1. Advanced Lighting and Shading
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Advanced Lighting and Shading

2. Radiometry and Photometry : Definition
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Radiometry and Photometry : Definition
Radiometry
Radiometry deal with the measurement of radiation throughout the electromagnetic spectrum
This range includes the infrared(적외선), visible(가시선), and ultraviolet(자외선) regions of the electromagnetic spectrum
wavelength from 1000 to 0.01 micrometer (=10-6 meter =10-3 millimeter)
Photometry
Photometry is like radiometry except that it weights everything by the sensitivity of the human eye
deals with only the visible spectrum (=visible band)
a wavelength range of about 380 to 780 nanometer (=10-9 meter)
do not deal with the perception of color itself, but rather the perceived strength of various wavelengths

3. Radiometry and Photometry : Difference
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Radiometry and Photometry : Difference
Conversion & difference
The result of radiometric computations are converted to photometric units by multiplying by the CIE photometirc curve
The conversion curve and the units of measurement are the only difference between the theory of photometry and the theory of radiometry (Figure 6.1)

4. Radiometry and Photometry : Radiometry (1/6)
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Radiometry and Photometry : Radiometry (1/6)
Radiometry
radiant energy(Q)
basic unit of energy, measured joules(J)
the number of photon per joule :
radiant flux P or (= radiant power) of a light source
the number of joules per second emitted (=watt(W))

5. Radiometry and Photometry : Radiometry (2/6)
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Radiometry and Photometry : Radiometry (2/6)
radiant flux density
After photons leave a light source, the next step is to measure how they arrive at a surface
the radiant flux per unit area on a surface (=watts per square meter)
irradiance E (= radiant flux density)
when flux arrives at a surface
radiant exitance M (= radiosity B)
the amount of flux leaving a surface

6. Radiometry and Photometry : Radiometry (3/6)
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Radiometry and Photometry : Radiometry (3/6)
Solid angle (Figure 6.2)
the concept of a two-dimensional angle extended to three dimensions
measured in steradians (sr)
4 steradians would cover the whole area of the unit sphere
radiance L
the most important radiometric unit for computer graphics
radiance is what we store in a pixel
The amount of radiant flux coming from that direction and hitting the surface at a given point

7. Radiometry and Photometry : Radiometry (4/6)
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Radiometry and Photometry : Radiometry (4/6)
incoming radiance at a surface
defined as the amount of power (watt) per unit area, per unit solid angle
surface independent form of the radiance equation

8. Radiometry and Photometry : Radiometry (5/6)
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Radiometry and Photometry : Radiometry (5/6)
radiance distribution
The radiance in an environment can be thought of as a function of five {six} variables
a location (three), direction (two) { + wavelength }
an environment map of everything in the scene represents the incoming radiance for all directions
Image based rendering
lightfield, plenoptic function

9. Radiometry and Photometry : Radiometry (6/6)
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Radiometry and Photometry : Radiometry (6/6)
An object's radiance value is not affected by distance
a surface will have the same luminance regardless of its distance from viewer
this seems in contradiction to the basic law that a light's intensity drops off with the square of the distance.
only number of pixels that changes in relationship to the distance from the light
radiance remains constant

10. Radiometry and Photometry : Photometry
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Radiometry and Photometry : Photometry
Photometry
luminous energy (talbots)  radiant energy (joules)
lumen (lm)  the watt (W) (radiant flux의 측정단위)
Illumination (the luminous flux density)  irradiance
luminance  radiance
candela (cd) a measure of luminous power per solid angle
lux (lx) lumens(=luminous power) per square meter
candelas per square meter (nit)

11. Colorimetry : Definition (1/2)
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Colorimetry : Definition (1/2)
Colorimetry
Light is perceived in the visible band
from 380 to 780 nm
distribution of wavelengths (light's spectrum)
Human  distinguish 10 million different colors
three different types of cone receptors in the retina
Standard condition for measuring color (CIE) Figure 6.4

12. Colorimetry : Definition (2/2)
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Colorimetry : Definition (2/2)

13. Colorimetry : Color Model (1/12)
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Colorimetry : Color Model (1/12)
Color Matching (Color Models)
RGB Color Model (Figure 6.5)
Primary colors: RED, GREEN, BLUE.
Secondary colors: YELLOW = red + green, CYAN = green + blue, MAGENTA = blue + red.
WHITE = red + green + blue.
BLACK = no light.
Disadv
cannot directly represent all visible colors (negative weights)

