Light and Matter For Computer Graphics

1. Light and MatterFor Computer Graphics Comp 770 Lecture Spring 2009

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

3. 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).

4. 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).

5. 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.

6. 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.

7. 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°).

8. 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.

9. 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

10. 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.

11. 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.

12. 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

13. 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()

14. N I R i I|| T -M I M T|| t T Computing The Specular Transmission Vector

15. 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.

16. 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.

17. Basic Surface Models

18. 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.

19. shadow shadow Masked Light Surface Roughness • At a microscopic scale, all real surfaces are rough: • Cast shadows on themselves: • “Mask” reflected light:

20. 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.

21. Reflectance Distribution Model • Most surfaces exhibit complex reflectances. • Vary with incident and reflected directions. • Model with combination: • + + = specular + glossy + diffuse = reflectance distribution

22. 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?

23. 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)

24. 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.

25. 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.

26. 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.

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

28. 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?

29. 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?

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

31. 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.

32. 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.

33. 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.

34. 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).

35. 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

36. 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.