Rendering Geometry with Relief Textures

1. Rendering Geometry withRelief Textures L.Baboud X.Décoret ARTIS-GRAVIR/IMAG-INRIA

2. Height-field representation • What can we represent? • How to render it? • Fast ? • Exact? • Previous work • Our contributions

3. Height-field • Function from [0,1]2 to [0,1] • Represents a surface • Sampled in a texture • Memory/GPU efficient (a) Height texture (b) Reconstructed surface

4. Height-field • Function from [0,1]2 to [0,1] • Represents a surface • Sampled in a texture • Memory/GPU efficient (a) nearest • Theory: How do you reconstruct? • Practice: Which interpolation for texture lookups? (b) linear Refer to the paper for details

5. How to render? • Polygonalize • Simple & natural • Costly, not output sensitive • Aliasing -> LOD Small coverage • What if the object is not the “main” one? • Bump • Small objects Large coverage

6. How to render? • Polygonalize • Simple & natural • Costly, not output sensitive • Aliasing -> LOD • Ray-tracing • Slow? Feasible on GPU! • Output sensitive

7. Ray-tracing • Existing solution : VDM [Wang 2003] • Sampling in all viewing directions • Memory costly (4 Mb compressed for 128x128) • Use GPU capabilities instead

8. Principle (1/2) Top view 2D slice

9. Principle (2/2) • Comparing heights • Along ray • In the heightfield • Until we pass below

10. Policarpo [I3D 05] Binary search How many iterations? Is it correct?

11. Missed intersection Policarpo [I3D 05]

12. Policarpo [I3D 05] Fixed size steps Binary search Better but still potentially false

13. Policarpo [I3D 05] Fixed size steps Binary search Missed intersection Amounts to vertical slicing Size of steps along the ray depends on ray tilt

14. Policarpo [I3D 05]

15. Tatarchuk [I3D06] • Varying size steps (between two bounds) • Depending on ray tilt

16. Use it for bump Conclusion on existing methods • Advantages : speed • Drawbacks : missed intersections (at grazing angles) Policarpo05 Tatarchuk06

17. Being exact, what for? • Intellectually rewarding  • Usability large scale geometry • Terrain, buildings, architectural details • Objects (cars, etc.) How many polygons ?

18. Being exact, what for? • Intellectually rewarding  • Usability large scale geometry • Terrain, buildings, architectural details • Objects (cars, etc.) Only 6 quads !

19. Being exact, is it hard? • Problem with constant steps • Can always miss intersections

20. Being exact, is it hard? • Problem with constant steps • Can always miss intersections • Travel slowly above empty space

21. Being exact, is it hard? • Problem with constant steps • Can always miss intersections • Travel slowly above empty space • Our contributions • Amanatides based approach • Failsafe approach • But requires preprocess solves

22. Adapted Amanatides traversal • We run along the ray on texel edges

23. Adapted Amanatides traversal • We run along the ray on texel edges • Advantages : • very simple iterations • exact intersection fragment shader main loop

24. Adapted Amanatides traversal • We run along the ray on texel edges • Advantages : • very simple iterations • exact intersection • Drawbacks : • potentially many iterations • texture resolution dependent

25. Adapted Amanatides traversal • Texture resolution dependent • Double resolution  half speed • Ideally should depend on “variations” of heightfield, not sampling frequency • Binary search doesn’t have this drawback • Constant number of texture lookups

26. Analysis of binary search • At the moment we pass below • At least one intersection • But potentially several ? 2D slice

27. Analysis of binary search • At the moment we pass below • At least one intersection • But potentially several • Ideally : at most one intersection ? 2D slice How can we guarantee this? Precompute safety radius

28. What is safety radius ? • Local information Which step ? T Precomputed radius ? For any possible viewing ray passing above T Top view

29. considered texel Safety radius What is safety radius ? • Local information Viewing direction

30. What is safety radius ? • Local information • In 3D : for each texel : • Scan every direction • Keep the minimum radius

31. Failsafe binary search

32. Failsafe binary search

33. Failsafe binary search

34. Failsafe binary search

35. Failsafe binary search

36. Failsafe binary search

37. Failsafe binary search

38. Failsafe binary search

39. Failsafe binary search

40. Failsafe binary search

41. Various details • Textures • Can have different resolutions • Normal, color, height • Can be packed/compressed • Needs recent fragment shaders supporting dynamic loops

42. Results • Fast and exact • Height-field regularity dependent • Correct interaction with Z-buffer • Output sensitive

43. Height-field representation • What can we represent? • How to render it? • Fast ? • Exact? • Previous work • Our contributions

44. More than bump • Previous methods : small scale bump • Curved surfaces : warping considerations • VDM [Wang 03] • [Policarpo05] • We want to do large scale • Problem : limited expressiveness • orthogonal height-fields

45. Expressiveness of heightfields • Lack of samples on vertical sides

46. Projective height-fields

47. Projective height-fields • Similar to “cubist images” [Hanson 98] • Projective transforms preserve lines • Unmodified algorithm

48. Projective height-fields • Wasted fillrate • Many eventually discarded fragments • Easy to solve : clip the bounding box (b) clipped (a) not clipped

49. Multiple height-fields

50. Conclusion • Remember fast and exact is possible! • Efficient representation • Small memory footprint • Automatic LOD • Two useful methods (dynamic/static)