Hierarchical Penumbra Casting

1
Hierarchical Penumbra Casting

• Samuli Laine
• Timo Aila
• Helsinki University of Technology
• Hybrid Graphics, Ltd.

2
Introduction

• Rendering soft shadows
• As usual, area light sources are sampled with a
  number of light samples
• Multiple receiver points to be shaded
• The main problem is solving the visibility
• which light samples are visible to which receiver
  points

3
Whats Happening?
Light source
Shadow caster
Visible surface
4
On the Scale of the Problem

• With R receiver points and L light samples there
  are RL visibility relations to solve
• For example, 1024768 resolution and 256 light
  samples gives over 200 million relations
• Ray casting is the usual solution for solving the
  visibility relations
• With T triangles, the cost of casting one shadow
  ray is O(log T)
• Total cost becomes O(RL log T)

5
About Ray Casting

• The standard ray casting approach considers only
  one ray at a time
• This inevitably leads to linear performance with
  respect to RL
• However, this is highly flexible
• We need to generate only one ray at a time
• Sub-linear complexity with respect to T is
  achieved by placing the triangles into an
  acceleration hierarchy

6
Transposing the Algorithm

• Goal sub-linear complexity w.r.t. RL
• Requires rearranging the rendering loop

Ray Tracingfor each receiver point r for
each light sample l find triangle that
blocks ray l ? r
linear to R linear to L sub-linear to T
Our Approachfor each triangle T find all l ?
r rays blocked by T
linear to T sub-linear to RL
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About Our Algorithm

• Sub-linear complexity with respect to RL is
  achieved by placing the receiver points and light
  samples into acceleration hierarchies
• Therefore, all receiver points must be gathered
  before computing the shadows
• We process one triangle at a time
• Good no need for triangle BSP
• Bad linear complexity with respect to T

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About Our Algorithm, part 2

• The full rendering process goes as follows
• 1. Ray-trace or rasterize the image without
  shadows to get the receiver points
• 2. Build the acceleration structures for receiver
  points and light samples
• 3. Process all triangles to solve the visibility
  relations between light samples and receiver
  points
• 4. Perform shading

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The Acceleration Structures

• Fixed three-level bounding volume hierarchy is
  used for the light samples
• Assuming a polygonal light source, bounding
  volumes are actually bounding polygons
• Standard bounding volume hierarchy is used for
  the receiver points
• Axis-aligned boxes as bounding volumes

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Light Sample Hierarchy

• Three levels
• All nodes have a bounding volume

Root node
Middle nodes
Leaf nodes
Entire light source
Light sample groups
Light samples
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Storing the visibility information

• A bit mask with L bits is assigned for every
  receiver point
• bit 0 light sample is visible
• bit 1 light sample is occluded
• Initially, all bits are zero
• When a triangle is found to occlude a light
  sample from a receiver point, the corresponding
  bit is set to one

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Penumbra Volumes

• All points where a triangle may block a ray from
  a bounding volume are inside the corresponding
  penumbra volume

Triangle
Penumbra volume
Bounding volume in light hierarchy
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Processing a Triangle

• First build penumbra volumes for all nodes in the
  light sample hierarchy
• For individual light samples (leaf nodes) these
  become hard shadow volumes

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Processing a Triangle

• Traverse down the receiver point hierarchy
• Step 1 Test intersection between main penumbra
  volume and bounding volume of receiver node

Triangle
Main penumbra volume
Bounding volume of entire light source
Receiver node
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Processing a Triangle

• Step 2 Update the list of active light sample
  groups
• At beginning of traversal, all groups are active

Triangle
Bounding volumes of light sample groups
Receiver node
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Processing a Triangle

• Step 3 Recurse into child nodes in receiver
  hierarchy
• With pruned list of active light sample groups

Triangle
Main penumbra volume
Bounding volume of entire light source
Child nodes
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Processing a Triangle

• Step 4 In leaf node, test receiver points vs.
  hard shadow volumes of light samples
• Update the visibility relation bits

Triangle
Light samples in active groups
Receiver points
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Summary of Recursion

• Traverse down the receiver point hierarchy
• Maintain list of active light sample groups
• Initially all groups are active
• First ensure that receiver node intersects the
  main penumbra volume, terminate otherwise
• Then prune the active light sample group list by
  intersecting receiver node vs. penumbra volumes
  of active light sample groups
• In leaf node, test receiver points against hard
  shadow volumes of remaining light samples

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Optimizations

• Umbra bits for early traversal termination
• With receiver hierarchy rebuilding to ensure
  balance
• Active plane sets
• Lazy penumbra volume and hard shadow volume
  construction
• On-demand bit mask allocation
• Coarse blocker sorting

20
Extensions

• Multiple light sample sets
• To remove banding artifacts
• Alpha matte textures
• Often used in e.g. vegetation textures
• Adaptive antialiasing
• Volumetric light sources

21
Results

• Compared against Mental Ray 3.2
• Benchmarked only the solving of the visibility
  relations
• For Mental Ray, computed both with and without
  shadows and took the difference
• More detailed results in the paper

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Grids
32K triangles256 light samples
Resolution Peak mem usage Speedup factor
12809600 058M 13.5
25601920 228M 16.7
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Flowers
903K triangles256 light samples
Resolution Peak mem usage Speedup factor
12809600 039M 3.5
25601920 154M 7.8
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Sponza
1.27M triangles256 light samples
Resolution Peak mem usage Speedup factor
12809600 062M 8.2
25601920 244M 11.4
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Results Analysis

• Sub-linearity with respect to R
• Increasing output resolution gives better
  relative performance
• Due to hierarchical processing of receiver points
• Sub-linearity with respect to L
• Using more light samples gives better relative
  performance (results in the paper)
• Due to using analytic penumbra volumes that
  represent many light samples at once

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Results More Analysis

• Somewhat high memory usage
• Depends on the output resolution
• Depends on the complexity of the shadows
• Does not depend on the number of triangles in the
  scene
• New problem dependence on the spatial size of
  light source
• Penumbra volumes become larger
• Leads to lower performance

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Conclusions

• Nice properties
• Exactly the same result as with ray casting
• No need to store all triangles at any point
• Sub-linear dependence on output resolution and
  number of light samples
• Not so nice properties
• Linear dependence on triangle count
• Memory usage can be high
• Dependence on the spatial size of light source

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Future Work

• Process multiple triangles at a time?
• Could experiment with full light sample
  hierarchy, which should (in theory) have better
  performance

29
Thank You

• Questions

Funding National Technology Agency of Finland,
Bitboys, Hybrid Graphics, Remedy Entertainment,
Nokia, ATI