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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. Optics Materials and Surfaces Radiometry and Photometry Color Energy Transport. Optics.

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light and matter for computer graphics

Light and MatterFor Computer Graphics

Comp 770 Lecture

Spring 2009

overview
Overview
  • A very high-level introduction to some concepts and definitions underlying image synthesis.
    • Optics
    • Materials and Surfaces
    • Radiometry and Photometry
    • Color
    • Energy Transport
optics
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).
reflection and transmission
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
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 reflection1
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
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°).
types of gloss1
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.
computing the specular reflection vector

N’

N’

I

R

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

i

r

types of transmission
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.
index of refraction
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.
snell s law of refraction

N

I

i

t

T

sint

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 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

total internal reflection
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()

surface models
Surface Models
  • Perfect mirrors and reflections don’t 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.
basic surface models
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.
what s missing
What’s Missing?
  • What we’ve 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.
surface roughness

shadow

shadow

Masked Light

Surface Roughness
  • At a microscopic scale, all real surfaces are rough:
  • Cast shadows on themselves:
  • “Mask” reflected light:
surface roughness1
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.
reflectance distribution model
Reflectance Distribution Model
  • Most surfaces exhibit complex reflectances.
    • Vary with incident and reflected directions.
    • Model with combination:
    • + + =

specular + glossy + diffuse = reflectance distribution

anisotropy
Anisotropy
  • So far we’ve 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?
slide23
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)
properties of the brdf
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
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.
radiometry
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.
radiometry vs photometry
Radiometry vs. Photometry
  • Photometry: Science of human perception of light.
    • Perceptual analog of Radiometry.
    • All measurements relative to perception.
  • More in COMP238
color
Color
  • If we stopped here we’d 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?
sampling wavelength
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?
where to sample
Where to Sample?
  • Photometry tells us that some wavelengths are more important than others to human perception.
    • Human response curve looks something like this:
where to sample1
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.
light transport
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.
local vs global illumination
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.
  • Don’t 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.
for next time
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).
references
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/publications/techreports/00-021.pdf
more detail scattering
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.