Fast Non-Linear Projections using Graphics Hardware

1. Fast Non-Linear Projections using Graphics Hardware Jean-Dominique Gascuel, Nicolas Holzschuch, Gabriel Fournier, Bernard Péroche I3D 2008

2. Non-linear projections: What & Why ? [wiki.panotools.org, Ben Kreunen] [lensmateonline.com]

3. [Kautz et al., 2004] Cosine sphere for local shadows [Osman et al., 2006] Dual parabola shadowmaps Motivations [Heidrich & Seidel,1998]Introduced Parabola envmaps

4. Previous work [Kautz 2004] CPU rasterization Close papers: [Fournier 2005] Indirect illumination [Loyd 2006] Logarithmic shadow maps [Hou 2006] Multi perspective reflections [Liu 2007] Non linear beam tracing GPU based, same rendering pipeline & FS

5. Our contributions Targeted to a specific class of non-linear projections • Single center of projection • Convex, C1, and invertible • Each triangle maps to one simple shape. • Simple equations for projected edges. • Fast  ~x2 to x4 times faster than cubemaps or hemicubes. • Everything is done on the GPU

6. Plan • Introduction • Case studies • Sphere projection • Parabola projection • Other projections • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

7. Sphere projection 1/5

8. Sphere projection 2/5

9. Sphere projection 3/5

10. Sphere projection 4/5

11. Sphere projection 5/5

12. Triangles made of known ellipses Looking at the2D screen:

13. Plan • Introduction • Case studies • Sphere projection • Parabola projection • Other projections • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

14. Parabola projection 1/3

15. Parabola projection 2/3

16. Parabola projection 3/3

17. Parabola: 3D line  2D circle 1/2

18. Triangles made of arcs2/2

19. Plan • Introduction • Case studies • Sphere projection • Parabola projection • Other projections • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

20. Other projections… Fisheyes arcs with: • single minimum in normal direction, • possible maximumat extremities.

21. Application-driven choice • Sphere lighting solid angle x cos • Parabola envmaps less distortions • Lambert ambient occlusion  equal area • Fish eye 2 Ideal photographic fish-eye

22. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

23. Rendering strategy

24. FS: Ray-casting FS discards pixels outside original 3D triangle • unproject: 2D fragment coordinates  3D ray direction • ray/triangle intersection

25. FS: Interpolations Mimic linear interpolation inside the 3D triangle  Non-linear interpolation in 2D screen For all vertex varying attributes: normals, colors, texture coordinates, etc. Ray-intersect gives barycentric coordinates α, β  dot product: (1, α, β) . (C0, C1-C0, C2-C0)

26. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Basic Triangle • Near plane Clipping • Concave Covering Triangle • Quad Based Bounding • Demo & Results • Conclusion

27. Bounding triangle 1/2

28. Bounding Triangle 2/2

29. Triangle Covering

30. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Basic Triangle • Near plane Clipping • Concave Covering Triangle • Quad Based Bounding • Demo & Results • Conclusion

31. Camera Plane Clipping 1/3

32. Camera Plane Clipping 2/3

33. Camera Plane Clipping 3/3

34. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Basic Triangle • Near plane Clipping • Concave Covering Triangle • Quad Based Bounding • Demo & Results • Conclusion

35. Concave Covering Triangle 1/2

36. Concave Covering Triangle 2/2 1 input triangle  1 to 4 bounding triangles

37. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

38. Needed because • We don’t have easy tangents for Fisheyes projections • G80 geometry shader take worst case timing:4 output triangles in some rare case  x4 slowdown everywhere in GS…

39. Oriented Bounding Box “Easy” for a single ellipse.

40. Quad coverage scheme Merge extremal points into a single aaBB

41. Parabola projection …Bent triangles are made of circles… • Any axis will work.  optimal axis aligned bounding box

42. Plan • Introduction • Case studies • Rendering Pipeline • Triangle Based Bounding • Quad Based Bounding • Demo & Results • Conclusion

43. Example scenes Lemmings

44. Triangles 37% overdraw

45. Aligned bbox 107% overdraw But FASTER on G80

46. Test scene 2/4 Cubemaps/hemicube

47. Test scene 3/4 Columns = Thin triangles, With large deformations

48. Test scenes 4/4 Sphere – 560K triangles « Real life »

49. Facades Inside the OpenGL pipeline

50. Better quality than cubemaps Heidrich, Laine, Osman Lower memory footprint Low triangle scenes:~ x2 to x4 speedups (better on hi res) Cubemap vs. Parabola-map