mit eecs 6.837, durand and cutler local illumination
TRANSCRIPT
MIT EECS 6.837, Durand and Cutler
Local Illumination
MIT EECS 6.837, Durand and Cutler
Outline
• Introduction
• Radiometry
• Reflectance
• Reflectance Models
MIT EECS 6.837, Durand and Cutler
The Big Picture
MIT EECS 6.837, Durand and Cutler
Radiometry
• Energy of a photon
• Radiant Energy of n photons
• Radiation flux (electromagnetic flux, radiant flux) Units: Watts
dt
dQ
sm csJhhc
e /103 1063.6 834
n
i i
hcQ
1
MIT EECS 6.837, Durand and Cutler
Radiometry
ddA
dL
cos)(
2
steradianmeter
WattUnits
:
2
• Radiance – radiant flux per unit solid angle per unit projected area– Number of photons arriving
per time at a small area
from a particular direction
MIT EECS 6.837, Durand and Cutler
Radiometry
• Irradiance – differential flux falling onto differential area
• Irradiance can be seen as a density of the incident flux falling onto a surface.
• It can be also obtained by integrating the radiance over the solid angle.
dA
dE
2
:meter
WattUnits
MIT EECS 6.837, Durand and Cutler
Light Emission
• Light sources: sun, fire, light bulbs etc.
• Consider a point light source that emits light uniformly in all directions
Surface
n
sourcelight the todistance
sourcelight theofpower 4
4
cos22
d
dL
dE
s
ss
MIT EECS 6.837, Durand and Cutler
Outline
• Introduction
• Radiometry
• Reflectance
• Reflectance Models
MIT EECS 6.837, Durand and Cutler
Reflection & Reflectance
• Reflection - the process by which electromagnetic flux incident on a surface leaves the surface without a change in frequency.
• Reflectance – a fraction of the incident flux that is reflected
• We do not consider:– absorption, transmission, fluorescence
– diffraction
MIT EECS 6.837, Durand and Cutler
Reflectance
• Bidirectional scattering-surface distribution Function (BSSRDF)
Surface
Source: Jensen et.al 01
MIT EECS 6.837, Durand and Cutler
Reflectance
• Bidirectional scattering-surface distribution Function (BSSRDF)
),,,(
),,,(),,,,,,,(
iiiii
rrrrrrriirrii yxd
yxdLyxyxS
steradianmeterUnits
1:
2
Surface
MIT EECS 6.837, Durand and Cutler
Reflectance
• Bidirectional Reflectance Distribution Function (BRDF)
ir
i r
),(
),(),,,(
iii
rrrrriir dE
dLf
steradian
Units1
:
Li
Lr
MIT EECS 6.837, Durand and Cutler
Isotropic BRDFs
• Rotation along surface normal does not change reflectance
ir
d
),(
),(),,(),,(
dii
drrdririrrir dE
dLff
Li
Lr
MIT EECS 6.837, Durand and Cutler
Anisotropic BRDFs
• Surfaces with strongly oriented microgeometry elements
• Examples: – brushed metals,
– hair, fur, cloth, velvet
Source: Westin et.al 92
MIT EECS 6.837, Durand and Cutler
Properties of BRDFs
• Non-negativity
• Energy Conservation
• Reciprocity
),( allfor 1),(),,,( iirrrriir df
),,,(),,,( iirrrrriir ff
0),,,( rriirf
MIT EECS 6.837, Durand and Cutler
How to compute reflected radiance?
• Continuous version
• Discrete version – n point light sources
iiiirir
iirirrr
dndLf
dEfL
)cos()( ),(
)(),()(
21
1
4
cos),(
),()(
j
sjj
n
jrijr
j
n
jrijrrr
df
EfL
),(
MIT EECS 6.837, Durand and Cutler
Outline
• Introduction
• Radiometry
• Reflectance
• Reflectance Models
MIT EECS 6.837, Durand and Cutler
How do we obtain BRDFs?
• Measure
BRDF values
directly
• Analytic Reflectance Models– Physically-based models
• based on laws on physics
– Empirical models• “ad hoc” formulas that work
Source: Greg Ward
MIT EECS 6.837, Durand and Cutler
Ideal Diffuse Reflectance
• Assume surface reflects equally in all directions.
• An ideal diffuse surface is, at the microscopic level, a very rough surface.– Example: chalk, clay, some paints
Surface
MIT EECS 6.837, Durand and Cutler
Ideal Diffuse Reflectance
• BRDF value is constant
Surface
i
dB
dA
idAdB cos
ir
iir
iirirrr
Ef
dEf
dEfL
)(
)(),()(
n
MIT EECS 6.837, Durand and Cutler
• Ideal diffuse reflectors reflect light according to Lambert's cosine law.
Ideal Diffuse Reflectance
MIT EECS 6.837, Durand and Cutler
Ideal Diffuse Reflectance
• Single Point Light Source– kd: The diffuse reflection coefficient.
