gautron egsr2004 hemispherical

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Published on June 19, 2007

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A Novel Hemispherical Basis for Accurate and Efficient Rendering:  A Novel Hemispherical Basis for Accurate and Efficient Rendering P. Gautron J. Křivánek S. Pattanaik K. Bouatouch Eurographics Symposium on Rendering 2004 15th Eurographics Workshop on Rendering - 21-23 June, Norrköping, Sweden Problem Statement:  Problem Statement BRDF Incoming/Outgoing Radiance F(, )  Sample set Problem Statement:  Problem Statement Original Function Piecewise linear approximation  Need a more compact and smoothed representation Better fitting Fast computation of integrals Contribution:  Contribution New set of basis functions Formula similar to Spherical Harmonics Designed for representing hemispherical functions Several rotation methods for projected functions Applications in lighting simulation Outline:  Outline Outline:  Outline Previous work Three approaches to hemispherical rotation Applications BRDF representation Environment mapping Directional radiance caching Basis functions Representation of hemispherical functions The new basis Definition Basis Functions:  Basis Functions Spherical Harmonics:  Spherical Harmonics = Spherical Harmonics:  Spherical Harmonics Main Properties Simple projection and reconstruction Analytical rotations SH For Hemispherical Functions:  SH For Hemispherical Functions Zero Hemisphere Equator discontinuity Artifacts Original SH SH For Hemispherical Functions:  SH For Hemispherical Functions Improve accuracy Avoid equator discontinuity Original Even Reflection [Westin92] Least-Squares Approximation [Sloan03] SH For Hemispherical Functions:  SH For Hemispherical Functions No rotation No dot product SH For Hemispherical Functions:  SH For Hemispherical Functions Conclusion Do not fit the hemisphere Specific improvements Hemispherical Basis Functions:  Hemispherical Basis Functions Outline:  Outline Previous work Three approaches to hemispherical rotation Applications BRDF representation Environment mapping Directional radiance caching Basis functions Representation of hemispherical functions The new basis Definition Our Novel Basis:  Our Novel Basis Spherical Harmonics Our Novel Basis:  Our Novel Basis Shifting Our Novel Basis:  Our Novel Basis Hemispherical Harmonics HSH Rotation:  HSH Rotation Intuitive: conversion of HSH coefficients to SH Analytic: Comparison of SH and HSH basis functions Brute Force: Precomputation of rotation matrices 3 Methods HSH Rotation:  HSH Rotation Intuitive HSH SH R(SH) R(HSH) HSH Rotation:  HSH Rotation Intuitive HSH SH R(SH) R(HSH) C RSH C-1 Sparse Computed Numerically HSH Rotation:  HSH Rotation Intuitive: conversion of HSH coefficients to SH Analytic: Comparison of SH and HSH basis functions Brute Force: Precomputation of rotation matrices 3 Methods Reminders: Euler rotation angles Hemispherical data rotation Euler’s Rotation Theorem:  Euler’s Rotation Theorem « An arbitrary rotation may be described by only three parameters » ZYZ Angles HSH Rotation:  HSH Rotation Rotation Around Vertical Axis HSH Rotation:  HSH Rotation Rotation Around Other Axes Partial Deletion:  Partial Deletion Deleting vanishing part HSH Rotation:  HSH Rotation Analytic Idea: Use SH rotation matrices HSH-projected function SH-projected function using same coefficients SH rotation Impact of SH rotation on HSH projected function βSH = arccos(2cos(βHSH)-1) HSH Rotation:  HSH Rotation Brute Force Precomputed Rotation Matrices 50° Rotation around Y Axis ? Outline:  Outline Previous work Three approaches to hemispherical rotation Applications BRDF representation Environment mapping Directional radiance caching Basis functions Representation of hemispherical functions The new basis Definition Application: BRDF Representation:  Application: BRDF Representation Principle BRDF = 4D Function Parabolic Parameterization Application: BRDF Representation:  Application: BRDF Representation Application: BRDF Representation:  Application: BRDF Representation SH HSH Less Ringing Higher Frequency Accuracy Application: Environment Mapping:  Application: Environment Mapping Principle For each vertex Additional Step Application: Environment Mapping:  Application: Environment Mapping Performance Rotation on CPU for SH and HSH Added conversion (sparse matrix) Accuracy overcomes computational overhead Application : Radiance Caching:  Application : Radiance Caching Goal : computation of indirect diffuse lighting Irradiance Caching Scheme   Application : Radiance Caching:  Application : Radiance Caching Goal : computation of indirect diffuse lighting Irradiance Caching Scheme Application : Radiance Caching:  Application : Radiance Caching Interpolation Goal : computation of indirect diffuse lighting Irradiance Caching Scheme Application : Radiance Caching:  Application : Radiance Caching HSH HSH Goal : computation of indirect glossy lighting Application : Radiance Caching:  Application : Radiance Caching Goal : computation of indirect glossy lighting Application : Radiance Caching:  Application : Radiance Caching Interpolation Goal : computation of indirect glossy lighting Application : Radiance Caching:  Application : Radiance Caching Incident Radiance BRDF  dot product  Goal : computation of indirect glossy lighting Application : Radiance Caching:  Application : Radiance Caching Low frequency BRDFs New translational gradients formulas Rotational gradient replaced by rotation Results Conclusion:  Conclusion New basis more accurate than SH 3 methods for computing rotations Easy to use in SH applications : BRDF Representation, Environment Mapping, Global Illumination More details on Radiance Caching in « Radiance Caching for Efficient Global Illumination Computation » (J. Krivanek, P. Gautron, S. Pattanaik, K. Bouatouch) IRISA Technical Report #1623 Perspectives:  Perspectives Any Questions ?:  Any Questions ? Rendered using Radiance Caching Papers Download:  Papers Download http://www.cgg.cvut.cz/~xkrivanj/papers/index.htm A Novel Hemispherical Basis for Accurate and Efficient Rendering Radiance Caching for Efficient Global Illumination Computation BRDF Representation Accuracy:  BRDF Representation Accuracy Phong BRDF BRDF Representation Accuracy:  BRDF Representation Accuracy Anisotropic Ward BRDF

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