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Chapter 5: Sources, Shadows, ShadingLight source: Anything emits light that is internally generated

Exitance: The internally generated power per unit area around a point

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The geometry (e.g., point, line, area) of the

source has profound effects on the distribution

of light around the source.

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5.2.4 Area Sources (e.g., overcast sky) -- Modeled as surface patches whose radiance is independent of direction, i.e.,

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The radiosity at scene point P due to source point Q

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5.2.3 Line Sources (e.g., fluorescent light bulb)

-- Modeled as a thin cylinder with diameter

(2) The radiosity of patches changes as the reciprocal of distance to the source rather than the square of the distance

/ r(1) The length of the source does not change, but the width does as

Remarks:

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5.3 Local Shading Model

-- Describes radiosity at a scene point due to light sources

Object Mesh Model Shaded Model

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○ Shadows occur when the patch can not see sources

point source area source

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5.3.3 Ambient Illumination

○ Strategies for dealing with ambient illumination i) Add a constant term ii) Model the world as polygons of constant radiosity

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5.4 Application: Photometric Stereo -- Determines depths of pixels from a number of images taken under different illuminations. The variations in brightness code the shapes of scene surfaces

Basketball

。 Example:

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。 Monge curve -- A 2D curve can be formulated by an explicit function, i.e., ( )y f x

Slope:

( ) tan

dy df x

dx dx

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where C: ending at h: representing the height of the surface at the start point

( , )x y

Derivatives give changes in surface heightReconstructing the surface by summing derivatives along some path C

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5.5 Interreflections, Global Shading Models

Interreflection: A surface patch is illuminated by light reflected off other patches Global Shading Model: A shading model incorporates interreflection effects

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patch ( ) ( ) visible( , ) ( , )j i d j Q

jB P P P Q K P Q B dA

5.5.2 Solving for Radiosity Subdivide the world into small, flat patches with constant radiosity The radiosity at P on patch i due to the radiosity of patch j is

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5.5.3 Qualitative Effects of Interreflections Local shading model describes the world poorly Global shading model involves unknown terms

Assume the exitance of each patch is constant

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○ Qualitative effects of interreflection

Example 1:

ObservedPredicted

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Example 2:

Predicted Observed

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Example 3:

ObservedPredicted

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Example 4:

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