysis N∼ the multidimensional case. Numerische Mathematik, 34,:247-270. 1980. Bloomenthal J.: Polygonization of implicit surfaces. Computer Aided Geometric Design, 5,:341-355. 1988. Wand, M., Fischer, M., Peter, I., Heide, F. M., Straβer W.: The Randomized z-Buffer Algorithm: Interactive Rendering of Highly Complex Scenes In SIGGRAPH 2001, 361-370. 2001. Zwicker, M., Pfister, H., Van baar, J., Gross M.: Surface splatting In SIGGRAPH 2001, 371-378. 2001. Ratschek, H., Rokne J.: New Computer Methods for Global Optimisation. Ellis Horwood, London . 1988. 1990; 10 1991; 15 2000; 24 1987; 7 1998 1996 1994 2005 2004 2003 1992 2002 2001; 25 2001; 20 1986; 2 1987; 21 1990 2001 2000 1519 June 2004 1988; 5 1980; 34 1996; 61 1985 1994; 14 1997; 16 1983 1996; 20 2629 July 2005 1989 1988 2003; 23 Stolte N. (e_1_2_7_28_2) 1998 e_1_2_7_3_2 e_1_2_7_2_2 Synder J. M. (e_1_2_7_33_2) 1992 e_1_2_7_6_2 e_1_2_7_18_2 Moore R. E. (e_1_2_7_19_2) 1996 Botsch M. (e_1_2_7_8_2) 2002 Foley J. D. (e_1_2_7_12_2) 1990 Botsch M. (e_1_2_7_7_2) 2004 e_1_2_7_14_2 Kalaiah A. (e_1_2_7_16_2) 2003 e_1_2_7_13_2 e_1_2_7_11_2 e_1_2_7_10_2 Balsys R. J. (e_1_2_7_5_2) 2005 e_1_2_7_26_2 Stolte N. (e_1_2_7_30_2) 2005 e_1_2_7_27_2 Heckbert P. (e_1_2_7_15_2) 1989 Stolte N. (e_1_2_7_29_2) 2003 Balsys R. J. (e_1_2_7_4_2) 1519 Chiu K. (e_1_2_7_9_2) 1994 Zwicker M. (e_1_2_7_41_2) 2004 Ratschek H. (e_1_2_7_22_2) 1988 Witkin A. P. (e_1_2_7_39_2) 1994 e_1_2_7_25_2 Zwicker M. (e_1_2_7_40_2) 2001 e_1_2_7_23_2 e_1_2_7_31_2 e_1_2_7_32_2 e_1_2_7_21_2 e_1_2_7_20_2 e_1_2_7_34_2 e_1_2_7_35_2 e_1_2_7_36_2 e_1_2_7_37_2 e_1_2_7_38_2 Rösche A. (e_1_2_7_24_2) 1997 Levoy M. (e_1_2_7_17_2) 1985 |
| References_xml | – reference: Apery F.: The Boy Surface. Advances in Mathematics, 61,: 185-266. 1996. – reference: Suffern, K. G., Fackerell E. D.: Interval methods in computer graphics. Computers and Graphics, 15,:331-40. 1991. – reference: Rockwood A.: A Generalised Scanning Technique for Display of Parametrically Defined Surfaces, IEEE Computer Graphics and Applications, 7,:8:15-26. 1987. – reference: Wyvill, C. G., Mcpheeters, C., Wyvill B.: Data structures for soft objects. The Visual Computer, 2,:227-234. 1986. – reference: De figueiredo L. H. Gomes J.: Sampling implicit surfaces with physically-based particle systems, Computers and Graphics, 20,:3:365-375. 1996. – reference: Lorenson, W. E., Cline.H. E.: Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics, 21,:163-170. 1987. – reference: Synder J. M.: Generative modelling for computer graphics and CAD, Boston , Academic Press, 1992. – reference: Foley, J. D., Van dam, A., Feiner, S. K., Hughes J. F.: Computer graphics: principles and practice (2 ed.), Addison-Wesley, Reading , MA . 1990. – reference: Ratschek, H., Rokne J.: New Computer Methods for Global Optimisation. Ellis Horwood, London . 1988. – reference: Balsys, R. J., Suffern, K. G.: Visualisation of implicit surfaces, Computers and Graphics, 25,:89-107. 2001. – reference: Witkin A. P., Heckbird P. S.: Using Particles to Sample and Control Implicit Surfaces. Proceedings of SIGGRAPH 94. In Computer Graphics Proceedings, Annual Conference Series, 269-277. 1994. – reference: Schmidt M. F. W.: Cutting cubes - visualizing implicit surfaces by adaptive polygonization. The Visual Computer, 10,:101-115. 1990. – reference: Taubin G.: Rasterizing algebraic curves and surfaces. IEEE Computer Graphics and Applications, 14,:14-23. 1994. – reference: Bloomenthal J.: Polygonization of implicit surfaces. Computer Aided Geometric Design, 5,:341-355. 1988. – reference: Kalaiah, A., Varshney A.: Statistical Point Geometry Eurographics Symposium on Geometrical Processing, 371-378. 