Fast ray tracing of arbitrary implicit surfaces with interval and affine arithmetic

Computer Graphics Forum

Volumn 28, Issue 1, 2009, Pages 26-40

  Knoll, A ^a,c   Hijazi, Y ^b,c   Kensler, A ^a   Schott, M ^a   Hansen, C ^a,c   Hagen, H ^b,c  

^a UNIVERSITY OF UTAH   (United States)

^b Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^c International Research Training Group (IRTG 1131)

Author keywords

Ray tracing; Reduced affine arithmetic; Shader metaprogramming

Indexed keywords

ALGEBRA; ITERATIVE METHODS; RENDERING (COMPUTER GRAPHICS);

AFFINE ARITHMETIC; AUTOMATIC GENERATION; INTERACTIVE PERFORMANCE; INTERVAL ARITHMETIC; ITERATIVE ALGORITHM; META PROGRAMMING; RAY-TRACING ALGORITHM; SYMBOLIC EXPRESSION;

RAY TRACING;

EID: 60849088003     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2008.01189.x     Document Type: Article

References (39)

1. Bloomenthal J. : An implicit surface polygonizer. In Graphics Gems IV, 1994, New York, Academic Press, pp. 324 349.
2. Bigler J., Stephens A., Parker S. : Design for parallel interactive ray tracing systems. In Proceedings of the IEEE Symposium on Interactive Ray Tracing (2006 pp. 187 195.
3. Capriani O., Hvidegaard L., Mortensen M., Schneider T. : Robust and efficient ray intersection of implicit surfaces. Reliable Computing 6 (2000 9 21.
4. Comba J. L. D., Stolfi J. : Affine arithmetic and its applications to computer graphics. In Proc. VI Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'93) (1993 pp. 9 18.
5. de Cusatis Junior A., de Figueiredo L., Gattas M. : Interval methods for raycasting implicit surfaces with affine arithmetic. In Proceedings of XII SIBGRPHI (1999 pp. 1 7.
6. de Toledo R., Levy B., Paul J.-C. : Iterative methods for visualization of implicit surfaces ongpu. In ISVC, International Symposium on Visual Computing (Lake Tahoe, Nevada /California, November 2007 Lecture Notes in Computer Science, SBC - Sociedade Brasileira de Computacao, Springer. pp. 598 609.
7. Fryazinov O., Pasko A. : Interactive ray shading of FRep objects. In WSCG 2008 Communications Papers Proceedings (2008 pp. 145 152.
8. Florez J., Sbert M., Sainz M., Vehi J. : Improving the interval ray tracing of implicit surfaces. In Lecture Notes in Computer Science (2006 Vol. 4035, pp. 655 664.
9. Gamito M. N., Maddock S. C. : Ray casting implicit fractal surfaces with reduced affine arithmetic. The Visual Computer 23, 3 (2007 155 165.
10. Günther J., Popov S., Seidel H.-P., Slusallek P. : Realtime ray tracing on GPU with BVH-based packet traversal. In Proceedings of the IEEE / Eurographics Symposium on Interactive Ray Tracing 2007 (September 2007 pp. 113 118.
11. Hanrahan P. : Ray tracing algebraic surfaces. In SIGGRAPH '83: Proceedings of the 10th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1983 ACM Press, pp. 83 90.
12. Hart J. C. : Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12, 10 (1996 527 545.
13. Heidrich W., Seidel H.-P. : Ray-tracing procedural displacement shaders. In Proceedings of Graphics Interface (1998 pp. 8 16.
14. Hadwiger M., Sigg* C., Scharsach H., Buhler K., Gross* M. : Real-time ray-casting and advanced shading of discrete isosurfaces. Computer Graphics Forum 24, 3 (2005 303 312.
15. K3dsurf: The K3DSurf project. Available at http://k3dsurf.sourceforge. net/.
16. Kalra D., Barr A. H. : Guaranteed ray intersections with implicit surfaces. In SIGGRAPH '89: Proceedings of the 16th Annual Conference on Computergraphics and Interactive Techniques (New York, NY, USA, 1989 ACM Press, pp. 297 306.
17. Knoll A., Hansen C., Wald I. : Coherent Multiresolution Isosurface Ray Tracing. Tech. Rep. UUSCI-2007-001, SCI Institute, University of Utah, 2007 To appear in The Visual Computer).
