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Local, Deformable Precomputed Radiance Transfer

This research focuses on local details in global illumination renders using Precomputed Radiance Transfer (PRT). The study rotates transfer models to enhance illumination effects by neglecting gross shadowing. Through the use of Spherical Harmonics (SH) and Zonal Harmonics (ZH), the method efficiently handles lighting orders and rotations for improved lighting accuracy. Various models like Thin Membrane and Wrinkle models are utilized for realistic lighting simulation. The process involves generating LDPRT models over meshes and optimizing textures to achieve accurate lighting effects. The study concludes with promising results for both current and future applications in dynamic geometry rendering.

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Local, Deformable Precomputed Radiance Transfer

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

  2. “Local” Global Illumination Renders GI effects on local details Rotates transfer model Neglects gross shadowing

  3. “Local” Global Illumination Original Ray Traced Rotated

  4. Bat Demo

  5. Precomputed Radiance Transfer (PRT) Transfer Vector illuminate response

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

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

  8. Spherical Harmonics (SH) • Spherical Analog to the Fourier basis • Used extensively in graphics • [Kajiya84;Cabral87;Sillion91;Westin92;Stam95] • Polynomials in R3 restricted to sphere projection reconstruction

  9. Spherical Harmonics (SH) • Spherical Analog to the Fourier basis • Used extensively in graphics • [Kajiya84;Cabral87;Sillion91;Westin92;Stam95] • Polynomials in R3 restricted to sphere projection reconstruction

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

  11. SH SH SH Rotational Invariance rotate rotate

  12. Spherical Harmonics (SH) nth order, n2 coefficients Evaluation O(n2)

  13. Zonal Harmonics (ZH) Polynomials in Z Circular Symmetry

  14. SH Rotation Structure O(n3) Too Slow!

  15. ZH Rotation Structure O(n2)

  16. What’s that column? z Rotate delta function  so that z→ z’ : • Evaluate delta function at z = (0,0,1) • Rotating scales column C by dl • Equals y(z’) due to rotation invariance z’

  17. What’s that column? z Rotate delta function  so that z→ z’ : • Evaluate delta function at z = (0,0,1) • Rotating scales column C by dl • Equals y(z’) due to rotation invariance z’

  18. z Efficient ZH Rotation g(s)

  19. z Efficient ZH Rotation g(s)

  20. z z’ Efficient ZH Rotation g’(s) g(s)

  21. z z’ Efficient ZH Rotation g’(s) g(s)

  22. z z’ Efficient ZH Rotation g’(s) g(s)

  23. + + + Transfer Approx. Using ZH • Approximate transfer vector t by sum of N “lobes”

  24. Transfer Approx. Using ZH • Approximate transfer vector t by sum of N “lobes”

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

  26. 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

  27. Multiple Lobes

  28. Random vs. PRT Signals

  29. Energy Distribution of Transfer Signals

  30. Energy Distribution and Subsurface Scatter

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

  32. Light Specialized Rendering

  33. Light Specialized Rendering

  34. Light Specialized Rendering

  35. Light Specialized Rendering

  36. Light Specialized Rendering Quadratic Cubic O(Nn2) → O(Nn) Quartic Quintic

  37. 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 (d) wrinkle model (c) thin-membrane model

  38. LDPRT Texture Pipeline • Start with “tileable” heightmap • Simulate 3x3 grid • Extract and fit LDPRT • Store in texture maps

  39. Thin Membrane Model • Single degree of freedom (DOF) • “optical thickness”: light bleed in negative normal direction

  40. Wrinkle Model • Two DOF • Phase, position along canonical wrinkle

  41. Wrinkle Model • Two DOF • Phase, position along canonical wrinkle • Amplitude, max magnitude of wrinkle

  42. 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

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

  44. Demo

  45. 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

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

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