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Physically-based Illumination Models (2)

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Physically-based Illumination Models (2) CPSC 591/691 Bump Mapping Map texture values to perturbations of surface normals Bump Mapping Map texture values to ... – PowerPoint PPT presentation

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Title: Physically-based Illumination Models (2)


1
Physically-based Illumination Models (2)
  • CPSC 591/691

2
Better (Realistic) Local Illumination Models
  • Blinn-Torrance-Sparrow (1977)
  • isotropic reflectors with smooth microstructure
  • Cook-Torrance (1982)
  • wavelength dependent Fresnel term
  • Kajiya (1985)
  • Cabral-Max-Springmeyer (1987)
  • Anisotropic surfaces
  • Wolff (1990)
  • adds polarization
  • He-Torrance-Sillion-Greenberg (1991)
  • adds polarization, statistical microstructure,
    self-reflectance

3
Phong Lighting Model

4
Cook-Torrance Lighting Model

5
Cook-Torrance Illumination Model (summary)
A linear combination of a number of completely
different models and approximations
AMBIENT term ? to approximate global illumination
  • SPECULAR term
  • Fresnel term ? gives dependence of specular
    intensity and color on incidence angle
  • Microfacet model term ? spreads the specular
    intensity, giving an off-specular bump

Lambertian DIFFUSE term ? model color
6
  • D ? statistical distribution function of the
    microfacets slope
  • G ? geometric attenuation term, which deals with
    how the individual microfacets shadow and mask
    each other.
  • F ? Fresnel term deals with the amount of light
    that is reflected versus absorbed as the incident
    angle changes (an example of this is often seen
    when driving on a straight road, and the road
    appearing mirror-like when viewed from grazing
    angles).

7
Lambertian Lighting Model (diffuse)
8
Attenuation Term
The fraction of light that reaches the surface as
an effect of light attenuation.
c1, c2, c3 The coefficients for constant, linear
and quadratic attenuation of the light source,
respectively.
d the distance to the light
9
Lambertian Lighting Model (diffuse)
10
Oren-Nayar Lighting Model

11
Oren-Nayar Lighting Model
"Generalization of the Lambertian Model and
Implications for Machine Vision," S. K. Nayar
and M. Oren, International Journal of Computer
Vision, Vol. 14, pp. 227-251, 1995.
12
Oren-Nayar Lighting Model
  • BRDF to generalize the Lambertian diffuse
    lighting model.
  • This BRDF can reproduce several rough surfaces
    very well, including wall plaster, sand, sand
    paper, clay, and others.
  • Very computationally expensive, and it requires
    the calculation of azimuth and zenith angles.

13
Minnaert Lighting Model

14
Minnaert Lighting Model
Lambertian lighting
Darkening factor
  • Minnaert added darkening limbs to the lighting
    equations to make the surface seem darker from
    certain viewing/lighting directions.
  • This effect is seen in some types of clothing
    (such as velvet).

15
Phong Lighting Model

16
Cook-Torrance Lighting Model

17
Blinn Lighting Model

18
Blinn Lighting Model
  • BRDF to generalize the Lambertian diffuse
    lighting model.
  • This BRDF can reproduce several rough surfaces
    very well, including wall plaster, sand, sand
    paper, clay, and others.
  • Very computationally expensive, and it requires
    the calculation of azimuth and zenith angles.

19
Remaining Hard Problems
  • Reflective Diffraction Effects
  • thin films
  • feathers of a blue jay
  • oil on water
  • CDs
  • Anisotropy
  • brushed metals
  • strands pulled materials
  • Satin and velvet cloths

20
Cook-Torrance Illumination Model (summary)
Microfacet model term ? spreads the specular
intensity, giving an off-specular bump
  • NOT entirely satisfactory
  • It is based on a one-dimensional
    cross-sectional model

21
Isotropic, Anisotropic Surfaces
  • An isotropic surface has the property that for
    any given point on the surface, the light
    reflected does not change when the surface is
    rotated about the normal
  • This is the case for many materials, but some
    materials such as brushed metal or hair this is
    not the case.
  • The reason for these anisotropic surfaces is that
    the micro facets that make up the surface have a
    preferred direction in the form of parallel
    grooves or scratches

