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A Novel Hemispherical Basis for Accurate and Efficient Rendering

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Eurographics Symposium on Rendering 2004 15th Eurographics Workshop on Rendering - 21-23 June, Norrk ping, Sweden A Novel Hemispherical Basis for Accurate and ... – PowerPoint PPT presentation

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Title: A Novel Hemispherical Basis for Accurate and Efficient Rendering


1
A Novel Hemispherical Basis for Accurate and
Efficient Rendering
Eurographics Symposium on Rendering 2004
15th Eurographics Workshop on Rendering - 21-23
June, Norrköping, Sweden
  • P. Gautron J. Krivánek
  • S. Pattanaik K. Bouatouch

2
Problem Statement
BRDF
Incoming/Outgoing Radiance
F(?, ?) ? Sample set
3
Problem Statement
?
Original Function
Piecewise linear approximation
Need a more compact and smoothed representation
Better fitting
Fast computation of integrals
4
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
5
Outline
6
Outline
Previous work
Basis functions
Representation of hemispherical functions
The new basis
Definition
Three approaches to hemispherical rotation
Applications
BRDF representation
Environment mapping
Directional radiance caching
7
Basis Functions
8
Spherical Harmonics

9
Spherical Harmonics
Main Properties
Simple projection and reconstruction
Analytical rotations
10
SH For Hemispherical Functions
Zero Hemisphere
Original
SH
Equator discontinuity
Artifacts
11
SH For Hemispherical Functions
Even Reflection Westin92
Least-Squares Approximation Sloan03
Original
Avoid equator discontinuity
Improve accuracy
12
SH For Hemispherical Functions
No rotation
No dot product
13
SH For Hemispherical Functions
Conclusion
Do not fit the hemisphere
Specific improvements
14
Hemispherical Basis Functions
15
Outline
Previous work
Basis functions
Representation of hemispherical functions
The new basis
Definition
Three approaches to hemispherical rotation
Applications
BRDF representation
Environment mapping
Directional radiance caching
16
Our Novel Basis
Spherical Harmonics
17
Our Novel Basis
Shifting
18
Our Novel Basis
Hemispherical Harmonics
19
HSH Rotation
3 Methods
Intuitive conversion of HSH coefficients to SH
Analytic Comparison of SH and HSH basis functions
Brute Force Precomputation of rotation matrices
20
HSH Rotation
Intuitive
HSH
SH
R(SH)
R(HSH)
21
HSH Rotation
Intuitive
RSH
C
C-1
HSH
SH
R(SH)
R(HSH)
Sparse Computed Numerically
22
HSH Rotation
3 Methods
Intuitive conversion of HSH coefficients to SH
Analytic Comparison of SH and HSH basis functions
Brute Force Precomputation of rotation matrices
Reminders
Euler rotation angles
Hemispherical data rotation
23
Eulers Rotation Theorem
 An arbitrary rotation may be described by only
three parameters 
ZYZ Angles
24
HSH Rotation
Rotation Around Vertical Axis
25
HSH Rotation
Rotation Around Other Axes
26
Partial Deletion
Deleting vanishing part
27
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
ßSH arccos(2cos(ßHSH)-1)
28
HSH Rotation
Brute Force
50 Rotation around Y Axis ?
Precomputed Rotation Matrices
29
Outline
Previous work
Basis functions
Representation of hemispherical functions
The new basis
Definition
Three approaches to hemispherical rotation
Applications
BRDF representation
Environment mapping
Directional radiance caching
30
Application BRDF Representation
Principle
BRDF 4D Function
Parabolic Parameterization
31
Application BRDF Representation
32
Application BRDF Representation
Accuracy
Less Ringing
Higher Frequency
SH
HSH
33
Application Environment Mapping
Principle For each vertex
Additional Step
34
Application Environment Mapping
Performance
Rotation on CPU for SH and HSH
Added conversion (sparse matrix)
Accuracy overcomes computational overhead
35
Application Radiance Caching
Irradiance Caching Scheme
Goal computation of indirect diffuse lighting
?
?
36
Application Radiance Caching
Irradiance Caching Scheme
Goal computation of indirect diffuse lighting
37
Application Radiance Caching
Irradiance Caching Scheme
Goal computation of indirect diffuse lighting
Interpolation
38
Application Radiance Caching
Goal computation of indirect glossy lighting
HSH
HSH
39
Application Radiance Caching
Goal computation of indirect glossy lighting
40
Application Radiance Caching
Goal computation of indirect glossy lighting
Interpolation
41
Application Radiance Caching
Goal computation of indirect glossy lighting
?
Incident Radiance
BRDF
? dot product
42
Application Radiance Caching
Results
Low frequency BRDFs
Rotational gradient replaced by rotation
New translational gradients formulas
43
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
44
Perspectives
45
Any Questions ?
Rendered using Radiance Caching
46
Papers Download
A Novel Hemispherical Basis for Accurate and
Efficient Rendering
Radiance Caching for Efficient Global
Illumination Computation
http//www.cgg.cvut.cz/xkrivanj/papers/index.htm
47
BRDF Representation Accuracy
Phong BRDF
48
BRDF Representation Accuracy
Anisotropic Ward BRDF
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