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Shadows (2)

©Anthony Steed 2002

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Overview

Shadows – Umbra Recap Penumbra• Analytical v. Sampling

Analytical• Aspect graphs• Discontinuity meshing

Sampling• Accumulation buffer• Convolution

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Shadows

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Analytical v. Sampling

AnalyticalFind all boundaries within the penumbra.

Done almost exclusively for polygonal light sources

SamplingApproximate solution that treat the light

source as a set of points. Any shape source is possible.

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Extremal Shadow Boundaries

What is the potential area of the penumbra and umbra?

For penumbra:• Bounded by planes define by a pair of source

vertex and occluder edge where the source is in the front space and the occluder on the back

For umbra:• Similarly defined planes, but where source and

occluder are in the back space

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Extremal Shadow Boundaries

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Shading Using Extremal Planes

If you write these planes into object space

We can use a scan-conversion as we have before• At each pixel we must estimate the

proportion of the light source that can be seen

• Usually done with SVBSP tree(s)

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More Analysis

Borrowing aspect graphs from computer vision

Define critical surfaces where visual events occur• EV surfaces: planes defined by edge and vertex• EEE surfaces: quadratic surfaces defined by three

non-adjacent edges.

Penumbra volumes so far have used EV only

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EV and EEE Surfaces

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Discontinuity Meshing

Discontinuities of the illumination of a polygon occur at the places where EV and EEE surfaces intersect the polygon

Discontinuities occur at different degrees

Discontinuities are written into the geometry of the scene as before

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Shadows and Discontinuities

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Storing the Discontinuity Mesh

DM-Tree which uses both 2D BSP tree and winged edge data structure

13George Drettakis

14George Drettakis

15David Hedley

16David Hedley

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Sampling Methods

Model an area light source by multiple n point light sources

At rendering time render n times moving the light each time

Compose the image into an accumulation buffer

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Accumulation Buffer

Yet another set of hardware buffers Can be cleared (like the colour buffer) You repeatedly copy the colour buffer to it,

using a 1/N scale each time After N iterations, the A-buffer holds the

average of the N frames Obviously requires precision! • (Spend more $$)

http://www.sgi.com/software/opengl/advanced96/programs.html

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Example

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Recap

Penumbra is difficult to render correctly• Boundaries are formed by very complex

shapes Discontinuity meshing is an analytical

solution• Difficult to implement

Sampling is obviously less accurate• Potentially fast enough (soon) to do in real-

time