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.

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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



  • 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.

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

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.



  • 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.


  • 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.






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