RADIOSITY Submitted by CASULA, BABUPRIYANK. N. Computer Graphics Computer Graphics Application Image...
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Transcript of RADIOSITY Submitted by CASULA, BABUPRIYANK. N. Computer Graphics Computer Graphics Application Image...
RADIOSITYRADIOSITY
Submitted by
CASULA, BABUPRIYANK. N
Computer GraphicsComputer Graphics
Computer Graphics
Application
Image Synthesis
Animation
Hardware &Architecture
Image Synthesis Image Synthesis
Image Synthesis
Modeling•2d/3d Rendering
•Radiosity•Illumination models•Visibility•Ray Tracing•Texture Mapping
Viewing2d/3d
RadiosityRadiosity
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.
SamplesSamples
Background needed… Background needed…
LightLight TransportRadiometryReflection Functions
LightLight
The visible light
can be polarizedOptics is the area
that studies about
these radiations
OpticsOptics
Optics
Geometric Physical Quantum
Shadows Optical Interference Photons
laws
To study radiosity Geometric Optics is needed
Light TransportationLight 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..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.
AnglesAngles
2D angle 3D/Solid Angle
Solid AngleSolid 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 QRadiant 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/) dL is called radiance
RadiometryRadiometry
Science of Measuring light
Analogous science called Photometry is based on human perception
Radiometry contd..Radiometry contd..The radiometric quantities that characterize
the distribution of light in the environment are:
Radiant EnergyRadianceRadiant PowerIrradianceRadiosityRadiant Intensity
RadianceRadiance
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
RadianceRadiance
For computer graphics the basic particle is not the photon and the energy it carries but the ray and its associated radiance.
n
dA
L d
Radiance is constant along a ray.
Properties of Radiance
1)Fundamental quantity -all other quantities derived from it2) Invariant along a ray - quantity used by ray tracers3) Sensor response is proportional to
radiance -eye/camera response depends on
radiance
Radiant Power(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
dL1 ddA1 = L2 ddA2
ddA2 /r2 and ddA1 /r2
Throughput T = ddA1 = ddA2
= dA1 dA2/ r2
Irradiance
Irradiance: Radiant power per unit area
incident on a surface
E = Li(x,cos d
RadiosityOfficial 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() =
Irradiance due to a Point Light
Irradiance on a differential surface due to
an isotropic point light source is
E = ddA
= I() d()
dA
= cos(
x – xs|2
Reflection FunctionsReflection 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.
BRDFBRDF
Bidirectional Reflection Distribution Function
f(x, i , r) =Lr(x,r)/ dEi(x,r)
In short this is the ratio of radiance in a reflected direction to the differential irradiance that created
ir
Incident ray
Reflected ray
Illumination hemisphere
f(p, i , r )
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 di
Integrating over the hemisphere gives thereflectance equation:
Lr(x,r)= f(x, i , r) * Li(xi,cos di
ReflectanceReflectanceReflectance: ratio of reflected flux to incident
flux
= dr/ do= Lr(r) cos r dr
r
Li(i) cos i di
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, i , r) * Li(xi,cos di
= f r ,diffuse(x, i , r) Li(xi,*cos di
= f r ,diffuse(x, i , r) E
Lambertian Diffuse Reflection
Reflected radiance is independent of direction
Therefore the radiosity is simply:
B = Lr,diffuse(x,cos d
Lr,diffuse
f r ,diffuse(x, i , r) E
Lambertian Diffuse Reflection
= dr/ do= Lr(r) cos r dr
r
Li(i) cos i di
i
= Lr,diffuse cos r dr
r
E
= f r ,diffuse
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 integralinto a surface integral
di = cos o dA |x-x`| 2
The Projected solid angle is
cos i di = cosi coso dA |x-x`| 2
Global IlluminationGeometry term:G(x,x1) = cosi coso
|x-x`| 2
cosi di = G(x,x1) dA Rewriting the reflectance equation:
Lr(x`,`)= f(x, -, `)L(xi,G(x,x’)V(x,x`)dAs
Global IlluminationReparameterizing gives:Lr(x`,`)= f(x, -, `)L(xi,G(x,x’)V(x,x`)dAs
Lr(x`,x``)= f(x x` x``)L(x x`G(x,x’)V(x,x`)dA
Lr(x`,x``)=Lr(x`,x``)+ x L (x x`G(x,x’)V(x,x`)dAs
s
The radiance sent from x’ to x’’ is simply the amount of radiance sent from all other visible points xin 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`)dAs
The radiance sent from x’ to x’’is simply the amount of radiancedirectly emitted from x’ to x’’ plusthe radiance sent from all othervisible points x in the sceneand then reflected to x’’
Radiosity EquationRadiosity Equation
More importantly the outgoing radiance is same in all directions and in fact equals B/
B(x) = E(x) +x B(x`) G(x,x’)V(x,x`)dA
s
AdvantagesAdvantages
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.
DisadvantagesDisadvantages
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.
ReferencesReferences
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/radioity/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