Transcript RADIOSITY - Lamar University

RADIOSITY
Submitted by
CASULA, BABUPRIYANK. N
Computer Graphics
Hardware &
Architecture
Application
Computer
Graphics
Image
Synthesis
Animation
Image Synthesis
Image
Synthesis
Modeling
•2d/3d
Rendering
•Radiosity
•Illumination models
•Visibility
•Ray Tracing
•Texture Mapping
Viewing
2d/3d
Radiosity

Surfaces in a scene reflect & emit light.
– Some of this light reaches the viewer; this
makes the surface visible.
– But much of this reflected/emitted light will
illuminate other surfaces.
– This light will then reflect of these other
surfaces; in fact, every surface in a scene will
illuminate other surfaces in the scene.
Samples
Background needed…

Light
 Light Transport
 Radiometry
 Reflection Functions
Light

The visible light
can be polarized
 Optics is the area
that studies about
these radiations
Optics
Optics
Geometric
Physical
Quantum
Shadows Optical Interference Photons
laws
To study radiosity Geometric Optics is needed
Light Transportation

Light travels in the form of
particles(photons)
 Total number of particles in a small
differential volume dV is
P(x) = p(x) dV
particle density
P(x) = p(x) (v dt cos()) dA
Light Transportation contd..
Not all particles flow with the same speed and
same direction.
The particle density is now a function of two
independent variables x, .
Then we have
P(x, ) = p(x, ) cos d dA
Here d is called the differential solid angle.
Angles
2D angle
3D/Solid Angle
Solid Angle
Definition :The SA subtended by an object
from a point P is the area of projection of
the object onto the unit sphere centered at P.
Area (dA) = (r d) (r sin d)= r2 sin d d
The differential solid angle :
d = dA cos / r2 = cos sin d d
Radiant Energy Q
Rendering systems consider the stuff that
flows as radiant energy or radiant power()
The radiant energy per unit volume is the
photon volume density times the energy of
a single photon(hc/).
L(x,) =  p(x, , ) (hc/) d
L is called radiance
Radiometry
Science of Measuring light
Analogous science called Photometry is based
on human perception
Radiometry contd..
The radiometric quantities that characterize
the distribution of light in the environment
are:
 Radiant Energy
 Radiance
 Radiant Power
 Irradiance
 Radiosity
 Radiant Intensity
Radiance

Radiance (L) is the flux that leaves a
surface, per unit projected area of the
surface, per unit solid angle of direction.
n

dA
L
Radiance

For computer graphics the basic particle is not
the photon and the energy it carries but the ray
and its associated radiance.
n

L
dA
Radiance is constant along a ray.
d
Properties of Radiance
1)Fundamental quantity
-all other quantities derived from it
2) Invariant along a ray
- quantity used by ray tracers
3) Sensor response is proportional to
radiance
-eye/camera response depends on
radiance
Radiant Power()
Flow of energy.
Power is the energy per unit time.
Also called as radiant flux.
 = dQ/dt.
The differential flux is the radiance in small
beam with cross sectional area dA and solid
angle d
d = L(x, ) cos d dA
Invariance of Radiance
d = L1 d1 dA1 = L2 d2 dA2
d1 =dA2 /r2 and d2 =dA1 /r2
Throughput T = d1 dA1 = d2 dA2
= dA1 dA2/ r2
Irradiance
Irradiance: Radiant power per unit area
incident on a surface
E =  Li(x,) cos  d

Radiosity
Official term : Radiant Exitance
Radiosity: Radiant power per unit area
exiting a surface
B =  Lo(x,) cos  d

Radiant Intensity
Radiant Intensity: Radiant power per solid
angle of a point source
I() = d( )/d()
 =  I() d()

For an isotropic point source: I() = /4p
Irradiance due to a Point
Light
Irradiance on a differential surface due to
an isotropic point light source is
E = d/ dA
= I() d()
dA
=  cos()
4p |x – xs|2
Reflection Functions
Reflection is defined as the the process by
which the light incident on a surface leaves
the surface from the same side.
The nomenclature and the general properties
of reflection functions are discussed.
BRDF
f(p, i , r )
Bidirectional Reflection
Distribution Function r
f(x, i , r) =Lr(x,r)/
dEi(x,r)
i
Reflected ray
Incident ray
In short this is the ratio of
radiance in a reflected
direction to the differential
irradiance that created
Illumination hemisphere
Properties of the BRDF
1)Reciprocity
f(x, i , r) = f(x, r , i)
 2)Anisotropy
If the incident and the reflected light are
fixed and the underlying surface is rotated
about the surface normal, the percentage of
light reflected may change.

