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## Light and Matter For Computer Graphics

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Presentation Transcript

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

- 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: “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).
- 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

- 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: dr / dr , 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.

N’

I

R

Computing The Specular Reflection VectorN

I

R

Given: I, N, R are coplanar. IN = 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

- 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

- 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.

I

i

t

T

sint

Snell’s Law of Refraction- Governs the geometry of refraction.

i()sini = t()sint

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.

sini

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()sinc = t()sin( / 2)

sinc = t () / i()

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

- 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 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.

shadow

Masked Light

Surface Roughness- At a microscopic scale, all real surfaces are rough:
- Cast shadows on themselves:
- “Mask” reflected light:

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

- Most surfaces exhibit complex reflectances.
- Vary with incident and reflected directions.
- Model with combination:
- + + =

specular + glossy + diffuse = reflectance distribution

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?

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

- 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.
- 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: 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

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

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

- 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?

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

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

- 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

- 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…

- 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

- 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

- 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.

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