Part I: Basics of Computer Graphics

1. Part I:Basics of Computer Graphics Chapter 5 Representing Light and Isotropic Reflection Models 6-1

2. How do we represent light? • RGB? • No! • Light spectrum: • Therefore shading calculation should be performed on the light spectrum. • How? Taking samples on the spectrum. • [Hall89] proposed to take 9 samples on the curves. • Calculate shading for each sampled wavelength, e.g. invoke Phong reflection model “9” times. 5-2

3. How do we represent light? • Is the surface reflectivity also wavelength dependent? • YES! • But “How can we display the final light spectrum on the RGB monitor?” • Different spectrums may produce same response in our eyes. • Hence no need to reproduce the exact light spectrum. • But reproduce another spectrum that gives us the “same” perceptual color. 5-3

4. Color Matching Experiment • Three types of color receptors (cones) on our retina: responsible for short, middle and long wavelengths • A matching experiment of Sensations, not matching of spectral curve. • A statistical, psychological experiment. May vary for different individual. 5-4

5. Color Matching Experiment • 3 lights are chosen • X: 445nm • Y: 535nm • Z: 630nm • Not necessary equal to RGB on your monitor • e.g. wavelength 570nm has the same response as 0 X + 0.7 Y + 1.0 Z 5-5

6. From Light Spectrum to RGB • An ideal sampling approach: • Take 9 samples on the spectral curve. • Invokes reflection models (say Phong model) 9 times. • Convert the light spectrum to XYZ • From XYZ to RGB: spectral curve of RGB primitives can also be expressed as, R = a X + b Y + c Z G = d X + e Y + f Z B = g X + h Y + i Z • In other words, 5-6

7. From Light Spectrum to RGB • Practically, most graphics systems don’t care. • They only sample at 3 wavelength R G B. • Obviously, it is not accurate or correct. • Two monitors may not display the same image equally. Reference • [Hall89] Roy Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag 1989. 5-7

8. Phong Reflection Model • Notation: • Many variations, the following is a common model:reflected = ambient + diffuse + specular Ambient • Models the contribution of the surrounding environment except the light sources. • It is assumed constant. Obviously wrong! • Phong model is a local illumination model. Global illumination models (ray-tracing, radiosity) solve this more accurately. 6-2

9. Phong Reflection Model Diffuse • Models multiple scattering within rough surface • Viewpoint independent • Depends on cos q, since the surface element is not maximally illuminated if the light source is not from the top. • cos q projects the surface elements along the L direction. 6-3

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11. Phong Reflection Model Specular • Model the glossy appearance of shiny object. • Viewpoint dependent • Efficient modification:N.H replaces R.V • Diffuse + Specular 6-5

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14. Torrance-Sparrow Model • Comparing Phong model with real surface. Phong real surface • Flaw 1: height of the specular bump varies with the direction of light source. • Flaw 2: direction of peak specular reflection is not exactly along the mirror reflection direction.Off-specular reflection phenomenon • Both flaws related to the specular reflection. 6-8

15. Torrance-Sparrow Model • In 1967, Torrance and Sparrow [Torrance67] proposed a reflection model based on microfacet approach. • It accounts for the off-specular phenomenon. • Blinn [Blinn77] proposed a reflection model for computer graphics based on Torrance-Sparrow model. • Modifications are done for the specular term. • D, Distribution function of the directions of microfacets on the rough surface. • G, Geometry attenuation factor due to self-shadowing or masking • F, Fresnel reflection (physical law). 6-9

16. Ni a Distribution Function • Models the surface roughness using a statistical function • Several functions have been proposed • Guassian distribution (normal distribution)a is the angle from the average normal N to the facet normal Ni • m controls the bell shape (standard derivation) of the Guassian function • Beckmann modelm is the RMS (root mean square) slope of microfacets, actually a parameter to control the shape of the bump 6-10

17. Distribution Function • Most models use Guassian distribution as a component. • Easy to handle. May derive close-form solution • Frequently found in natural phenomenon (A claim). • Replace the cos function in Phong Model by this factor 6-11

18. Geometry Attenuation • Accounts for self-shadowing or masking • Explains off-specular reflection phenomenon Case a Case b Case c 6-12

19. Geometry Attenuation • To calculate geometry attenuation factor G,we assume • each facet comprises one side of a symmetric V-groove cavity • longitudinal axis of the cavity is parallel to the plane of the mean surface • upper edges of V-grooves are all in the same plane • the grooves do not have a preferred orientation, i.e., they are in all directions along the surface • But, the assumptions are not realistic. • However, it does explain the off-specular reflection. • For cases b and c, the attenuation equals to the factor (reuse m) 6-13

20. Geometry Attenuation Case c: L & V interchange 6-14

21. Fresnel Reflection • The fraction of light incident on a facet which is actually reflected (as opposed to being absorbed).qi is angle of incidencesin qt = sin qi / n where is refraction index • It can be rewritten as where • When qi =p/2, no absorption, all reflected.qi =0, max absorption. 6-15

22. References • [Blinn77] James F. Blinn, “Models of Light Reflection For Computer Synthesized Pictures”, SIGGRAPH Proceedings’ 77, p192-198, 1977. • [Cook81] Robert Cook and Kenneth Torrance, “A Reflectance Model for Computer Graphics”, SIGGRAPH Proceedings’81, p307-316, 1981. • [Phong75] Bui-Tuong Phong, “Illumination for Computer Generated Images”, Communcation of ACM, vol. 18, no. 6, p311-317, 1975. • [Torrance67] Kenneth Torrance and Ephraim Sparrow, “Theory for Off-Specular Reflection from Roughened Surface”, Journal of Optical Society of America, vol. 57, no. 9, 1967. 6-16