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Direct Illumination with Lazy Visibility EvaluationPowerPoint Presentation

Direct Illumination with Lazy Visibility Evaluation

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### Direct Illumination with Lazy Visibility Evaluation

David Hart

Philip Dutré

Donald P. Greenberg

Cornell University

SIGGRAPH 99

Motivation

- To compute the direct illumination in a three-dimensional scene:
- Determines the visibility between any surface point and an area light source.
- An efficient processing of the visibility function is often the key for rendering fast and accurate soft shadows.

- Integrates the incoming radiance function due to the light source.

- Determines the visibility between any surface point and an area light source.

Distinguishing Features

- Two phases:
- Visibility function
- Rendering equation

- The visibility pass detects blocker-light source pairs.
- Do NOT construct a complete discontinuity mesh in object space.

- The second phase clips the light sources according to the stored blockers.
- The remaining light source area defines the integration domain for the illumination integral.

- We store no visibility information that will not be needed during the illumination computations.

Rendering Equation

- Too complex!

Analytic Integration

- The luminaires are a (disjoint) set of polygons.
- The exitant radiance is a constant for a given light source.
- The receiving surface is diffuse.
- Use Stoke’s theorem:

Monte Carlo Integration

- Regardless of the type of BRDF.
- Domain reduction
- A fraction of the generated samples will evaluate to zero causing significant noise in the image.
- A reduction of the integration domain to the visible parts of the light sources would decrease noise significantly.

- Solid angle sampling
- The integration domain can be transformed from the area of the light sources to the solid angle subtended by the light sources on the hemisphere around.

Construction of The Blocker-Map

- Shadow rays
- A ray is cast through the center of each pixel find the nearest visible point and a number of shadow rays starting from that point are generated for each light source.
- If one of these rays hits an intervening object, this blocker-light source pair is stored.

- Flood-fill algorithm
- The blocker is projected onto the light source and neighboring pixels are examined.
- If the two polygons (blocker and light source) overlap, the pair will be added to the blocker-map.

Anti-Aliasing

- If more than one ray per pixel is generated for illumination computations as part of an anti-aliasing algorithm.
- The blocker-light source list might be invalid.
- The surface points might be located in very different positions in object space.

- The coherency of the penumbra regions over the image plane can again be exploited. Due to the flood-fill, we know that a blocker is at least valid for the center location of all covered pixels. Blah blah …
- If we allow the flood-fill algorithm to include the boundary pixels for which the flood-fill test fails, we can safely assume that we have stored all possible blockers.
- To generate multiple sample rays for illumination computations, without increasing the number of rays used for constructing the blocker-map.
- High-frequency geometry, such as small objects, might be overlooked.

Discussion

- Missing blockers.
- Increases the number of shadow rays.
- Concludes any rather than the nearest intersecting polygon.

- Receiver surfaces.
- Produces soft shadows on any surface type.

- Small blockers.
- Clip a very small piece of the light source.
- A whole set of small blockers might significantly affect the visibility of a light source, thus they cannot be ignored.

- Requires a full clipping operation.
- This is a worst-case scenario for our current algorithm.

- Clip a very small piece of the light source.

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