GPGPU: Distance Fields

1. GPGPU: Distance Fields Avneesh Sud and Dinesh Manocha Feb 12, 2007

2. So Far • Overview • Intro to GPGPU using OpenGL • Current Architecture (Cell, G80) • Programming (CUDA, Compilers) • Applications (Vision)

3. Interesting Reading on Parallel Computing • The Landscape of Parallel Computing Research: A View from Berkeley

4. This Lecture • Distance Fields and Voronoi Diagrams • Hands on demo • Advanced: Optimization • Discussion: Why fast on a GPU?

5. This Lecture • Distance Fields and Voronoi Diagrams • Hands on application demo • Parallel algorithm • Example code: 2D • Visual Debugging (imdebug) • Example code: 3D • Advanced: Optimization • Discussion: Why fast on a GPU?

6. Outline • Distance Fields and Voronoi Diagrams • Hands on application demo • Advanced: Optimization • Discussion: Why fast on a GPU?

7. Distance Field Given a set of geometric primitives (sites), it is a scalar field representing the minimum distance from any point to the closest site Sites 2D Distance field

8. Generalized Voronoi Diagram Given a collection of sites, it is a subdivision of space into cells such that all points in a cell are closer to one site than to any other site Voronoi Site Voronoi cell Sites Voronoi diagram

9. Region where distance function contributes to final distance field = Voronoi Region Voronoi Diagram and Distance Fields Distance field Voronoi diagram

10. Distance Functions: 2D A scalar function f (x)representing minimum distance from a point x to a site graph z = f (x,y) f (x,y)=√x2+y2

11. Distance Functions: 3D • Distance function of a site to plane is a quadric Point Site Circular Paraboloid Line Site Elliptic Cone Plane Site Plane

12. Why Should We Compute Them? Collision Detection & Proximity Queries Robot Motion Planning Surface Reconstruction Non-Photorealistic Rendering Surface Simplification Mesh Generation Shape Analysis

13. Why Difficult? • Exact Computation • Compute analytic boundaries Analytic Boundary

14. Why Difficult? • Exact Computation • Compute analytic boundaries • Boundaries composed of high-degree curves and surfaces and their intersections • Complex and difficult to implement • Robustness and accuracy problems

15. Approximate Computation Approximate Algorithms Discretize Sites Discretize Space GPU

16. Outline • Distance Fields and Voronoi Diagrams • Hands on application demo • Parallel algorithm • Example code: 2D • Visual Debugging (imdebug) • Demo: 3D • Advanced: Optimization • Discussion: Why fast on a GPU?

17. Brute-force Algorithm Record ID of the closest site to each sample point Coarsepoint-samplingresult Finerpoint-samplingresult

18. Slight Variation…   =  For each site, compute distances to all sample pts Given sites and uniform sampling Composite through minimum operator Record IDs of closest sites

19. GPU Algorithm…   =  For each site, compute distances to all pixels Given sites and frame buffer Composite through depth test Read-back IDs of closest sites

20. GPU Algorithm: 2D • Demo: Point site Point coord (uniform parameter) Pixel coord

21. GPU Algorithm: 2D Source • Initialization • Setup GL State (Depth, Render Target) • Setup fragment program • Fragment program • Computation: For each point site • Set program parameters • Execute fragment program • Display • Display results

22. GPU Algorithm: 2D Source • Show source … • Compile cg source and show assembly

23. GPU Algorithm: Debugging • Visual debugging with imdebug (by Bill Baxter) • http://www.billbaxter.com/projects/imdebug/index.html • Steps • Modify fragment program • Readback and display buffer contents

24. GPU Algorithm: Debugging • Example

25. GPU Algorithm: 2D • Demo: Line site End-Point coords (uniform parameters) Pixel coord Careful: Equation is to an infinite line

26. GPU Algorithm: 2D • Line segment: Region closer to interior of line segment In remaining region?

27. GPU Algorithm: 3D • Graphics hardware computes one 2D slice • Sweep along 3rd dimension (Z-axis) computing 1 slice at a time 3D Voronoi Diagram

28. Outline • Distance Fields and Voronoi Diagrams • Hands on application demo • Advanced: Optimization • Discussion: Why fast on a GPU?

29. GPU Optimizations • Where to optimize? • Make fragment program run faster • GPU / Application dependent optimizations • Reduce memory bandwidth • Reduce number of invocations of fragment program • Geometric culling

30. GPU Optimizations: Recommended Reading • Practical Performance Analysis and Tuning • GPU Programming Guide • GPU Gems 2 • GPU Computation Strategies and Tips (Ian Buck) • GPU Program Optimization (Cliff Woolley)

31. GPU Optimizations • Where to optimize? • Make fragment program run faster • GPU / Application dependent optimizations • Reduce memory bandwidth • Reduce number of invocations of fragment program • Geometric culling

32. Optimization: Fragment Program • Reduce number of instructions! • Do we need dist(x, p) or dist2(x, p)? • Advantage: dist() requires an additional reciprocal sqrt • Show code + demo

33. Optimization: Fragment Program • Do we need to evaluate (x – p) in fragment program?

34. Optimization: Fragment Program • Do we need to evaluate (x – p) in fragment program? • Rasterization/G80 lectures: GPUs have VERY FAST dedicated hardware for linear interpolation (lerp) • Lerp color, textures, normals across triangle vertices

35. GPU: Linear Interpolation • Color example

36. Optimization: Fragment Program • Evaluate (x – p) at polygon vertices and use dedicated hardware to lerp at each pixel ! • What about line / triangle sites? • Can be linearly interpolated too ! • More details later

37. GPU Optimizations • Where to optimize? • Make fragment program run faster • GPU / Application dependent optimizations • Reduce memory bandwidth • Reduce number of invocations of fragment program • Geometric culling

38. Optimization: Memory Bandwidth • Reduce number of texture lookups, framebuffer writes • Pack data into fewer channels • Is bandwidth limited?

39. Optimization: Memory Bandwidth • Reduce number of texture lookups, framebuffer writes • Pack data into fewer channels • How?

40. Optimization: Memory Bandwidth • Pack data into fewer channels • Using fp32 render target • 32 bit = 4 billion site ids • We can use only 1 channel (red) for writing site id instead of 4 channels (RGBA)

41. GPU Optimizations • Where to optimize? • Make fragment program run faster • GPU / Application dependent optimizations • Reduce memory bandwidth • Reduce number of invocations of fragment program • Geometric culling

42. Linear Factorization Distance vector field: Gives vector from a point in 3D to closest point on a site Line Site Distance Vectors

43. Linear Factorization • Distance functions are non-linear (quadric) • Distance Vectors can be factored into linear terms • Linearly interpolated along each axis

44. Linear Factorization: 2D • Distance vectors are linearly interpolated Line Segment e f

45. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e p

46. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e b p a

47. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e b p a

48. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e b p a

49. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e b p a

50. Linear Factorization: 3D • Distance vectors are bi-linearly interpolated f e e b p a