Haik Lorenz, Jürgen Döllner



This paper presents an approach to real-time rendering of non-planar projections with a single center and straight projection rays. Its goal is to provide optimal and consistent image quality. It operates entirely in object space to remove the need for image resampling. In contrast to most other object-space approaches, it does not evaluate non-linear functions on the GPU, but approximates the projection itself by a set of perspective projection pieces. Within each piece, graphics hardware can provide optimal image quality. The result is a coherent and crisp rendering. Procedural textures and stylization effects greatly benefit from our method as they usually rely on screen-space operations. The real-time implementation runs entirely on GPU. It replicates input primitives on demand and renders them into all relevant projection pieces. The method is independent of the input mesh density and is not restricted to static meshes. Thus, it is well suited for interactive applications. We demonstrate it for an analytic and a freely designed projection.


  1. Agrawala, M., Zorin, D., and Munzner, T. (2000). Artistic multiprojection rendering. In Proc. of the Eurographics Workshop on Rendering Techniques 2000, pages 125-136. Springer-Verlag.
  2. Baerentzen, A., Nielsen, S. L., Gjøl, M., Larsen, B. D., and Christensen, N. J. (2006). Single-pass wireframe rendering. In ACM SIGGRAPH 2006 Sketches, page 149. ACM.
  3. Boubekeur, T. and Schlick, C. (2008). A flexible kernel for adaptive mesh refinement on GPU. Computer Graphics Forum, 27(1):102-114.
  4. Brosz, J., Samavati, F. F., Sheelagh, M. T. C., and Sousa, M. C. (2007). Single camera flexible projection. In Proc. of NPAR 7807, pages 33-42. ACM.
  5. Castan˜o, I. (2008). Tesselation of displaced subdivision surfaces in DX11. In XNA Gamefest 2008.
  6. Freudenberg, B., Masuch, M., and Strothotte, T. (2001). Walk-through illustrations: Frame-coherent pen-andink in game engine. In Proc. of Eurographics 2001, pages 184-191.
  7. Gascuel, J.-D., Holzschuch, N., Fournier, G., and Péroche, B. (2008). Fast non-linear projections using graphics hardware. In Symposium on Interactive 3D graphics and games SI3D 7808, pages 107-114. ACM.
  8. Glassner, A. S. (2004a). Digital cubism. IEEE Computer Graphics and Applications, 24(3):82-90.
  9. Glassner, A. S. (2004b). Digital cubism, part 2. IEEE Computer Graphics and Applications, 24(4):84-95.
  10. Heckbert, P. S. (1989). Fundamentals of texture mapping and image warping. Technical report, University of California at Berkeley, Berkeley, CA, USA.
  11. Heidrich, W. and Seidel, H.-P. (1998). View-independent environment maps. In HWWS 7898: Proc. of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, pages 39-45. ACM.
  12. Hoppe, H. (1996). Progressive meshes. In Proc. of SIGGRAPH 7896, pages 99-108. ACM.
  13. Hou, X., Wei, L.-Y., Shum, H.-Y., and Guo, B. (2006). Real-time multi-perspective rendering on graphics hardware. In EUROGRAPHICS Symposium on Rendering. Blackwell Publishing.
  14. Jo, K., Minamizawa, K., Nii, H., Kawakami, N., and Tachi, S. (2008). A GPU-based real-time rendering method for immersive stereoscopic displays. In ACM SIGGRAPH 2008 posters, page 1. ACM.
  15. Löffelmann, H. and Gröller, E. (1996). Ray tracing with extended cameras. Journal of Visualization and Computer Animation, 7(4):211-227.
  16. Lorenz, H. and Döllner, J. (2008). Dynamic mesh refinement on GPU using geometry shaders. In Proc. of the 16th WSCG.
  17. Persson, E. (2007). ATI radeon HD2000 programming guide. Technical report, AMD, Inc.
  18. Popescu, V. and Aliaga, D. G. (2006). The depth discontinuity occlusion camera. In SI3D, pages 139-143. ACM.
  19. Popov, S., Gunther, J., Seidel, H.-P., and Slusallek, P. (2007). Stackless kd-tree traversal for high performance gpu ray tracing. Computer Graphics Forum, 26:415-424.
  20. Rademacher, P. and Bishop, G. (1998). Multiple-center-ofprojection images. In SIGGRAPH, pages 199-206.
  21. Sander, P. V. and Mitchell, J. L. (2005). Progressive Buffers: View-dependent Geometry and Texture for LOD Rendering. In Symposium on Geometry Processing, pages 129-138. Eurographics Association.
  22. Spindler, M., Bubke, M., Germer, T., and Strothotte, T. (2006). Camera textures. In Proc. of the 4th GRAPHITE, pages 295-302. ACM.
  23. Tatarchuk, N. (2007). Real-time tessellation on GPU. In Course 28: Advanced Real-Time Rendering in 3D Graphics and Games. ACM SIGGRAPH 2007.
  24. Tatarinov, A. (2008). Instanced tessellation in DirectX10. In GDC 7808: Game Developers' Conference 2008.
  25. Trapp, M. and Döllner, J. (2008). A generalization approach for 3d viewing deformations of single-center projections. In Proc. of GRAPP 2008, pages 162-170. INSTICC Press.
  26. Wan, L., Wong, T.-T., and Leung, C.-S. (2007). Isocube: Exploiting the cubemap hardware. IEEE Trans. on Vis. and Comp. Graphics, 13(4):720-731.
  27. Wei, L.-Y., Liu, B., Yang, X., Ma, C., Xu, Y.-Q., and Guo, B. (2007). Nonlinear beam tracing on a GPU. Technical report, Microsoft, MSR-TR-2007-168.
  28. Wood, D. N., Finkelstein, A., Hughes, J. F., Thayer, C. E., and Salesin, D. H. (1997). Multiperspective panoramas for cel animation. In Proc. of ACM SIGGRAPH 7897, pages 243-250. ACM Press/AddisonWesley Publishing Co.
  29. Yang, Y., Chen, J. X., and Beheshti, M. (2005). Nonlinear perspective projections and magic lenses: 3d view deformation. IEEE Comput. Graph. Appl., 25(1):76-84.
  30. Yu, J. and McMillan, L. (2004). General linear cameras. In ECCV (2), volume 3022 of Lecture Notes in Computer Science, pages 14-27. Springer.

Paper Citation

in Harvard Style

Lorenz H. and Döllner J. (2009). REAL-TIME PIECEWISE PERSPECTIVE PROJECTIONS . In Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009) ISBN 978-989-8111-67-8, pages 147-155. DOI: 10.5220/0001786401470155

in Bibtex Style

author={Haik Lorenz and Jürgen Döllner},
booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},

in EndNote Style

JO - Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)
SN - 978-989-8111-67-8
AU - Lorenz H.
AU - Döllner J.
PY - 2009
SP - 147
EP - 155
DO - 10.5220/0001786401470155