cse3431-lecture14-radiosity
Advanced Rendering Concepts
Local phenomena
• Transparency – light can be transmitted through objects
• Shadows – light blocked by other objects
• Attenuation – light intensity reduces with the square of the distance
Global phenomena
• Reflection of objects on other objects
• Indirect diffuse light
Realistic surface detail
• Anisotropic reflection, microstructures (e.g. fibers)
Realistic light sources
• Sun, area light sources, monitors etc
Rendering Equation
Light arriving at p from p’ and light leaving p
must balance
• b(p,p’) is the flux of light (intensity for us) leaving p’ and
arriving at p.
• v visibility factor (0, or inverse function of distance)
• ϵ is emitting flux from p’ in the direction of p
• ρ is the reflectance function at p’
• integral sums the contributions of every other point p’’
sending light to p’ that is reflected towards p
Rendering Equation
• Simple but difficult to solve
• High dimensionality
– b is a function of 6 parameters,
– ρ is a function of 9 parameters
– and we have not even used a variable for color
(wavelength of light)
• Solutions use sampling of illumination, for example photon
mapping
Realistic models
Light sources
• Physics-based illumination models
• Fluorescent etc
Materials
• BRDF: Bidirectional reflectance function
Examples of a few simple diffuse
BRDFs (wikipedia)
Interesting Phenomena
Fluorescence
Text
Fluorescence
• Material absorbs electromagnetic radiation and emits light,
usually of longer wavelength (lower frequency)
• Typical example: Material absorbs ultraviolet radiation and
emits visible light
Text
Courtesy of Hannes Grobe at WikipediaCourtesy of Beo Beyond at Wikipedia
Phosphorescence
Phosphorescence
• Material absorbs electromagnetic radiation and emits
it as light at a later time (some times several hours
later)
• Examples: glow in the dark toys, clock dials that glow
• It lead to the discovery of radioactivity in 1896
• Ironically White Phosphorus is not phosphorescent it
is chemiluminescent (light emitted as a result of
chemical reaction)
Iridescence
Iridescence
• Material appears to change colour as the angle of
view or the angle or illumination changes
Text
Courtesy of Wikipedia user Tagishsimon
Text
Courtesy of Didier Descouens, Wikipedia
http://commons.wikimedia.org/wiki/User:Archaeodontosaurus
Iridescence
• Material appears to change colour as the angle of
view or the angle or illumination changes
Text
Courtesy of Rocky Bloniarz and his family
Text
Soft shadows (wikipedia)
Global Illumination Solutions
Computing light interface between all
surfaces
Radiosity
Ray tracing
Courtesy of Henrik Wann Jensen
Radiosity
Physics-based (heat transfer and
illumination engineering)
Suited for Diffuse reflection
Infinite reflections
Soft shadows
Radiosity algorithm
Break scene into small patches, Ai
Assume uniform reflection and emission
per patch
Energy balance for all patches:
Light leaving surface = emitted light + reflected light
Example
Image from
• https://www.cg.tuwien.ac.at/research/rendering/rays-radio/
https://www.cg.tuwien.ac.at/research/rendering/rays-radio/
Notation
• Flux: energy per unit time (W)
• Radiosity B: exiting flux density (W/m^2)
• E: exiting flux density for light sources
• Reflectivity R: fraction of incoming light reflected
(unitless)
• Form factor Fij: fraction of energy leaving Ai and
arriving at Aj determined by the geometry of polygons i
and j
Energy balance on surface
patches
Light leaving patch = emitted light + reflected light
Form factor reciprocity:
Final linear system:
Linear system for n patches
Matrix O(n^2)
Computing Form-factors
• This is where all the difficulty lies
Main assumption
• Diffuse patches
Example: The Cornell scene
Comparison (from wikipedia)
With Without
Rendering without global illumination. Areas that lie outside of
the ceiling lamp’s direct light lack definition. For example, the
lamp’s housing appears completely uniform. Without the
ambient light added into the render, it would appear uniformly
black.
Rendering with global illumination. Light is reflected by
surfaces, and colored light transfers from one surface to
another. Notice how color from the red wall and green wall (not
visible) reflects onto other surfaces in the scene. Also notable is
the caustic projected onto the red wall from light passing
through the glass sphere.
http://en.wikipedia.org/wiki/Caustic_(optics)
Radiosity summary
Object space algorithm
• Algorithm operates on patches of objects in world
space
Suited for diffuse reflections
• Patches are assumed to be diffuse only
Nice soft-shadows
• Objects and lights subdivided into small patches