Light and Matter
For Computer Graphics
Comp 770 Lecture
Spring 2009
Overview
 A very high-level introduction to some concepts
and definitions underlying image synthesis.
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Optics
Materials and Surfaces
Radiometry and Photometry
Color
Energy Transport
Optics
 The study of light has 3 sub-fields.
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Physical optics: study of the wave nature of light.
Geometric optics: study of the particle nature of light.
Quantum optics: study of the dual wave-particle nature of
light and attempt to construct unified theories to support
duality. Wave “packets” called photons.
 Computer graphics most concerned with geometric
optics (but need some of the others, too).
Reflection and Transmission
 Reflection: “process whereby light of a specific
wavelength incident on a material is at least partly
propagated outward by the material without change in
wavelength.”
 Transmission (or refraction): “process whereby light of a
specific wavelength incident on the interface (boundary)
between two materials passes (refracts) through the
interface without change in wavelength.”
(Definitions from Glassner1995).
Types of Reflection
 Specular (a.k.a. mirror or regular) reflection
causes light to propagate without scattering.
 Diffuse reflection sends light in all directions with
equal energy.
 Mixed reflection is a weighted
combination of specular and diffuse.
Types of Reflection
 Retro-reflection occurs when incident energy
reflects in directions close to the incident
direction, for a wide range of incident directions.
 Gloss is the property of a material surface that
involves mixed reflection and is responsible for
the mirror like appearance of rough surfaces.
Types of Gloss
 Gloss factors measured by the ratio of energy
() in the reflected and incident directions for
certain standard angles (i and r).
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Specularity measures the brightness of a highlight:
r /i (i = r = 60°).
Sheen measures the brightness of glancing
highlights: r /i (i = r = 85°).
Types of Gloss
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Contrast is the brightness of a glancing highlight relative to
the brightness in the surface normal direction
r /n. (i = r = 85°).
Distinctness of Image measures the clarity of the highlight or
the sharpness of its borders: dr / dr , or the rate of change
of reflected energy with reflected direction.
Absence of Bloom measures the haziness around the
highlight: r2 /r1, where r1 and r2 are only a few degrees
different.
Computing The Specular Reflection Vector
N
Given: I, N, R are coplanar. IN = R N
I
R
i
r
N’ = (I N)N
From the parallelogram shown at right, see:
R + I = 2N’
Or
R = 2N’ – I = 2(I N)N - I
N’
I
N’
R
Types of Transmission
 Specular transmission causes light to propagate
w/o scattering, as in clear
glass.
 Diffuse transmission sends light in all directions
with equal energy, as in
frosted glass.
 Mixed transmission is a weighted combination of
specular and diffuse transmission.
Index of Refraction
 The speed of light is not the same in all media.
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Reference medium is a perfect vacuum.
IOR: i() = c / v. c = speed of light in vacuum, v is speed
of light of wavelength  in the medium.
 Surface where two media touch called the interface.
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Light appears to bend when passing through the interface,
due to change in speed.
Amount of bending, or refraction, determined by the IOR of
both materials.
Snell’s Law of Refraction
 Governs the geometry of refraction.
i()sini = t()sint
i = IOR of incident medium
t = IOR of medium into which
the light is transmitted
If the light is transmitted into
a denser medium, it is refracted
toward the normal of the interface.
 If the light is transmitted into a rarer
medium, it is refracted away from the
normal of the interface.
sini
N
I
i

t
sint
T
Total Internal Reflection
 At some angle, called the critical angle, light is
bent to lie exactly in the plane of the interface.
 At all angles greater than this, the light is
reflected back into the incident medium: total
internal reflection (TIR).
 Snell’s law gives critical angle c
i()sinc = t()sin( / 2)
sinc = t () / i()
Computing The Specular Transmission Vector
I   I  cos  i  N
I   sin  i , T  cos  t , T||  sin  t , so :
M 

1
I  cos  i  N
sin  i

T  T  T||  M sin  t  N cos  t 
Apply Snell' s Law :



 sin  t
I  cos  i  N  N cos  t
sin  i
sin  t i

sin  i t

2
2
 
 
cos  t  1  sin 2  t  1   i  sin 2  i  1   i  1  cos 2  i
 t 
 t 
Substituti ng :
2

 



T   i I  N  i cos  i  1   i  1  cos 2  i  
t
 t

 t 



If 1   i
 t
2

 1  cos 2  i is negative, TIR has occurred.



