Shading

1
Shading Material Appearance
Lots of slides from Addy Ngan
2
Discussion about mass-spring

• Possible topics
• Implementation is hard
• Stability
• Damping
• Euler vs. Runge Kutta
• Constant tuning
• Difficulty of assignments

3
Assignment 4 Ray casting

• Lots of code design, more than for assignment 3
• We give you
• Image class
• VL
• parser
• Ray, Hit classes
• You have to design code
• Object3D, Sphere, plane, triangle
• Group, transform
• Material, diffuse shading
• Camera, orthographic, perspective
• different visualization (color, normal, t)
• Will be used in assignment 5 ray tracing
• Used to be two one-week assignment
• Prove that you can manage your time!

4
Material appearance

• Input for realistic rendering
• Geometry, Lighting and Materials
• Materials appearance
• Color
• Texture
• Intensity and shape of highlights
• Glossiness

Slide Addy Ngan
5
BRDF

• Bidirectional Reflectance Distribution Function
• Ratio of light coming from one directionthat
  gets reflected in another direction
• Focuses on angular aspects, not spatial variation
  of the material
• How many dimensions?

Incoming direction
Outgoing direction
6
BRDF

• Bidirectional Reflectance Distribution Function
• 4D
• 2 angles for each direction
• R(?i ,?i ?o, ?o)

7
Slice at constant incidence

• 2D spherical function

highlight
incoming
incoming
Example Plot of PVC BRDF at 55 incidence
8
Laser demo
9
Unit issues - radiometry

• We will not be too formal in this lecture
• Typical issues
• Directional quantities vs. integrated over all
  directions
• Differential terms per solid angle, per area,
  per time
• Power, intensity, flux

10
Light sources

• Today, we only consider point light sources
• For multiple light sources, use linearity
• We can add the solutions for two light sources
• I(ab)I(a)I(b)
• We simply multiply the solution when we scale the
  light intensity
• I(s a) s I(a)

a
b
11
Light intensity

• 1/r2 falloff
• Why?
• Same power in all concentric circles
• but in graphics we often cheat with or ignore
  this term.
• In particular, 1/(arb) is popular

12
Incoming radiance

• The amount of light received by a surface depends
  on incoming angle
• Bigger at normal incidence
• Similar to Winter/Summer difference
• By how much?
• Cos ? law
• Dot product with normal
• This term is sometimes included in the BRDF,
  sometimes not

n
?
13
Questions?
14
Ideal Diffuse Reflectance

• Assume surface reflects equally in all
  directions.
• An ideal diffuse surface is, at the microscopic
  level, a very rough surface.
• Example chalk, clay, some paints

15
Ideal Diffuse Reflectance

• Ideal diffuse reflectors reflect light according
  to Lambert's cosine law.

16
Ideal Diffuse Reflectance recap

• Single Point Light Source
• kd diffuse coefficient.
• n Surface normal.
• l Light direction.
• Li Light intensity
• r Distance to source

n
?
r
l
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Ideal Diffuse Reflectance More Details

• If n and l are facing away from each other, n l
  becomes negative.
• Using max( (n l),0 ) makes sure that the result
  is zero.
• From now on, we mean max() when we write .
• Do not forget to normalize your vectors for the
  dot product!

18
Questions?
19
Ideal Specular Reflectance

• Reflection is only at mirror angle.
• View dependent
• Microscopic surface elements are usually oriented
  in the same direction as the surface itself.
• Examples mirrors, highly polished metals.

n
?
?
l
r
20
Non-ideal Reflectors

• Real materials tend to deviate significantly from
  ideal mirror reflectors.
• Highlight is blurry
• They are not ideal diffuse surfaces either

21
Non-ideal Reflectors

• Simple Empirical Model
• We expect most of the reflected light to travel
  in the direction of the ideal ray.
• However, because of microscopic surface
  variations we might expect some of the light to
  be reflected just slightly offset from the ideal
  reflected ray.
• As we move farther and farther, in the angular
  sense, from the reflected ray we expect to see
  less light reflected.

22
The Phong Model

• How much light is reflected?
• Depends on the angle between the ideal reflection
  direction and the viewer direction ?.

n
r
?
?
l
Camera
?
v
23
The Phong Model

• Parameters
• ks specular reflection coefficient
• q specular reflection exponent

n
r
?
?
l
Camera
?
v
24
The Phong Model

• Effect of the q coefficient

25
Phong Examples

• The following spheres illustrate specular
  reflections as the direction of the light source
  and the coefficient of shininess is varied.

Phong
26
How to get the mirror direction?
n
r
?
?
l
r
27
The Phong Model

• Sum of three components
• diffuse reflection
• specular reflection
• ambient.

28
Ambient Illumination

• Represents the reflection of all indirect
  illumination.
• This is a total hack!
• Avoids the complexity of global illumination.

29
Putting it all together

• Phong Illumination Model

30
Questions?
31
Adding color

• Diffuse coefficients
• kd-red, kd-green, kd-blue
• Specular coefficients
• ks-red, ks-green, ks-blue
• Specular exponent
• q

32
Fresnel Reflection

• Increasing specularity near grazing angles.

