logging in or signing up gautron egsr2004 hemispherical GenX Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 167 Category: Product Traini.. License: All Rights Reserved Like it (0) Dislike it (0) Added: June 19, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 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 You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
gautron egsr2004 hemispherical GenX Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 167 Category: Product Traini.. License: All Rights Reserved Like it (0) Dislike it (0) Added: June 19, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 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