CSL 859: Advanced Computer Graphics

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CSL 859 Advanced Computer Graphics

• Dept of Computer Sc. Engg.
• IIT Delhi

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Lighting in OpenGL

• Per-vertex
• per-pixel with Cg
• Light and Material Properties
• glLightfv RGBA
• Color of light RGBA in 0255
• glMaterialfv RGBA
• Color of material RGBA in 0255
• glColor3f RGBA
• Uses glColorMaterial

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Spectrum
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Color Perception

• Energy?
• Q h/?
• Some colors are perceived brighter

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Definitions

• Energy per unit wavelength?
• Spectral Energy (Q in an interval ??)/?? ? dQ/d?
• Irradiance, H
• Spectral Power reaching surface per unit area
• Radiance
• ?H/?s, per unit solid angle

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Surface Radiance
l
?
n
Surface Radiance L
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Radiance Non-Attenuation
Both detectors see the same Radiance
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Surface Radiance
l
dA
?
?
n
dA cos?
Surface Radiance L
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BRDF

• Bi-directional Reflectance Function
• ?io Lo / Hlight

-i
o
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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

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Luminous Efficiency

• Lumens per watt (lm/W)
• Photopic efficiency lt 683 lm/W
• _at_ Monochromatic light with ? 555 nm (green).
• Scotopic efficiency lt 1700 lm/W
• _at_ ? 507 nm

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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

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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/(XYZ), y Y/(XYZ), Y
• x and y have chromaticity, Y has luminance

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CIE Chromaticity Diagram
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Color Spaces

• HSV
• RGB
• CMYK
• HDR
• Tone Mapping

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Hue, Saturation, Value
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Color in Hardware

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

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Hardware Color Mapping

• Normalize each component to 01
• Fixed number of steps
• Monitor dependent
• Typically 255
• Values 0..255 -gt v -gt intensity
• Displayed I a (Maximum I) vy

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Geometry of Local Lighting

• Vertex normals make it smooth
• Lights in Camera space
• Already specified so in OpenGL

L
n
l
v
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Diffuse Reflection

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

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Specular Reflection

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

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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

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Diffuse Reflection

• Lamberts 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
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Diffuse Reflection

• Unit vector l points to the light source

cl
n
l
fdiff
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Directional Light

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

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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
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Attenuation

• Sometimes, inverse square falloff behavior is
  hacked approximated
• A common damping of distance attenuation is

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Multiple Lights

• Additive
• Interference does happen
• E.g., soap bubbles

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Ambient Light

• Poor mans global illumination
• Same amount everywhere
• Often, famb is set to equal fdif

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Blinns Model

• Smooth gt well defined small highlights,
• Rough gt Blurred, larger
• Surface roughness modeled by microfacets
• Distribution of microfacet normals
• Polished
• Smooth
• Rough
• Rougher

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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
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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
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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

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Specular Highlights

• Higher exponent more narrow the highlight

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Shininess
n 1
n 5
n 10
n 50
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Specular Highlights

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

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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
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Cook Torrance

• Contributors
• Torrance Sparrow (1967)
• Blinn (1977)
• Models of Light Reflection for Computer
  Synthesized Pictures, SIGGRAPH77
• 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

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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 IiA f
• f 1/? ? (N.L) d?i
• Shortcut, f 1

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Intensity of Reflected Light

• IR IiARA ?l (Iil (NLl) ??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
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Cook-Torrance Model

• Rs F D G___
• ? (NL) (NV)

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
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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)

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Beckmann vs Blinn
m 0.2
m 0.6
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Geometric Attenuation

• 0 lt G lt 1
• No occlusion to full occlusion

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Geometric Attenuation
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Fresnel Factor

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

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Some Examples
Material s d m
Carbon .3 .7 .4
Rubber .4 .6 .3
Obsidian .8 .2 .15
Lunar Dust 0 1 X
Olive drab .3 .7 .5
Rust .2 .8 .35
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Some Examples

• Metal refractive index absorption coeff.
• Silver 0.177 3.638
• Copper 0.617 2.63
• Steel 2.485 3.433

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Results of Cook-Torrance
Copper vase

• Copper colored plastic

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

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

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Advanced Lighting

• Shadows
• Accurate reflection models
• Procedural shaders
• Global Illumination
• Volumetric effects (fog, translucency)
• Lens imperfections
• Exposure ( dynamic range)

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Shadow Map
Scene
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Shadow Map

• Find x,y in the light space
• Unproject camera, then Project light
• But x and y may not be integers
• Find nearest integers?
• Read Depth buffer
• Compare projected z with stored z.