程序代写代做代考 algorithm AI cse3431-lecture14-radiosity

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