14. Colorimetry : Color Model (2/12)
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Colorimetry : Color Model (2/12)
Greyscale
BLACK = 0% brightness, 100% grey.
WHITE = 100% brightness, 0% grey.
NTSC phosphors (older)
Y=0.30R+0.59G+0.11B
CRT and HDTV phosphors (modern)
Y=0.2125R G B
                                     

15. Colorimetry : Color Model (3/12)
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Colorimetry : Color Model (3/12)
CIE XYZ Color Model (Figure 6.6)

16. Colorimetry : Color Model (4/12)
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Colorimetry : Color Model (4/12)
chromaticity diagram
curved line  color of the spectrum
purple line  line connecting the ends of the spectrum
white point  x=y=z=1/3
Saturation  The relative distance of the color point compared to the distance to the edge of the region
Hue  the point on the region edge

17. Colorimetry : Color Model (5/12)
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Colorimetry : Color Model (5/12)
gamut

18. Colorimetry : Color Model (6/12)
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Colorimetry : Color Model (6/12)
Disadvantage
the 2D diagram failed to give a uniformly-spaced visual representation of what is actually a three-dimensional color space

19. Colorimetry : Color Model (7/12)
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Colorimetry : Color Model (7/12)
CIE LUV
CIE LUV
CIE LU’V’

20. Colorimetry : Color Model (8/12)
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Colorimetry : Color Model (8/12)
CIE LAB
retinal color stimuli are translated into distinctions
between light and dark
between red and green
between blue and yellow.
CIELAB indicates these values
with three axes: L*, a*, and b*.

21. Colorimetry : Color Model (9/12)
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Colorimetry : Color Model (9/12)
HSV (=HSB)
Hue, Saturation, Value (=Brightness)
HUE is the actual color.
measured in angular degrees around the cone
red = 0 or 360 (so yellow = 60, green = 120, etc.).
SATURATION is the purity of the color
measured in percent from the center of the cone (0) to the surface (100).
At 0% saturation, hue is meaningless.
BRIGHTNESS
measured in percent from black (0) to white (100).
At 0% brightness, both hue and saturation are meaningless.

22. Colorimetry : Color Model (10/12)
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Colorimetry : Color Model (10/12)
HLS
Hue, Lightness, Saturation
is similar to the HSV cone
but with the primary colors located at L = 0.5 and with the colors of black and white acting as ends of the cones.

23. Colorimetry : Color Model (11/12)
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Colorimetry : Color Model (11/12)
CMYK
Primary colors: CYAN, MAGENTA, and YELLOW.
Secondary colors: BLUE = cyan + magenta, RED = magenta + yellow, GREEN = yellow + cyan.
BLACK = cyan + magenta + yellow (in theory).
BLACK (K) INK is used in addition to C,M,Y to produce solid black.
WHITE = no color (on white paper, of course).
Standard Color Printer

24. Colorimetry : Color Model (12/12)
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Colorimetry : Color Model (12/12)
YIQ
Used by US commercial color television broadcasting (Used by NTSC standard)
Y: encodes luminance
I, Q: encode color (chromaticity)
For black and white TV, only the Y channel is used
People are more sensitive to the illuminance difference
We can use more bits (bandwidth) to encode Y and less bits to encode I and Q

25. BRDF Theory : Definition (1/2)
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BRDF Theory : Definition (1/2)
BRDF
Bidirectional Reflectance Distribution Function
Describe how lights reflected from a surface (Material properties)
Input
incoming and outgoing azimuth and elevation angles, wavelength of incoming light (Hue and saturation remain constant)
The relative amount of energy reflected in the outgoing direction, given the incoming direction

26. BRDF Theory : Definition (2/2)
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BRDF Theory : Definition (2/2)
Helmholtz reciprocity
I/O angles can be switched and the function alue will be same
Normalization
Total amount of out going energy must always be less than or equal to incoming energy
It is an approximation of BSSRDF
Bidirectional Surface Scattering Reflectance Distribution Function
Include the scattering of light within the surface
position change
Adding incoming and outgoing locations as inputs
Travel along the incoming direction
From one point to the other of the surface
Along the outgoing direction

27. BRDF Theory : Reflectance equation (1/2)
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BRDF Theory : Reflectance equation (1/2)
Reflectance equation
Given a BRDF and an incoming radiance distribution
The outgoing radiance for a given viewing direction
Integrating the incoming radiance from all directions on the hemisphere above surface
Determine the incoming radiance
Multiply it by BRDF for this direction and the outgoing direction
Scale by the incoming angle to the surface
integrate

