RADIOSITY

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RADIOSITY

• Submitted by
• CASULA, BABUPRIYANK. N

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Computer Graphics
Hardware Architecture

• Computer
• Graphics

Animation
Application
Image Synthesis
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Image Synthesis
Image Synthesis

• Modeling
• 2d/3d

Viewing 2d/3d

• Rendering
• Radiosity
• Illumination models
• Visibility
• Ray Tracing
• Texture Mapping

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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.

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Samples
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Background needed

• Light
• Light Transport
• Radiometry
• Reflection Functions

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Light

• The visible light
• can be polarized
• Optics is the area
• that studies about
• these radiations

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Optics

• Optics
• Geometric Physical Quantum
• Shadows Optical Interference Photons
• laws
• To study radiosity Geometric Optics is needed

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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

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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.

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Angles

• 2D angle 3D/Solid Angle

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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?

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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

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Radiometry

• Science of Measuring light
• Analogous science called Photometry is based on
  human perception

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Radiometry contd..

• The radiometric quantities that characterize the
  distribution of light in the environment are
• Radiant Energy
• Radiance
• Radiant Power
• Irradiance
• Radiosity
• Radiant Intensity

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Radiance

• Radiance (L) is the flux that leaves a surface,
  per unit projected area of the surface, per unit
  solid angle of direction.

n
L
?
dA
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Radiance

• For computer graphics the basic particle is not
  the photon and the energy it carries but the ray
  and its associated radiance.

Radiance is constant along a ray.
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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

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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

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Invariance of Radiance

• dF L1 dw1 dA1 L2 dw2 dA2
• dw1 dA2 /r2 and dw2 dA1 /r2
• Throughput T dw1 dA1 dw2 dA2
• dA1 dA2/ r2

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Irradiance

• Irradiance Radiant power per unit area
• incident on a surface
• E ? Li(x,w) cos q dw
• ?

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Radiosity

• Official term Radiant Exitance
• Radiosity Radiant power per unit area
• exiting a surface
• B ? Lo(x,w) cos q dw
• ?

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Radiant Intensity

• Radiant Intensity Radiant power per solid angle
  of a point source
• I(w) d(F )/d(w)
• F ? I(w) d(w)
• ?
• For an isotropic point source I(w) F/4p

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Irradiance due to a Point Light

• Irradiance on a differential surface due to
• an isotropic point light source is
• E dF/ dA
• I(w) d(w)
• dA
• F cos(q)
• 4p x xs2

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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.

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BRDF

• 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

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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.

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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,w) cos q
  dwi
• Integrating over the hemisphere gives the
• reflectance equation
• Lr(x,?r) ? f(x, ?i , ?r) Li(xi,w) cos q dwi
• ?

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Reflectance

• Reflectance ratio of reflected flux to incident
  flux
• r d?r/ d?o ? Lr(?r) cos q r dwr
• ?r
• ? Li(?i) cos q i dwi
• ?i
• Reflectance is always between 0 and 1
• but depends on incident radiance distribution

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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,w)
  cos q dwi
• ?
• f r ,diffuse(x, ?i , ?r) ? Li(xi,w) cos q
  dwi
• f r ,diffuse(x, ?i , ?r) E

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Lambertian Diffuse Reflection

• Reflected radiance is independent of direction
• Therefore the radiosity is simply
• B ? Lr,diffuse(x,w) cos q dw
• ?
• p Lr,diffuse
• p f r ,diffuse(x, ?i , ?r) E

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Lambertian Diffuse Reflection

• r d?r/ d?o ? Lr(?r) cos q r dwr
• ?r
• ? Li(?i) cos q i dwi
• ?i
• Lr,diffuse ? cos qr dwr
• ?r
  E
• p f r ,diffuse

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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
• dwi cos qo dA
• x-x 2
• The Projected solid angle is
• cos qi dwi cosqi cosqo dA
• x-x 2

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Global Illumination

• Geometry termG(x,x1) cosqi cosqo
• 
  x-x 2
• cosqi dwi G(x,x1) dA
• Rewriting the
• reflectance equation
• Lr(x,?)? f(x, -?, ?)L(xi,w) G(x,x)V(x,x)dA
• s

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Global Illumination

• Reparameterizing gives
• Lr(x,?)? f(x, -?, ?)L(xi,w) 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) r(x )/p ? L (x ? x)
  G(x,x)V(x,x)dA
  s
• 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

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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
• 
  

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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
• 
  s p

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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.

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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.

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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.siggrap
  h.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