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##### GPGPU: Distance Fields

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**GPGPU: Distance Fields**Avneesh Sud and Dinesh Manocha Feb 12, 2007**So Far**• Overview • Intro to GPGPU using OpenGL • Current Architecture (Cell, G80) • Programming (CUDA, Compilers) • Applications (Vision)**Interesting Reading on Parallel Computing**• The Landscape of Parallel Computing Research: A View from Berkeley**This Lecture**• Distance Fields and Voronoi Diagrams • Hands on demo • Advanced: Optimization • Discussion: Why fast on a GPU?**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?**Outline**• Distance Fields and Voronoi Diagrams • Hands on application demo • Advanced: Optimization • Discussion: Why fast on a GPU?**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**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**Region where distance function contributes to final distance**field = Voronoi Region Voronoi Diagram and Distance Fields Distance field Voronoi diagram**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**Distance Functions: 3D**• Distance function of a site to plane is a quadric Point Site Circular Paraboloid Line Site Elliptic Cone Plane Site Plane**Why Should We Compute Them?**Collision Detection & Proximity Queries Robot Motion Planning Surface Reconstruction Non-Photorealistic Rendering Surface Simplification Mesh Generation Shape Analysis**Why Difficult?**• Exact Computation • Compute analytic boundaries Analytic Boundary**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**Approximate Computation**Approximate Algorithms Discretize Sites Discretize Space GPU**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?**Brute-force Algorithm**Record ID of the closest site to each sample point Coarsepoint-samplingresult Finerpoint-samplingresult**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**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**GPU Algorithm: 2D**• Demo: Point site Point coord (uniform parameter) Pixel coord**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**GPU Algorithm: 2D Source**• Show source … • Compile cg source and show assembly**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**GPU Algorithm: Debugging**• Example**GPU Algorithm: 2D**• Demo: Line site End-Point coords (uniform parameters) Pixel coord Careful: Equation is to an infinite line**GPU Algorithm: 2D**• Line segment: Region closer to interior of line segment In remaining region?**GPU Algorithm: 3D**• Graphics hardware computes one 2D slice • Sweep along 3rd dimension (Z-axis) computing 1 slice at a time 3D Voronoi Diagram**Outline**• Distance Fields and Voronoi Diagrams • Hands on application demo • Advanced: Optimization • Discussion: Why fast on a GPU?**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**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)**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**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**Optimization: Fragment Program**• Do we need to evaluate (x – p) in fragment program?**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**GPU: Linear Interpolation**• Color example**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**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**Optimization: Memory Bandwidth**• Reduce number of texture lookups, framebuffer writes • Pack data into fewer channels • Is bandwidth limited?**Optimization: Memory Bandwidth**• Reduce number of texture lookups, framebuffer writes • Pack data into fewer channels • How?**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)**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**Linear Factorization**Distance vector field: Gives vector from a point in 3D to closest point on a site Line Site Distance Vectors**Linear Factorization**• Distance functions are non-linear (quadric) • Distance Vectors can be factored into linear terms • Linearly interpolated along each axis**Linear Factorization: 2D**• Distance vectors are linearly interpolated Line Segment e f**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e p**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e b p a**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e b p a**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e b p a**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e b p a**Linear Factorization: 3D**• Distance vectors are bi-linearly interpolated f e e b p a