Source Lafortune et al. 97
33
Questions?
34
Material appearance techniques

• BRDF models specular lobe
• Intuition
• maximum when view aligned with the reflected
  light
• Reflection-vector lobe
• (V R)n
• e.g. Phong 75, Lafortune 97
• Half-vector lobe
• (H N)n
• e.g. Ward 92, Cook-Torrance 81

35
Blinn-Torrance Variation of Phong

• Uses the halfway vector h between l and v.

n
h
?
l
Camera
v
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Lobe Comparison

• Half vector lobe
• Gradually narrower when approaching grazing
• Mirror lobe
• Always circular

Half vector lobe
Mirror lobe
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Half vector lobe

• Consistent with what we observe in the dataset.
• More details in our paper

Example Plot of PVC BRDF at 55 incidence
38
Questions?
39
Microfacet Theory

• Example
• Water surface as a microfacet distribution
• Bright pixels
• Microfacets aligned with the vector between sun
  and eye
• But not the ones in shadow
• And not the ones that are occluded

40
Microfacet Theory

• Model surface by tiny mirrors Torrance Sparrow
  1967

41
Microfacet Theory

• Value of BRDF at (L,V) is a product of
• number of mirrors oriented halfway between L and
  V

42
Microfacet Theory

• Value of BRDF at (L,V) is a product of
• number of mirrors oriented halfway between L and
  V

43
Microfacet Theory

• Value of BRDF at (L,V) is a product of
• number of mirrors oriented halfway between L and
  V

44
Microfacet Theory

• Value of BRDF at (L,V) is a product of
• number of mirrors oriented halfway between L and
  V
• ratio of the un(shadowed/masked) mirrors

45
Microfacet Theory

• Value of BRDF at (L,V) is a product of
• number of mirrors oriented halfway between L and
  V
• ratio of the un(shadowed/masked) mirrors
• Fresnel coefficient

46
Microfacet Theory-based Models

• Develop BRDF models by imposing simplifications
  Torrance-Sparrow 67, Blinn 77, Cook-Torrance
  81
• Microfacet normal distribution p(H)
• Gaussian-like

spherical plot of a Gaussian-like p(H)
47
Microfacet Theory-based Models

• Develop BRDF models by imposing simplifications
  Torrance-Sparrow 67, Blinn 77, Cook-Torrance
  81
• Microfacet normal distribution p(H)
• Gaussian-like
• Shadowing/Masking
• Assume V-cavities
• Independent of p(H)

spherical plot of a Gaussian-like p(H)
48
Dark blue paint
Acquired data
Lighting
Material Dark blue paint
49
Dark blue paint
Acquired data
Blinn-Phong
Material Dark blue paint
50
Dark blue paint
Acquired data
Cook-Torrance
Material Dark blue paint
51
Questions?
52
Observations

• Some materials impossible to represent with a
  single lobe

Acquired data
Cook-Torrance
Material Red Christmas Ball
53
Adding a second lobe

• Some materials impossible to represent with a
  single lobe

Acquired data
Cook-Torrance 2 lobes
Material Red Christmas Ball
54
Questions?
55
Anisotropic BRDFs

• Surfaces with strongly oriented microgeometry
  elements
• Examples
• brushed metals,
• hair, fur, cloth, velvet

Source Westin et.al 92
56
Anisotropic measurement

• Extension to Marschner 00, Matusik 03
• Cut multiple strips from material sample at
  different orientations

Cutting material strips at different orientations
57
Anisotropic Materials
Brushed Aluminum
Yellow Satin
Purple Satin
Red Velvet
58
Purple Satin

• Split specular reflection
• Impossible to model with Gaussian-like
  distribution

spherical plot of a Gaussian-like p(H)
Measured data
59
Purple Satin

• Split specular reflection
• Our estimated distribution shows two main peaks

spherical plot of the estimated p(H)
Measured data
60
Purple Satin

• Split specular reflection
• Possible explanation from the microgeometry

spherical plot of the estimated p(H)
Macro photograph cone pairs overlay
61
Questions
62
Spatially-varying materials

• Bidirectional Texture Function (BTF)
• 6D (2D for space, 2D for incoming light, 2D view)

Texture mapped
BTF
Sattler 03
Sattler 03
63
BTFs

• BTF acquired by Addy Ngan

64
Questions?

• Image Addy Ngan

65
Questions?
66
Shaders (Material class)

• Functions executed when light interacts with a
  surface
• Constructor
• set shader parameters
• Inputs
• Incident radiance
• Incident reflected light directions
• surface tangent (anisotropic shaders only)
• Output
• Reflected radiance

67
Shader

• Initially for production (slow) rendering
• Renderman in particular
• Now used for real-time (Games)
• Evaluated by graphics hardware

68
Questions?
69
Procedural Textures

• f (x,y,z) ? color

Image by Turner Whitted
70
Procedural Textures

• Advantages
• easy to implement in ray tracer
• more compact than texture maps (especially for
  solid textures)
• infinite resolution
• Disadvantages
• non-intuitive
• difficult to match existing texture

71
Questions?
Justin Legakis
Ken Perlin
Justin Legakis
72
(No Transcript)
73
BRDFs in the movie industry

• http//www.virtualcinematography.org/publications/
  acrobat/BRDF-s2003.pdf
• For the Matrix movies
• Clothes of the agent Smith are CG, with measured
  BRDF

74
How do we obtain BRDFs?

• Gonioreflectometer
• 4 degrees of freedom

Source Greg Ward
75
BRDFs in the movie industry

• http//www.virtualcinematography.org/publications/
  acrobat/BRDF-s2003.pdf
• For the Matrix movies

gonioreflectometer
Measured BRDF
Measured BRDF
Test rendering
76
Photo
CG
Photo
CG
77
Questions?