Reflectance Equation
The BRDF allows us to calculate outgoing light,
given incoming light:
Lr(x,r)= f(x, i , r) * dEi(x,r)
= f(x, i , r) * Li(xi,) cos  di
Integrating over the hemisphere gives the
reflectance equation:
Lr(x,r)=
 f(x,  ,  ) * Li(x ,) cos 
i

r
i
di
Reflectance

Reflectance: ratio of reflected flux to
incident flux

L ( ) cos  r d
r = dr/ do=
r
r
r
r
 L ( ) cos  i d
i
i
i
i
Reflectance is always between 0 and 1
but depends on incident radiance distribution

Lambertian Diffuse
Reflection

Reflection is equal in all directions
f r ,diffuse (x, i , r) is constant.
Lr(x,r)=
 f r ,diffuse(x,  ,  ) * Li(x ,) cos 
i
r
i

= f r ,diffuse(x, i , r)  Li(xi,) * cos  di
= f r ,diffuse(x, i , r) E
di
Lambertian Diffuse
Reflection
Reflected radiance is independent of
direction
Therefore the radiosity is simply:
B =  Lr,diffuse(x,) cos  d

=p Lr,diffuse
= p f r ,diffuse(x, i , r) E
Lambertian Diffuse
Reflection

L ( ) cos  r d
r = dr/ do=
r
r
r
r
 L ( ) cos  i d
i
=
i
Lr,diffuse  cos r dr
r
=
i
p f r ,diffuse
E
i
Global Illumination
Radiance is invariant along a ray
Li(x`, i) = Lr(x, r) V(x,x`)
V(x,x`) is the visibility from point x to x’
Converting the directional integral
into a surface integral
di = cos o dA
|x-x`| 2
The Projected solid angle is
cos i di = cosi coso dA
|x-x`| 2
Global Illumination
Geometry term:G(x,x1) = cosi coso
|x-x`| 2
cosi di = G(x,x1) dA
 Rewriting the
reflectance equation:
Lr(x`,`)= f(x, -, `)L(xi,) G(x,x’)V(x,x`)dA
s
Global Illumination
Reparameterizing gives:
Lr(x`,`)= f(x, -, `)L(xi,) G(x,x’)V(x,x`)dA
s
Lr(x`,x``)= f(x  x`  x``)L(x  x`) G(x,x’)V(x,x`)dA
Lr(x`,x``)=Lr(x`,x``)+
s
r(x )/p *  L (x  x`) G(x,x’)V(x,x`)dA
s
The radiance sent from
x’ to x’’ is simply the
amount of radiance sent
from all other visible points x
in the scene and then reflected to x’’
Rendering Equation

Adding in the radiance directly emitted from x’ to x’’
yields the rendering equation:
Lr(x`,x``)=Lr(x`,x``)+ f(x  x`  x``)L(x  x`) G(x,x’)V(x,x`)dA
s
The radiance sent from x’ to x’’
is simply the amount of radiance
directly emitted from x’ to x’’ plus
the radiance sent from all other
visible points x in the scene
and then reflected to x’’
Radiosity Equation
More importantly the outgoing radiance is
same in all directions and in fact equals B/ p.
 B(x) = E(x) +r(x )  B(x`) G(x,x’)V(x,x`)dA
p
s
Advantages
1)Highly realistic quality of the resulting images
by calculating the diffuse interreflection of
light energy in an environment.
2)Accurate simulation of energy transfer.
3)The viewpoint independence of the basic
radiosity algorithm provides the opportunity
for interactive "walkthroughs" of
environments.
4)Soft shadows and diffuse interreflection.
Disadvantages
1)Large computational and storage costs
for form factors.
2)Must preprocess polygonal
environments.
3)Non-diffuse components of light not
represented.
4)Will be very expensive if object(s) is
moving in the scene.
References
Radiosity Papers are available here
1)http://www.scs.leeds.ac.uk/cuddles/rover/radpap.htm
2)SIGGRAPH 1993 Education Slide Set, by Stephen Spencer
http://www.education.siggraph.org/materials/HyperGraph/radioit
y/overview_1.htm
Books:
1)Radiosity and Global Illumination Sillion and Puech
ISBN 1-55860-277-1
2)Radiosity and Realistic Image Synthesis.
Cohen and Wallace .ISBN 0-12-178270-0
Software:
1)www.acurender.com