22
Isotropic Surfaces
Tiny random bumps in the surface of the floor,
bumps possibly so small that you may not notice
the bumps, but you will notice their affect on
the reflection.
23
Anisotropic Surfaces
So now, what happens if these tiny bumps are in a
regular pattern? For example, brushed metals are
metals that have small grooves that all head in
the same direction. This causes reflections to
blur in a specific direction.
24
Real world brushed metal
25
Real world brushed metal
26
Real world example of a Christmas ornament
that's made up of fine synthetic hairs that all
travel in one direction
27
Wards Anisotropic Lighting Model

28
Wards Anisotropic Lighting Model
  • The X and Y terms are two perpendicular tangent
    directions on the surface.
  • They give represent the direction of the grooves
    in the surface.
  • The ? terms are the standard deviations of the
    slope in the X and Y direction (given by their
    respective subscripts).

29
Better (Realistic) Local Illumination Models
  • Blinn-Torrance-Sparrow (1977)
  • isotropic reflectors with smooth microstructure
  • Cook-Torrance (1982)
  • wavelength dependent Fresnel term
  • Kajiya (1985)
  • Cabral-Max-Springmeyer (1987)
  • Anisotropic surfaces
  • Wolff (1990)
  • adds polarization
  • He-Torrance-Sillion-Greenberg (1991)
  • adds polarization, statistical microstructure,
    self-reflectance

30
An Explicit Microfacet Model
  • Cabral, B., Max, N., Springmeyer, R.,
    Bidirectional Reflection Functions From Surface
    Bump Maps, SIGGRAPH 87, pp. 273-281
  • Construction of a surface of triangular
    microfacets
  • Reflection model
  • Pre-calculation (rather than simulation by a
    parametric distribution or function)
  • Table of reflectivities

31
Explicit Microfacet Model (Cabral et al 87)
  • Any surface whose microstructure can be
    represented can be modeled
  • Microstructure isotropic or anisotropic
  • Less restricted than using statistical
    distribution (Cook and Torrance)

32
Nature of the Microstructure
  • Controlled by varying size and vertex
    perturbation of triangular microfacets
  • Triangular microfaces construction bump map or
    height field (2D array of vertex heights)
  • Heights can be distributed in any desired way

33
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34
Bump Mapping
Map texture values to perturbations of surface
normals
35
Bump Mapping
Map texture values to perturbations of surface
normals
Straight Phong Shading
?approximates smoothly curved surface
Straight Phong Shading
Phong with bump mapping
?approximates smoothly curved surface
approximates bumpy surface
36
Irradiated Surface Element
Area
Normal
Mirror direction
37
Reflectivity Function
? sum of delta functions
Contribute a delta function
38
Reflectivity Function How to Build the
Information?
39
Max, N., "Horizon mapping shadows for
bump-mapped surfaces Visual Computer, 1988
40
Illuminating flux density
Fresnel factor
Energy incident on a microfacet
Max, N., "Horizon mapping shadows for
bump-mapped surfaces Visual Computer, 1988
41
How About for ALL microfacets?
42
N 24
43
N 24
44
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45
Energy flowing through one cell
46
returns the index of the cell hit by a ray fired
in direction R.
Mirror direction
Kronecker delta function
47
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48
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49
More than one microfacet is likely to contribute
energy to cell k
50
Energy incident to a microfacet
Energy flowing through one cell
Solid angle of cell k
51
FinallyTable of Reflectivities
52
Reflectivity
53
The fraction of incoming flux reflected by facet
Si
54
Gi ? the fraction of incoming flux reflected by
facet Si
Energy incident on a microfacet
55
Energy incident to a microfacet
Energy flowing through one cell
Solid angle of cell k
56
Energy incident to a microfacet
Energy flowing through one cell
57
Better (Realistic) Local Illumination Models
  • Blinn-Torrance-Sparrow (1977)
  • isotropic reflectors with smooth microstructure
  • Cook-Torrance (1982)
  • wavelength dependent Fresnel term
  • Kajiya (1985)
  • Cabral-Max-Springmeyer (1987)
  • Anisotropic surfaces
  • Wolff (1990)
  • adds polarization
  • He-Torrance-Sillion-Greenberg (1991)
  • adds polarization, statistical microstructure,
    self-reflectance
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