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Local, Deformable Precomputed Radiance Transfer Peter-Pike Sloan, Ben Luna Microsoft Corporation John Snyder Microsoft Research

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Local Global Illumination Renders GI effects on local details Neglects gross shadowing Rotates transfer model

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Local Global Illumination OriginalRay TracedRotated

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Bat Demo

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illuminateresponse Transfer Vector Precomputed Radiance Transfer (PRT)

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Related Work: Area Lighting [Kautz2004] [James2003] [Ramamoorthi2001] [Sloan2002] [Ng2003] [Liu2004;Wang2004] [Sloan2003] [Muller2004] [Zhou2005]

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Other Related Work Directional Lighting – [Malzbender2001],[Ashikhmin2002] – [Heidrich2000] – [Max1988],[Dana1999] Ambient Occlusion – [Miller1994],[Phar2004] – [Kontkanen2005],[Bunnel2005] Environmental Lighting – [McCallister2002]

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Spherical Harmonics (SH) Spherical Analog to the Fourier basis Used extensively in graphics – [Kajiya84;Cabral87;Sillion91;Westin92;Stam95] Polynomials in R 3 restricted to sphere projection reconstruction

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Spherical Harmonics (SH) Spherical Analog to the Fourier basis Used extensively in graphics – [Kajiya84;Cabral87;Sillion91;Westin92;Stam95] Polynomials in R 3 restricted to sphere projection reconstruction

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Low Frequency Lighting order 1 order 2 order 4 order 8order 16order 32original

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SH Rotational Invariance rotate SH

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Spherical Harmonics (SH) n th order, n 2 coefficients Evaluation O(n 2 )

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Zonal Harmonics (ZH) Polynomials in Z Circular Symmetry

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SH Rotation Structure O(n 3 ) Too Slow!

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ZH Rotation Structure O(n 2 )

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Whats that column? Rotate delta function so that z z : Evaluate delta function at z = (0,0,1) Rotating scales column C by d l – Equals y(z ) due to rotation invariance z z

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Whats that column? Rotate delta function so that z z : Evaluate delta function at z = (0,0,1) Rotating scales column C by d l – Equals y(z ) due to rotation invariance z z

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Efficient ZH Rotation z g(s)g(s)

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z g(s)g(s)

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z z g(s)g(s) g (s)

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Efficient ZH Rotation z z g(s)g(s) g (s)

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Efficient ZH Rotation z z g(s)g(s) g (s)

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Transfer Approx. Using ZH Approximate transfer vector t by sum of N lobes +++

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Transfer Approx. Using ZH Approximate transfer vector t by sum of N lobes

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Transfer Approx. Using ZH Approximate transfer vector t by sum of N lobes Minimize squared error over the sphere

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Single Lobe Solution For known direction s*, closed form solution Optimal linear direction is often good – Reproduces linear, formed by gradient of linear terms – Well behaved under interpolation – Cosine weighted direction of maximal visibility in AO

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Multiple Lobes

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Random vs. PRT Signals

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Energy Distribution of Transfer Signals

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Energy Distribution and Subsurface Scatter

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Rendering Rotate lobe axis, reconstruct transfer and dot with lighting Care must be taken when interpolating – Non-linear parameters – Lobe correspondence with multiple-lobes

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Light Specialized Rendering

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O(N n 2 ) O(N n) Quadratic QuinticQuartic Cubic

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Generating LDPRT Models PRT simulation over mesh – texture: specify patch (a) – per-vertex: specify mesh (b) Parameterized models – ad-hoc using intuitive parameters (c) – fit to simulation data (d) (a) LDPRT texture (b) LDPRT mesh (c) thin-membrane model (d) wrinkle model

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LDPRT Texture Pipeline Start with tileable heightmap Simulate 3x3 grid Extract and fit LDPRT Store in texture maps

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Thin Membrane Model Single degree of freedom (DOF) – optical thickness: light bleed in negative normal direction

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Wrinkle Model Two DOF – Phase, position along canonical wrinkle

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Wrinkle Model Two DOF – Phase, position along canonical wrinkle – Amplitude, max magnitude of wrinkle

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Wrinkle Model Fit Compute several simulations – 64 discrete amplitudes – 255 unique points in phase Fit 32x32 textures – One optimization for all DOF simultaneously – Optimized for bi-linear reconstruction – 3 lobes

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Glossy LDPRT Use separable BRDF Encode each row of transfer matrix using multiple lobes (3 lobes, 4 th order lighting) See paper for details

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Demo

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Conclusions/Future Work local global illumination effects – soft shadows, inter-reflections, translucency easy-to-rotate rep. for spherical functions – sums of rotated zonal harmonics – allows dynamic geometry, real-time performance – may be useful in other applications [Zhou2005] future work: non-local effects – articulated characters

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Acknowledgements Demos/Art: John Steed, Shanon Drone, Jason Sandlin Video: David Thiel Graphics Cards: Matt Radeki Light Probes: Paul Debevec

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