R
i I||




 i I  cos  i  N  N cos  t   i I  N  i cos  i  cos  t 
t
t
 t


N
I

-M

T
I
M
T|| t
T
Surface Models
 Perfect mirrors and reflections don’t exist.
 Perfect transmission requires a perfect vacuum.
 Real surfaces have some degree of roughness.
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Even most basic simulation must account for specular and
diffuse reflection / transmission.
More realism requires accounting for more factors.
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Wavelength dependence: dispersion, diffraction, interference
Anisotropy: angular-dependence of reflectance.
Scattering: absorption and re-emission of photons.
Basic Surface Models
 Non-physically based, as used in OpenGL.
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Materials have ambient, diffuse, and specular colors.
Ambient is a very coarse approx. Of light reflected
from other surfaces. (Global illumination).
Diffuse usually just the “color” of the surface.
Specular determines highlight color.
Basic Surface Models
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C  Ag As  Es   Dli Ds ( N  Li )  Ali As
i
C  color
A  ambient; E  emissive; D  diffuse;
N  normal vector; Li  light vect or
g  global; s  surface; l  light.
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What’s Missing?
 What we’ve seen so far is just the basics of
geometric optics.
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Enough for classical ray tracing, Phong illumination
model.
To get much better, we need more:
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Better modeling of surface properties.
Wavelength dependence.
Radiometry / Photometry.
Energy Transport.
Surface Roughness
 At a microscopic scale, all real surfaces are rough:
 Cast shadows on themselves:
 “Mask” reflected light:
shadow
shadow
Masked Light
Surface Roughness
 Notice another effect of roughness:
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Each “microfacet” is treated as a perfect mirror.
Incident light reflected in different directions by
different facets.
End result is mixed reflectance.
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Smoother surfaces are more specular or glossy.
Random distribution of facet normals results in diffuse
reflectance.
Reflectance Distribution Model
 Most surfaces exhibit complex reflectances.
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Vary with incident and reflected directions.
Model with combination:
+
+
=
specular + glossy + diffuse = reflectance distribution
Anisotropy
 So far we’ve been considering isotropic
materials.
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Reflection and refraction invariant with respect to
rotation of the surface about the surface normal
vector.
For many materials, reflectance and transmission
are dependent on this azimuth angle: anisotropic
reflectance/transmission.
Examples?
BRDF
 Bidirectional Reflectance Distribution Function
 (x, i, o)
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x is the position.
i = (i, i) represents the incoming direction.
(elevation, azimuth)
o = (o, o) represents the outgoing direction
(elevation, azimuth)
Properties of the BRDF
 Dependent on both incoming and outgoing
directions: bidirectional.
 Always positive: distribution function.
 Invariant to exchange of incoming/outgoing
directions: reciprocity principal.
 In general, BRDFs are anisotropic.
Dimensionality of BRDF
 Function of position (3D), incoming, outgoing
directions (4 angles), wavelength, and
polarization.
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Thus, a 9D function!
Usually simplify:
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Ignore polarization (geometric optics!).
Sometimes ignore wavelength.
Assume uniform material (ignore position).
Isotropic reflectance makes one angle go away.
Radiometry
 Radiometry: Science of measurement of light.
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Measurements are purely physical.
 Discusses quantities
like radiance and irradiance, flux,
and radiosity.
 Need some radiometry to go into more detail about
BRDF.
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Combine with light transport theory and optics to derive
radiosity computations.
 More in later lectures and in COMP238.
Radiometry vs. Photometry
 Photometry: Science of human perception of
light.
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Perceptual analog of Radiometry.
All measurements relative to perception.
 More in COMP238
Color
 If we stopped here we’d have grayscale images.
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Color is determined by the wavelength of visible light.
Can still use geometric optics.
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But need to account for wavelength in reflectance (BRDF)
and index of refraction.
What natural phenomena can you think of that are
wavelength dependent?
Sampling Wavelength
 We could try to compute image for every
possible wavelength and then combine.
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Would take forever.
 Sample a representative set of wavelengths.
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How many samples?
Where?
Where to Sample?
 Photometry tells us that some wavelengths are
more important than others to human perception.
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Human response curve looks something like this:
350
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600
650
700
750
Where to Sample?
 So, pick a few samples wavelengths.
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Compute an image for each.
Reconstruct with basis functions.
Weight of each sample determined by human
response curve.
(Also need color
space transformations).
More in COMP238.
350
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650
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Light Transport
 To compute images, we need to simulate transport of
light around a scene.
 Transport theory.
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Analysis techniques for flow of moving particles in 3D.
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Largely developed for neutrons in atomic reactors.
Can be applied to traffic flow, gas dynamics.
Most importantly, can be applied to light.
 Simulation
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techniques.
Ray tracing.
Radiosity.
Combinations and variations.
Local vs. Global Illumination
 Radiosity and ray tracing simulate
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global illumination.
Account for light transport between objects.
Not just between light sources and objects: local illumination.
 Don’t need global illumination
to use the concepts of
geometric optics, surface modeling, and BRDF.
 Have been used to create diverse shading models.
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Simplest and most common is Phong.
Next lecture: shading models.
For Next Time…
 Read:
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Henri Gouraud, “Continuous Shading of Curved Surfaces”.
IEEE Transactions on Computers; June 1971.
Bui Tuong Phong, “Illumination for Computer Generated
Pictures”. Communications of the ACM; June 1975.
James F. Blinn, “Models of Light Reflection for Computer
Synthesized Pictures.” Computer Graphics (SIGGRAPH
1977).
References
 Glassner, Principles of Digital Image Synthesis,
Volume Two.
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Highly detailed and low level.
 Cohen and Wallace, Radiosity and Realistic
Image Synthesis.
 Bastos dissertation,
ftp://ftp.cs.unc.edu/pub/publications/techreports/00-021.pdf
More Detail: Scattering
 When a photon hits an atom, one of two things
happens:
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Absorption: the photon (energy) is converted into
another form of energy.
Scattering: the photon is immediately re-emitted in a
new direction.