28. BRDF Theory : Reflectance equation (1/2)
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BRDF Theory : Reflectance equation (1/2)
Single Point light source
Simplify the notation
Replace the azimuth and elevation
The cosine term for light using the surface normal n
More than one light, computed and summed together
For diffuse surface, The BRDF is trivial

29. BRDF Theory : Theoretical models of BRDF (1/3)
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BRDF Theory : Theoretical models of BRDF (1/3)
Theoretical models of BRDF
How surfaces behave
Microfacets
Tiny, flat mirror on the surface, with random size and angle
Gaussian distribution of sizes and angles
Specular reflection
Direct reflections from some micro facets
Diffuse reflection
Interreflection off several facets, scattering with in the surface material itself (shadow, mask)
Height correlation
Microfacets have size near the wavelength of the light
Diffraction can be simulated

30. BRDF Theory : Theoretical models of BRDF (2/3)
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BRDF Theory : Theoretical models of BRDF (2/3)
Fresnel reflectance (Figure 6.11)
Importance for non-conductive or dielectric, matrials such as plastic, glass, and water
All materials become fully reflective at the shallowest grazing angle
Describes the reflectance of a given surface at various angles
conductive
dielectric

31. BRDF Theory : Theoretical models of BRDF (3/3)
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BRDF Theory : Theoretical models of BRDF (3/3)
Limitation of BRDF theoretical model
Do not account for anisotropy
If the viewer and the light source do not move and a flat sample of the material changes its appearance when it is rotated about its normal
Brushed metal, vanished wood, woven cloth, fur, hair
Anisotropic BRDF
Both fi and fo are needed to evaluate the BRDF (four angles)
Isotropic BRDF
Relative angle f = fi - fo (three angles)
Not necessarily useful for representing some given material sample

32. BRDF Theory : Another approach (1/3)
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BRDF Theory : Another approach (1/3)
Another approach to represent BRDF
Acquire BRDF data from the actual surface
With basis summation techniques
Capture the BRDF’s surface as the weighted sum of a set of functions
Phong/Blinn lighting model represent BRDF by just two functions
A diffuse component and a specular lobe

33. Implementing BRDFs Implementing BRDFs To save on computation
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Implementing BRDFs
Implementing BRDFs
To save on computation
To store data for a large number of elevations and azimuths
Memory intensive
Care needs to be taken, as measured data is usually noisy and have gaps in the set
Compact representation
Advantages
Avoid the evaluation costs for precise theoretical models
Avoid storage requirements and noisiness of acquired datasets
Two approaches
Factorization
Environment map filtering

34. Implementing BRDFs : Factorization (1/2)
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Implementing BRDFs : Factorization (1/2)
Factorization
Convert a BRDF into a set of pairs of 2D textures
One texture is accessed by the incoming direction
The other by outgoing
(Figure 6.13)

35. Implementing BRDFs : Factorization (2/2)
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Implementing BRDFs : Factorization (2/2)
Forming the texture pairs
The incoming and outgoing direction vectors are evaluated at each vertex of the model
Two pairs of texture coordinates are then used generated using the same reparameterization
These texture coordinates are then used to access the textures on the surface
Multiply the two resulting pixel colors together
Successive pairs of textures are multiplied in the same fashion and added to the final pixel color.
Limitation
At least two texture accesses are needed for every light source in the scene
Only point and directional light sources can be used

36. Implementing BRDFs : Environment Mapping Filtering (1/3)
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Implementing BRDFs : Environment Mapping Filtering (1/3)
Environment Mapping Filtering
Environment map
Render a perfectly shiny surface
Extended to glossy and diffuse surfaces (reflection map)
Fuzzy reflection
Uniformly blur the EM
Use the phong specular equation
Weighted contribution

37. Implementing BRDFs : Environment Mapping Filtering (2/3)
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Implementing BRDFs : Environment Mapping Filtering (2/3)
Irradiance environment map
Gives the diffuse and ambient lighting for that direction
Lumped into a single ambient term (Phong lighting model)
Quickly and accurately
Two ways to store and access lighting
Sphere map
Photograph a sphere painted with flat white paint
valid for only one eye direction
Cube map
Advantage
Eliminating per vertex lighting calculation from pipeline
Limitations
Lights and reflected object are distant
Do not change with location of objected viewed

38. Implementing BRDFs : Environment Mapping Filtering (3/3)
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Implementing BRDFs : Environment Mapping Filtering (3/3)
Problem with environment mapping
The dynamic range of the light captured is usually limited to 8 bits per color channel
Not enough to simultaneously capture the full range of incident illumination
Solution
High Dynamic Range Image (HDRI)
Reference HDR Shop