CSL 859: Advanced Computer Graphics

1. CSL 859: Advanced Computer Graphics Dept of Computer Sc. & Engg. IIT Delhi

2. Lighting in OpenGL • Per-vertex • per-pixel with Cg • Light and Material Properties • glLightfv: RGBA • Color of light – RGBA in [0:255] • glMaterialfv: RGBA • Color of material – RGBA in [0:255] • glColor3f: RGBA • Uses glColorMaterial

3. Spectrum

4. Intensity λ Color Perception • Energy? • Q = h/λ • Some colors are perceived brighter

5. Definitions • Energy per unit wavelength? • Spectral Energy: (Q in an interval ∆λ)/∆λ→ dQ/dλ • Irradiance, H • Spectral Power reaching surface per unit area • Radiance • ∆H/∆σ, per unit solid angle

6. Surface Radiance l θ n Surface Radiance L =

7. Radiance Non-Attenuation Both detectors see the same Radiance

8. Surface Radiance l dA θ θ n dA cosθ Surface Radiance L =

9. BRDF • Bi-directional Reflectance Function • ρio = Lo / Hlight -i o

10. Types of BRDFs • Isotropic • Reflectance independent of rotation about a given surface normal • Smooth plastics • Anisotropic • Reflectance changes with rotation around a given surface normal • Brushed metal, satin, hair

11. Luminous Efficiency • Lumens per watt (lm/W) • Photopic efficiency < 683 lm/W • @ Monochromatic light with λ = 555 nm (green). • Scotopic efficiency < 1700 lm/W • @ λ = 507 nm

12. Tri-Stimulus Theory • Metamers appear the same • Eyes have sensors: • Rods (low resolution, Peripheral, Many) • Cones (High res, in fovea, few, 3 types) • Maximum response at 420 nm (blue), • Maximum response at 534 nm (Bluish-Green), • Maximum response at 564 nm (Yellowish-Green). • Integrating (Filtering) Sensors

13. CIE Color Standard • Three components • X Y Z • Y has luminance (perceived brightness) • X and Z have brightness • C = X + Y + Z • Represented as • x = X/(X+Y+Z), y = Y/(X+Y+Z), Y • x and y have chromaticity, Y has luminance

14. CIE Chromaticity Diagram

15. Color Spaces • HSV • RGB • CMYK • HDR • Tone Mapping

16. Hue, Saturation, Value

17. Color in Hardware • RED is not the same on every monitor • Not even the same everytime on the same HW • User knobs, Ambient lighting • 0:1, in a normalized space • No limit in reality • 1 => Maximum screen brightness • 0 => Minimum screen brightness • Why R, G, B? • Engineering convenience • Gamma correction • Gamma can be commonly set by the user

18. Hardware Color Mapping • Normalize each component to [0:1] • Fixed number of steps • Monitor dependent • Typically 255 • Values 0..255 -> v -> intensity • Displayed I α (Maximum I) vy

19. Geometry of Local Lighting • Vertex normals make it “smooth” • Lights in Camera space • Already specified so in OpenGL L n l v

20. Diffuse Reflection • Reflection uniformly in all directions • Matte (Non-shiny) appearance • Eg, chalk • Most materials are not ideally diffuse

21. Specular Reflection • Light reflects in a single direction • Shiny • Eg, silvered mirror • Most materials are not ideally specular

22. Diffuse/Specular Reflection • Most materials are a combination of diffuse and specular • Reflection distribution function • Need not be in a plane • Need not be isotropic

23. Diffuse Reflection • Lambert’s law • “Amount” of incident light per unit area is proportional to the cosine of the angle between the normal and the light rays l3 l2 n l1 surface

24. Diffuse Reflection • Unit vector l points to the light source cl n l fdiff

25. Directional Light • Distant light source • A unit length direction vector d and a color c • l = -d • Color shining on the surface cl = c