2003. – reference: Wand, M., Fischer, M., Peter, I., Heide, F. M., Straβer W.: The Randomized z-Buffer Algorithm: Interactive Rendering of Highly Complex Scenes In SIGGRAPH 2001, 361-370. 2001. – reference: Moore R. E.: Interval analysis. Prentice-Hall, Englewood Cliffs , NJ .1996. – reference: Tanaka S., Morisaki A., Nakata S, Fukuda Y., Yamamoto H.: Sampling implicit surfaces based on stochastic differential equations with converging constraint, Computers & Graphics, 24,:419-431. 2000. – reference: Tanaka, S., Shibata, A., Yamamoto, H., Kotsuru H.: Generalized Stochastic Sampling Method for Visualization and Investigating of Implicit Surfaces, Proc. Eurographics 2001, Computer Graphics Forum, 20,:3:359-367. 2001. – reference: Zwicker, M., Pfister, H., Van baar, J., Gross M.: Surface splatting In SIGGRAPH 2001, 371-378. 2001. – reference: Hansen E. R.: Global optimisation using interval analysis N∼ the multidimensional case. Numerische Mathematik, 34,:247-270. 1980. – reference: Suffern, K. G. Balsys R. J.: Rendering the Intersections of implicit surfaces, IEEE Computer Graphics and Applications, 23,:5:70-77. 2003. – year: 1985 – volume: 15 start-page: 331 year: 1991 end-page: 40 article-title: Interval methods in computer graphics publication-title: Computers and Graphics – volume: 61 start-page: 185 year: 1996 end-page: 266 article-title: The Boy Surface publication-title: Advances in Mathematics – start-page: 25 year: 2004 end-page: 32 – start-page: 53 year: 2002 end-page: 64 – start-page: 200 year: 2003 end-page: 205 – start-page: 138 year: 1994 end-page: 148 – volume: 25 start-page: 89 year: 2001 end-page: 107 article-title: Visualisation of implicit surfaces publication-title: Computers and Graphics – start-page: 325 year: 2003 end-page: 334 – year: 2001 – volume: 10 start-page: 101 year: 1990 end-page: 115 article-title: Cutting cubes ‐ visualizing implicit surfaces by adaptive polygonization publication-title: The Visual Computer – year: 1989 – volume: 5 start-page: 341 year: 1988 end-page: 355 article-title: Polygonization of implicit surfaces publication-title: Computer Aided Geometric Design – volume: 23 start-page: 70 issue: 5 year: 2003 end-page: 77 article-title: Rendering the Intersections of implicit surfaces publication-title: IEEE Computer Graphics and Applications – volume: 7 start-page: 15 issue: 8 year: 1987 end-page: 26 article-title: A Generalised Scanning Technique for Display of Parametrically Defined Surfaces publication-title: IEEE Computer Graphics and Applications – year: 1996 – start-page: 81 year: 1998 end-page: 87 – year: 1990 – start-page: 147 year: 1989 end-page: 156 – start-page: 371 year: 2001 end-page: 378 – year: 1992 – volume: 20 start-page: 359 issue: 3 year: 2001 end-page: 367 article-title: Generalized Stochastic Sampling Method for Visualization and Investigating of Implicit Surfaces publication-title: Computer Graphics Forum – start-page: 257 year: 2629 July 2005 end-page: 263 – start-page: 371 year: 2003 end-page: 378 – volume: 34 start-page: 247 year: 1980 end-page: 270 article-title: Global optimisation using interval analysis N∼ the multidimensional case publication-title: Numerische Mathematik – volume: 14 start-page: 14 year: 1994 end-page: 23 article-title: Rasterizing algebraic curves and surfaces publication-title: IEEE Computer Graphics and Applications – volume: 21 start-page: 163 year: 1987 end-page: 170 article-title: Marching cubes: a high resolution 3D surface construction algorithm publication-title: Computer Graphics – start-page: 361 year: 2001 end-page: 370 – volume: 2 start-page: 227 year: 1986 end-page: 234 article-title: Data structures for soft objects publication-title: The Visual