gautron egsr2004 hemispherical

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