– n: Surface normal.
– l: Light direction.
2 4 )()(
dkL s
dr
ln
Surface
l
n
MIT EECS 6.837, Durand and Cutler
Ideal Diffuse Reflectance – More Details
• If n and l are facing away from each other, n • l becomes negative.
• Using max( (n • l),0 ) makes sure that the result is zero.– From now on, we mean max() when we write •.
• Do not forget to normalize your vectors for the dot product!
MIT EECS 6.837, Durand and Cutler
Ideal Specular Reflectance
• Reflection is only at mirror angle.– View dependent
– Microscopic surface elements are usually oriented in the same direction as the surface itself.
– Examples: mirrors, highly polished metals.
Surface
l
n
r
MIT EECS 6.837, Durand and Cutler
Ideal Specular Reflectance
• Special case of Snell’s Law– The incoming ray, the surface normal, and the reflected
ray all lie in a common plane.
Surface
l l
n
rr
rl
rl
rrll
nn
nn
sinsin
MIT EECS 6.837, Durand and Cutler
Non-ideal Reflectors
• Snell’s law applies only to ideal mirror reflectors.
• Real materials tend to deviate significantly from ideal mirror reflectors.
• They are not ideal diffuse surfaces either …
MIT EECS 6.837, Durand and Cutler
Non-ideal Reflectors
• Simple Empirical Model:– We expect most of the reflected light to travel in the
direction of the ideal ray.
– However, because of microscopic surface variations we might expect some of the light to be reflected just slightly offset from the ideal reflected ray.
– As we move farther and farther, in the angular sense, from the reflected ray we expect to see less light reflected.
MIT EECS 6.837, Durand and Cutler
The Phong Model
• How much light is reflected?– Depends on the angle between the ideal reflection
direction and the viewer direction .
Surface
l
nr
Camera
v
MIT EECS 6.837, Durand and Cutler
The Phong Model
• Parameters– ks: specular reflection coefficient
– q : specular reflection exponent
Surface
l
nr
Camera
v
22 4
)(
4
)(cos)(
dk
dkL sq
ssq
sr
rv
MIT EECS 6.837, Durand and Cutler
The Phong Model
• Effect of the q coefficient
MIT EECS 6.837, Durand and Cutler
The Phong Model
Surface
l
n
r
r
lnlnr
nlr
)(2
cos 2
2
2
4
))(
4
)()(
dk
dkL
sqs
sqsr
lnlnv
rv
)(2(
MIT EECS 6.837, Durand and Cutler
Blinn-Torrance Variation
• Uses the halfway vector h between l and v.
Surface
l
n
Camera
v
||vl||
vlh
h
22 4
)(
4
)(cos)(
dk
dkL sq
ssq
sr
hn
MIT EECS 6.837, Durand and Cutler
Phong Examples
• The following spheres illustrate specular reflections as the direction of the light source and the coefficient of shininess is varied.
Phong Blinn-Torrance
MIT EECS 6.837, Durand and Cutler
The Phong Model
• Sum of three components:diffuse reflection +
specular reflection +
“ambient”.
Surface
MIT EECS 6.837, Durand and Cutler
Ambient Illumination
• Represents the reflection of all indirect illumination.
• This is a total hack!
• Avoids the complexity of global illumination.
ar kL )(
MIT EECS 6.837, Durand and Cutler
Putting it all together
• Phong Illumination Model
2 4
)()()( )(
dkkkL sq
sdar
rvln
MIT EECS 6.837, Durand and Cutler
For Assignment 3
• Variation on Phong Illumination Model
iq
sdadr LkkLkL )( )()()( rvln
MIT EECS 6.837, Durand and Cutler
Adding color
• Diffuse coefficients:– kd-red, kd-green, kd-blue
• Specular coefficients:– ks-red, ks-green, ks-blue
• Specular exponent:q
MIT EECS 6.837, Durand and Cutler
Phong Demo
MIT EECS 6.837, Durand and Cutler
Fresnel Reflection
• Increasing specularity near grazing angles.
Source: Lafortune et al. 97
MIT EECS 6.837, Durand and Cutler
Off-specular & Retro-reflection
• Off-specular reflection– Peak is not centered at the reflection direction
• Retro-reflection:– Reflection in the direction of incident illumination
– Examples: Moon, road markings
MIT EECS 6.837, Durand and Cutler
The Phong Model
• Is it non-negative?
• Is it energy-conserving?
• Is it reciprocal?
• Is it isotropic?
MIT EECS 6.837, Durand and Cutler
Shaders (Material class)
• Functions executed when light interacts with a surface
• Constructor:– set shader parameters
• Inputs:– Incident radiance
– Incident & reflected light directions
– surface tangent (anisotropic shaders only)
• Output:– Reflected radiance
MIT EECS 6.837, Durand and Cutler
Questions?