Dr. Scott Schaefer

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Radiosity

• Dr. Scott Schaefer

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Radiosity
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Radiosity

• Physically based model for light interaction
• View independent lighting
• Accounts for indirect
• illumination
• Color bleeding
• Soft shadows

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The Rendering Equation
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The Rendering Equation
Outgoing radiance from surface at p in the
direction v
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The Rendering Equation
Emitted radiance from surface at p in the
direction v
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The Rendering Equation
BRDF of surface at p
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The Rendering Equation
Ray cast from p in the direction of l
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The Rendering Equation
Output radiance of intersected surface in the
direction of -l
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The Rendering Equation
Angle between l and n
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The Rendering Equation
Integral about hemisphere centered at p
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BRDFs

• Bidirectional Reflectance Distribution Function
• Determines amount of incoming light from
  direction l reflected from
• surface in the direction of v

Image taken from A Data-Driven Reflectance Model
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Discretizing the Rendering Equation

• Assume perfectly diffuse surfaces
• Discretize space into
• patches
• Color is constant per
• patch

Image taken from Radiosity on Graphics Hardware
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Discretizing the Rendering Equation
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Discretizing the Rendering Equation
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
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Geometric Computation of Form Factors
Project patches onto hemisphere
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Geometric Computation of Form Factors
Project spherical patches onto tangent plane
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Geometric Computation of Form Factors
Divide by area of disc in tangent plane ( for
surfaces)
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Geometric Computation of Form Factors
Divide by area of disc in tangent plane ( for
surfaces)
Fi,j form factor
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
Jacobi iteration
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
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Matrix Computation of Radiosity
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Radiosity Examples
Image taken from http//www.9jcg.com/tutorials/jas
on_jacobs/radiosity_01.jpg
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Radiosity Examples
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Radiosity Examples
Image taken from www.cs.dartmouth.edu/spl/Academi
c/ComputerGraphics/Fall2004/radiosityExample.jpg
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Advantages of Radiosity

• Global illumination method modeling diffuse
  inter-reflection
• Color bleeding a red wall next to a white one
  casts a reddish glow on the white wall
• Soft shadows an area light source casts a soft
  shadow from a polygon
• No ambient hack
• View independent assigns a brightness to every
  surface

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Disadvantages of Radiosity

• Radiation is uniform in all directions
• Radiosity is piecewise constant
• No surface is transparent or translucent
• Must determine how to subdivide shapes into small
  enough patches