Radiometry, Surfaces and Rendering

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Radiometry, Surfaces and Rendering

• COMP238

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Goal

• To investigate formally some methods for
  physically-based realistic rendering
• Why physically based?
• What follows in course

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Outline

• Radiometric Concepts
• Surface Properties
• Light Transport

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Radiometry

• Science of measuring light
• Analogous science called photometry is based on
  human perception.

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Radiometric Quantities

• Function of wavelength, time, position,
  direction, polarization.

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Wavelength

• Assume wavelengths independent
• No phosphorescence

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Time

• Equilibrium
• Light travels fast
• No luminescence

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Polarization

• Ignore it
• Would likely need wave optics to simulate

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Result five dimensions

• With little loss in usefulness
• Two quantities
• Position (3 components)
• Direction (2 components)

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Radiant Energy - Q

• Think of photon as carrying quantum of energy
  (hc/? where c is speed of light and h is Plancks
  constant)
• Total energy, Q, is then energy of the total
  number of photons.

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Power - ?

• Flow of energy (important for transport)
• Also called radiant flux.
• Energy per unit time (joules / s)
• Units watts
• ? dQ/dt

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Radiant Flux Area Density

• This is a measure we need for energy
  arriving/leaving a surface

dA
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Radiant Flux Area Density

• Units of watts per meter squared
• Graphics doesnt use this term instead

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Irradiance

• Power per unit area incident on a surface.
• E d ?/dA
• Units watts / m2

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Radiant Exitance

• Radiant flux area density leaving surface
• Also known as Radiosity
• B d ?/dA
• Same units as irradiance, just direction changes.

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What about a point source?
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Intensity

• Flux per unit solid angle
• Units watts per steradian
• Note term intensity is heavily overloaded.

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Solid Angle

• Size of a patch, dA, is
• Solid angle is

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Isotropic Point Source

• Even distribution over sphere

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Irradiance on Differential Patch

• This is the Square Law

x
?
xs
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Projected Area

• Ap A (N V) A cos ?

V
N
V
?
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Radiance

• Power per unit projected area per unit solid
  angle.
• Units watts per steradian m2
• We have now introduced projected area, a cosine
  term.

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Why the Cosine Term?

• Foreshortening is by cosine of angle.
• Radiance gives energy by effective surface area.

d cos?
?
d
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Irradiance from Radiance

• cos? d? is projection of a differential area

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Reciprocity

• Radiance from dS to dR

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• Radiance from dS to dR (l is distance)

Projected area
Solid angle
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Reciprocity

• Which is radiance from dS to dR

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Total flux leaving one side flux arriving other
side, so
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therefore
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so

• Radiance doesnt change with distance!

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Radiance at a sensor

• Sensor of a fixed area sees more of a surface
  that is farther away.
• However, the solid angle is inversely
  proportional to distance.
• Response of a sensor is proportional to radiance.

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Radiance as a unit of measure

• Radiance doesnt change with distance
• Therefore its the quantity we want to measure in
  a ray tracer.
• Radiance proportional to what a sensor (camera,
  eye) measures.
• Therefore its what we want to output.

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Photometry and Radiometry

• Photometry (begun 1700s by Bouguer) deals with
  how humans perceive light.
• All measurements relative to perception of
  illumination
• Units different from radiometric but conversion
  is scale factor -- weighted by spectral response
  of eye (over about 360 to 800 nm).

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CIE curve

• Response is integral over all wavelengths

Violet
Green
Red
CIE, 1924, many more curves available, see
http//cvision.ucsd.edu/lumindex.htm
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Photometric Units

• Talbot ? Joules
• Lumens ? Watt
• Nit, Lux, Candela

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Radiometry

• Energy
• Power
• Irradiance and Radiosity
• Intensity
• Radiance

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Surface Properties

• Reflected radiance is proportional to incoming
  flux and to irradiance (incident power per unit
  area).

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Bidirectional Reflectance Distribution Function
(BRDF)
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Dimensionality

• Function of position, four angles (two incident,
  two reflected), as well as wavelength and
  polarization (both usually ignored).
• Material is usually considered uniform, so
  position is ignored.
• If isotropic, one angle goes away.
• Result - 3 or 4 dimensional.

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Properties

• Reciprocity

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Lambertian (diffuse) Surface

• BRDF is a constant.
• Independent of direction of incoming light.
• Radiosity over irradiance is constant.

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Mirror (ideally specular) Surface

• Reflection on a plane perpendicular to surface.
• Angle of reflectance angle of incidence.
• BRDF cast as delta functions.

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Glossy

• Between lambertian and specular.

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Complex BRDF

• Combination of the three.

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Representations

• 4D function, so awkward to represent directly.
• Most often represented as parametric equation
  (Phong, Cook-Torrance, etc.).
• Sometimes with basis functions (such as spherical
  harmonics).

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Rendering Equation

• Not from Kajiya 86 (more like Radiosity
  equation).
• Often approximated by splitting diffuse,
  specular, and glossy.

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Transport

• Now we have models of reflection.
• How do we transfer energy?

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Transport Approximations

• Classical ray tracing
• Direct lambertian
• Global specular
• Radiosity
• Diffuse to diffuse global illumination
• View independent.

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Next

• Formulation of Radiosity
• Practical aspects for computing a solution

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References

• Chapter 2 (by Hanrahan) in Cohen and Wallace,
  Radiosity and Realistic Image Synthesis.
• Glassner, Principles of Digital Image Synthesis,
  pp. 648 659 and Chapter 13.
• Radiometry FAQ (PDF local, html remote)
• Bastos dissertation, Chapter 3 in
  http//www.cs.unc.edu/bastos/PhD/2and3.pdf