Computer – start-page: 83 year: 1983 end-page: 90 – year: 1988 – volume: 16 start-page: 295 issue: 5 year: 1997 end-page: 306 – start-page: 335 year: 2000 end-page: 342 – start-page: 7 year: 1519 June 2004 end-page: 14 – start-page: 269 year: 1994 end-page: 277 – start-page: 247 year: 2004 end-page: 254 – volume: 20 start-page: 365 issue: 3 year: 1996 end-page: 375 article-title: Sampling implicit surfaces with physically‐based particle systems publication-title: Computers and Graphics – volume: 24 start-page: 419 year: 2000 end-page: 431 article-title: Sampling implicit surfaces based on stochastic differential equations with converging constraint publication-title: Computers & Graphics – start-page: 414 year: 2005 end-page: 426 – start-page: 343 year: 2000 end-page: 352 – ident: e_1_2_7_10_2 doi: 10.1109/PCCGA.2003.1238274 – ident: e_1_2_7_14_2 doi: 10.1007/BF01396702 – ident: e_1_2_7_26_2 doi: 10.1007/BF01901946 – ident: e_1_2_7_25_2 doi: 10.1145/344779.344940 – start-page: 247 volume-title: Eurographics Symposium on Point‐Based Graphics year: 2004 ident: e_1_2_7_41_2 – start-page: 295 volume-title: Computer Graphics Forum year: 1997 ident: e_1_2_7_24_2 – ident: e_1_2_7_37_2 doi: 10.1109/38.267467 – start-page: 414 volume-title: DGCI 2005 year: 2005 ident: e_1_2_7_30_2 – start-page: 371 volume-title: Surface splatting In SIGGRAPH 2001 year: 2001 ident: e_1_2_7_40_2 – start-page: 257 volume-title: International Conference on Computer Graphics, Imaging and Vision year: 2005 ident: e_1_2_7_5_2 – start-page: 269 volume-title: Using Particles to Sample and Control Implicit Surfaces. Proceedings of SIGGRAPH 94 year: 1994 ident: e_1_2_7_39_2 – ident: e_1_2_7_20_2 – start-page: 138 volume-title: In Heckbert P. S. Ed., Graphics Gems IV year: 1994 ident: e_1_2_7_9_2 – ident: e_1_2_7_21_2 doi: 10.1145/344779.344936 – ident: e_1_2_7_23_2 doi: 10.1109/MCG.1987.276916 – ident: e_1_2_7_35_2 doi: 10.1016/S0097-8493(00)00037-6 – ident: e_1_2_7_13_2 doi: 10.1145/964967.801136 – ident: e_1_2_7_34_2 doi: 10.1007/BF01900346 – volume-title: Computer graphics: principles and practice (2 ed.) year: 1990 ident: e_1_2_7_12_2 – start-page: 200 volume-title: Proceedings Computer Graphics and Imaging year: 2003 ident: e_1_2_7_29_2 – ident: e_1_2_7_36_2 doi: 10.1111/1467-8659.00528 – ident: e_1_2_7_11_2 doi: 10.1016/0097-8493(96)00005-2 – ident: e_1_2_7_31_2 doi: 10.1016/0097-8493(91)90002-Y – ident: e_1_2_7_3_2 doi: 10.1016/S0097-8493(00)00110-2 – ident: e_1_2_7_18_2 doi: 10.1145/37402.37422 – volume-title: Generative modelling for computer graphics and CAD year: 1992 ident: e_1_2_7_33_2 – start-page: 25 volume-title: Eurographics Symposium on Point‐Based Graphics year: 2004 ident: e_1_2_7_7_2 – volume-title: Interval analysis. year: 1996 ident: e_1_2_7_19_2 – ident: e_1_2_7_2_2 doi: 10.1016/0001-8708(86)90080-0 – ident: e_1_2_7_27_2 doi: 10.1145/74333.74348 – start-page: 81 volume-title: Implicit Surfaces'98 year: 1998 ident: e_1_2_7_28_2 – ident: e_1_2_7_38_2 doi: 10.1145/383259.383299 – volume-title: Masters thesis, University of California at Berkeley, Dept. of Elec. 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| Snippet | We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a... We are concerned with producing high-quality images of parametric and implicit surfaces, in particular those with non-manifold features. We present a... |
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| SubjectTerms | Computer graphics I.3.3 [Computer Graphics] Display algorithms intervals non-manifold surface octrees point rendering Studies |
| Title | Point-Based Rendering of Non-Manifold Surfaces |
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