26. Point Lights • Radiates light equally in all directions • Intensity from a point light source drops off proportionally to the inverse square of the distance from the light p cpnt l n cl v fdiff

27. Attenuation • Sometimes, inverse square falloff behavior is hacked approximated • A common damping of “distance attenuation” is:

28. Multiple Lights • Additive • Interference does happen • E.g., soap bubbles

29. Ambient Light • Poor man’s “global illumination” • Same amount everywhere • Often, famb is set to equal fdif

30. Blinn’s Model • Smooth => well defined small highlights, • Rough => Blurred, larger • Surface roughness modeled by microfacets • Distribution of microfacet normals Polished: Smooth: Rough: Rougher:

31. Specular Highlights • To compute the highlight intensity, we start by finding the unit length ‘halfway’ vector h, which is halfway between the vector l pointing to the light and the vector e pointing to the eye (camera) n h cl e l fspec

32. Specular Highlights • The halfway vector h represents the direction that a mirror-like microfacet would have to be aligned in order to cause the maximum highlight intensity n h cl e l fspec

33. Specular Highlights • The microfacet normals generally point in the direction of the macro surface normal • The further h is from n, fewer facets are likely to align with h • The Blinn lighting model: • s is shininess or specular exponent

34. Specular Highlights • Higher exponent more narrow the highlight

35. Shininess n = 1 n = 5 n = 10 n = 50

36. Specular Highlights • To account for highlights, we simply add an additional contribution to our total lighting equation • Blinn lighting model.

37. Classic Lighting Models • Lambert • Blinn • Phong • Considers angle between normal and viewer • Cook-Torrance n n h cl cl e e l l fspec fspec Phong Blinn

38. Cook & Torrance • Contributors: • Torrance & Sparrow (1967) • Blinn (1977) • Models of Light Reflection for Computer Synthesized Pictures, SIGGRAPH’77 • Cook & Torrance (1982) • A Reflectance Model for Computer Graphics, ACM TOG 1(1) • Thermodynamics and geometric optics • Explains off-cpecular peaks • No electromagnetics • Fails for very smooth surfaces

39. Cook & Torrance • Ei = Ii (N.L) di • R = Ir/Ei • Ir = R Ii (N.L) di • R = sRs + dRd, s + d = 1. • IrA= RA IiAf • f = 1/ ∫ (N.L) di • Shortcut, f = 1

40. Intensity of Reflected Light IR = IiARA + l (Iil (N•Ll) ∆il(sRs + dRD)) l: Individual lights Iil: Average intensity of the incident light N: Surface unit normal Ll: Unit vector in the direction of light l ∆il: solid angle of a beam of incident light

41. Cook-Torrance Model Rs = F D G___  (N•L) (N•V) F: Fresnel term D: Facet slope distribution: Fraction of facets oriented along H (Roughness) G: Geometrical attenuation factor (occlusion) V: Unit vector in the direction of the viewer

42. Roughness • Blinn: D = ce-(/m)2 : angle between H and N (H: angular bisector of V and L) m: root mean square (rms) slope of the facets • Beckmann: D = 1/(m2cos4) e-(tan2/m2)

43. Beckmann vs Blinn m = 0.2 m = 0.6

44. Geometric Attenuation • 0 <= G <= 1 • No occlusion to full occlusion

45. Geometric Attenuation

46. Fresnel Factor • Wavelength dependent. • Refractive Index • Mirror-like at grazing angles

47. Some Examples Metal :: refractive index :: absorption coeff. Silver :: 0.177 :: 3.638 Copper :: 0.617 :: 2.63 Steel :: 2.485 :: 3.433

48. Results of Cook-Torrance Copper colored plastic Copper vase

49. Compared to Phong 30o Incidence 70o Incidence Torrance et al. Phong

50. Shading • Gouraud • Light vertices • Interpolate colors • glShadeModel(GL_SMOOTH) • Phong • Per-pixel (Phong) lighting • Interpolate normals • Need pixel-programs