Light and Matter For Computer Graphics

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Light and MatterFor Computer Graphics

• Comp 770 Lecture
• Spring 2009

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Overview

• A very high-level introduction to some concepts
  and definitions underlying image synthesis.
• Optics
• Materials and Surfaces
• Radiometry and Photometry
• Color
• Energy Transport

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Optics

• The study of light has 3 sub-fields.
• 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).

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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).

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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.

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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.

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Types of Gloss

• Gloss factors measured by the ratio of energy (?)
  in the reflected and incident directions for
  certain standard angles (?i and ?r).
• Specularity measures the brightness of a
  highlight ?r /?i (?i ?r 60).
• Sheen measures the brightness of glancing
  highlights ?r /?i (?i ?r 85).

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Types of Gloss

• 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.

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Computing The Specular Reflection Vector
N
I
R
Given I, N, R are coplanar. I?N R ?N N (I
?N)N From the parallelogram shown at right,
see R I 2N Or R 2N I 2(I ?N)N - I
?r
?i
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Types of Transmission

• Specular transmission causes light to propagate
  w/o scattering, as in clearglass.
• Diffuse transmission sends light in all
  directions with equal energy, as infrosted
  glass.
• Mixed transmission is a weighted combination of
  specular and diffuse transmission.

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Index of Refraction

• The speed of light is not the same in all media.
• 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.
• 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.

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Snells 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 intoa 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
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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).
• Snells law gives critical angle ?c
• ?i(?)sin?c ?t(?)sin(? / 2)
• sin?c ?t (?) / ?i(?)

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Computing The Specular Transmission Vector
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Surface Models

• Perfect mirrors and reflections dont exist.
• Perfect transmission requires a perfect vacuum.
• Real surfaces have some degree of roughness.
• Even most basic simulation must account for
  specular and diffuse reflection / transmission.
• More realism requires accounting for more
  factors.
• Wavelength dependence dispersion, diffraction,
  interference
• Anisotropy angular-dependence of reflectance.
• Scattering absorption and re-emission of
  photons.

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Basic Surface Models

• Non-physically based, as used in OpenGL.
• 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.

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Basic Surface Models
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Whats Missing?

• What weve seen so far is just the basics of
  geometric optics.
• Enough for classical ray tracing, Phong
  illumination model.
• To get much better, we need more
• Better modeling of surface properties.
• Wavelength dependence.
• Radiometry / Photometry.
• Energy Transport.

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Surface Roughness

• At a microscopic scale, all real surfaces are
  rough
• Cast shadows on themselves
• Mask reflected light

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Surface Roughness

• Notice another effect of roughness
• Each microfacet is treated as a perfect mirror.
• Incident light reflected in different directions
  by different facets.
• End result is mixed reflectance.
• Smoother surfaces are more specular or glossy.
• Random distribution of facet normals results in
  diffuse reflectance.

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Reflectance Distribution Model

• Most surfaces exhibit complex reflectances.
• Vary with incident and reflected directions.
• Model with combination
• 
  
• specular glossy diffuse reflectance
  distribution

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Anisotropy

• So far weve been considering isotropic
  materials.
• 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?

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BRDF

• Bidirectional Reflectance Distribution Function
• ?(x, ?i, ?o)
• x is the position.
• ?i (?i, ?i) represents the incoming direction.
  (elevation, azimuth)
• ?o (?o, ?o) represents the outgoing direction
  (elevation, azimuth)

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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.

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Dimensionality of BRDF

• Function of position (3D), incoming, outgoing
  directions (4 angles), wavelength, and
  polarization.
• Thus, a 9D function!
• Usually simplify
• Ignore polarization (geometric optics!).
• Sometimes ignore wavelength.
• Assume uniform material (ignore position).
• Isotropic reflectance makes one angle go away.

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Radiometry

• Radiometry Science of measurement of light.
• Measurements are purely physical.
• Discusses quantities like radiance and
  irradiance, flux, and radiosity.
• Need some radiometry to go into more detail about
  BRDF.
• Combine with light transport theory and optics to
  derive radiosity computations.
• More in later lectures and in COMP238.

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Radiometry vs. Photometry

• Photometry Science of human perception of light.
• Perceptual analog of Radiometry.
• All measurements relative to perception.
• More in COMP238

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Color

• If we stopped here wed have grayscale images.
• Color is determined by the wavelength of visible
  light.
• Can still use geometric optics.
• But need to account for wavelength in reflectance
  (BRDF) and index of refraction.
• What natural phenomena can you think of that are
  wavelength dependent?

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Sampling Wavelength

• We could try to compute image for every possible
  wavelength and then combine.
• Would take forever.
• Sample a representative set of wavelengths.
• How many samples?
• Where?

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Where to Sample?

• Photometry tells us that some wavelengths are
  more important than others to human perception.
• Human response curve looks something like this

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Where to Sample?

• So, pick a few samples wavelengths.
• Compute an image for each.
• Reconstruct with basis functions.
• Weight of each sample determined by human
  response curve.
• (Also need colorspace transformations).
• More in COMP238.

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Light Transport

• To compute images, we need to simulate transport
  of light around a scene.
• Transport theory.
• Analysis techniques for flow of moving particles
  in 3D.
• Largely developed for neutrons in atomic
  reactors.
• Can be applied to traffic flow, gas dynamics.
• Most importantly, can be applied to light.
• Simulation techniques.
• Ray tracing.
• Radiosity.
• Combinations and variations.

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Local vs. Global Illumination

• Radiosity and ray tracing simulate global
  illumination.
• Account for light transport between objects.
• Not just between light sources and objects local
  illumination.
• Dont need global illumination to use the
  concepts of geometric optics, surface modeling,
  and BRDF.
• Have been used to create diverse shading models.
• Simplest and most common is Phong.
• Next lecture shading models.

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For Next Time

• Read
• 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).

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References

• Glassner, Principles of Digital Image Synthesis,
  Volume Two.
• Highly detailed and low level.
• Cohen and Wallace, Radiosity and Realistic Image
  Synthesis.
• Bastos dissertation, ftp//ftp.cs.unc.edu/pub/publ
  ications/techreports/00-021.pdf

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More Detail Scattering

• When a photon hits an atom, one of two things
  happens
• Absorption the photon (energy) is converted into
  another form of energy.
• Scattering the photon is immediately re-emitted
  in a new direction.