Local, Deformable Precomputed Radiance Transfer

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
Liu2004Wang2004
7
Other Related Work

• Directional Lighting
• Malzbender2001,Ashikhmin2002
• Heidrich2000
• Max1988,Dana1999
• Ambient Occlusion
• Miller1994,Phar2004
• Kontkanen2005,Bunnel2005
• Environmental Lighting
• McCallister2002

8
Spherical Harmonics (SH)

• Spherical Analog to the Fourier basis
• Used extensively in graphics
• Kajiya84Cabral87Sillion91Westin92Stam95
• Polynomials in R3 restricted to sphere

projection
reconstruction
9
Spherical Harmonics (SH)

• Spherical Analog to the Fourier basis
• Used extensively in graphics
• Kajiya84Cabral87Sillion91Westin92Stam95
• Polynomials in R3 restricted to sphere

projection
reconstruction
10
Low Frequency Lighting
order 1
order 2
order 4
order 8
order 16
order 32
original
11
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
Whats 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
Whats 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
Efficient ZH Rotation
g(s)
19
Efficient ZH Rotation
g(s)
20
Efficient ZH Rotation
g(s)
g(s)
21
Efficient ZH Rotation
g(s)
g(s)
22
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(N n2) ? O(N n)
Quintic
Quartic
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
Glossy LDPRT

• Use separable BRDF
• Encode each row of transfer matrix using
  multiple lobes (3 lobes, 4th order lighting)
• See paper for details

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