18. Knoll A., Hijazi Y., Wald I., Hansen C., Hagen H. : Interactive ray tracing of arbitrary implicits with simd interval arithmetic. In Proceedings of the 2nd IEEE / EG Symposium on Interactive Ray Tracing (2007 pp. 11 18.
19. Loop C., Blinn J. : Real-time GPU rendering of piecewise algebraic surfaces. In SIGGRAPH '06: ACM SIGGRAPH 2006 Papers (New York, NY, USA, 2006 ACM Press, pp. 664 670.
20. Messine F. : Extentions of affine arithmetic: Application to unconstrained global optimization. Journal of Universal Computer Science 8, 11 (2002 992 1015.
21. Meyer M. D., Georgel P., Whitaker R. T. : Robust particle systems for curvature dependent sampling of implicit surfaces. In SMI '05: Proceedings of the International Conference on Shape Modeling and Applications 2005 (SMI' 05) (Washington, DC, USA, 2005 IEEE Computer Society, pp. 124 133.
22. Midonick H. O. : The Treasury of Mathematics. Philosophical Library, 1965.
23. Mitchell D. : Robust ray intersection with interval arithmetic. In Proceedings on Graphics Interface 1990 (1990 pp. 68 74.
24. Moore R. E. : Interval Analysis. Prentice Hall, Englewood Cliffs, NJ, 1966.
25. Purcell T. J., Buck I., Mark W. R., Hanrahan P. : Ray tracing on programmable graphics hardware. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH) 21, 3 (2002 703 712.
26. Popov S., Günther J., Seidel H.-P., Slusallek P. : Stackless kd-tree traversal for high performance gpu ray tracing. Computer Graphics Forum 26, 3 (2007). (Proceedings of Eurographics).
27. Perlin K., Hoffert E. M. : Hypertexture. In SIGGRAPH '89: Proceedings of the 16th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1989 ACM Press, pp. 253 262.
28. Paiva A., Lopes H., Lewiner T., De Figueiredo L. H. : Robust adaptive meshes for implicit surfaces. In 19th Brazilian Symposium on Computer Graphics and Image Processing (2006 pp. 205 212.
29. Romeiro F., Velho L., De Figueiredo L. H. : Hardware-assisted rendering of CSG models. In SIBGRAPI (2006 pp. 139 146.
30. Sanjuan-Estrada J. F., Casado L. G., Garcia I. : Reliable algorithms for ray intersection in computer graphics based on interval arithmetic. In XVI Brazilian Symposium on Computer Graphics and Image Processing, 2003. SIBGRAPI 2003 2003 pp. 35 42.
31. Stolte N., Kaufman A. : Voxelization of implicit surfaces using interval arithmetics. Graphical Models 63, 6 (2001 387 412.
32. Toth D. L. : On ray tracing parametric surfaces. In SIGGRAPH '85: Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1985 ACM Press, pp. 171 179.
33. Varadhan G., Krishnan S., Zhang L., Manocha D. : Reliable Implicit surface polygonization using visibility mapping. In SGP '06: Proceedings of the Fourth Eurographics Symposium on Geometry Processing (Aire-la-Ville, Switzerland, Switzerland, 2006 Eurographics Association, pp. 211 221.
34. Van Wijk J. : Ray tracing objects defined by sweeping a sphere. Computers & Graphics 9 (1985 283 290.
35. Wald I., Benthin C., Slusallek P. : OpenRT - A Flexible and Scalable Rendering Engine for Interactive 3D Graphics. Tech. rep., Saarland University, 2002. Available at http://graphics.cs.unisb.de/Publications.
36. Witkin A. P., Heckbert P. S. : Using particles to sample and control implicit surfaces. In SIGGRAPH '94: Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques (New York, NY, USA, 1994 ACM Press, pp. 269 277.
37. Wald I., Ize T., Kensler A., Knoll A., Parker S. G. : Ray tracing animated scenes using coherent grid traversal. ACM Transactions on Graphics 25, 3 (2006 485 493 Proceedings of ACM SIGGRAPH).
38. Wyvill G., Mcpheeters C., Wyvill B. : Data structure for soft objects. The Visual Computer 2 (1986 227 234.
39. Woodwark J., Quinlan K. : The derivation of graphics from volume models by recursive subdivision of object space. In Proceedings of Computer Graphics'80 Conference, Brighton, UK (1980 pp. 335 343.