Split-Plane Shadow Volumes

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Split-Plane Shadow Volumes

• Samuli Laine

Helsinki University of Technology Hybrid
Graphics, Ltd.
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Shadow Volumes

• Shadow volume Closed volume that is in shadow
• Constructed by extruding silhouette edges
• Rendering a shadow volume Identifying the
  pixels that are inside it
• After this, we have shadow information in stencil
  buffer
• Rendering shadow volumes is slow
• Our goal is to make it faster

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Z-Pass Algorithm

• Count enter/exit events along a ray from the eye
• Update stencil when SV primitive is in front of
  pixel
• Problems with near plane clipping fixed recently
  ZP algorithm Hornus et al. 2005

Eye
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Z-Fail Algorithm

• Count enter/exit events along a ray from infinity
• Update stencil when SV primitive is behind pixel

Eye
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Lets Render a 2D Shadow Volume

• 2D analog for a volume is a polygon
• Easier to illustrate, since I only have 2D slides

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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Z-Pass Algorithm Example

• Render 4-sided 2D shadow volume one side at a time

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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Z-Fail Algorithm Example

• The same situation

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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When is Z-Pass Good?

• No stencil updates where SV primitives are behind
  geometry

Good
Redundant update region
Eye at Infinity
Not good
Stencil buffer
Contents of the depth buffer
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When is Z-Fail Good?

• No stencil updates where SV primitives are in
  front of geometry

Redundant update region
Not good
Eye at Infinity
Good
Stencil buffer
Contents of the depth buffer
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Meanwhile in 3D ...
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Previous Solution Depth Bounds

• The depth bounds hardware extension NVIDIA
  bounds the update regions
• Application specifies min and max depth values
  for the update regions for each shadow volume
• If pixels are outside these bounds, no updates
  performed
• Problem bounds are often quite conservative

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Depth Bounds Example 1

• Best case no updates are needed

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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Depth Bounds Example 2

• Unfortunately, it doesnt always work that well
• This is a commoncase in 3D

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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Introducing the Split Plane

• Count enter/exit events either from eye or from
  infinity, depending on which side of plane pixel
  is
• ? Combination of Z-Pass and Z-Fail

Eye
Split plane
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Mathematically Speaking

• The formula for stencil buffer updates
• Test between zfrag and zpixel is the depth test
• Test between zpixel and zsplit is the new split
  test
• Split test chooses between Z-Pass and Z-Fail

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Why Is This A Good Idea?

• The update region is limited between SV primitive
  and the split plane

Eye at Infinity
Split plane
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Split Line Example

• Works well with the problematic shadow volume
• Assuming that we have chosen the split plane
  wisely

Eye at Infinity
Stencil buffer
Contents of the depth buffer
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Z-Pass Updates
Z-Fail Updates
Split Plane Shown
SPSV Updates
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Computing the Split Test

• How should we actually perform the split test?
• Naive Compute zsplit and compare against zpixel
• Better Construct the point representing the
  pixel and classify against plane equation P of
  the split plane

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Constructing the Split Plane

• The choice of the split plane is important
• Goal is to have the split depth inside the shadow
  volume
• Two heuristic methods presented in the paper
• Method 1 Point-Camera-Light
• Method 2 Point-Point-Light

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Method 1 Point-Camera-Light

• Span the split plane according to
• Pre-selected point p inside the object
• Position of the light source l
• Orient the plane so that it is maximally
  orthogonal to the ray from camera position c to
  light source l

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Method 1 Example
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Method 2 Point-Point-Light

• Span the split plane according to
• Two pre-selected points p1 and p2 inside the
  object
• Position of the light source l
• Camera position not taken into account

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Method 2 Example
Method 1 Point-Camera-Light
Method 2 Point-Point-Light
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Shadow Caster Decomposition

• Optimization that is useful in conjunction with
  the split-plane shadow volume algorithm
• Decompose shadow-casting object into a number of
  sub-objects
• Assign individual split plane for each sub-object
• Can give a significant reduction in number of
  stencil updates
• Actually, it also helps a bit with depth bounds

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Shadow Caster Decomposition, part 2

• Example a tree decomposed into 49 sub-objects
• 71 avg. reduction in pixel processing counts

Scene with shadows
Decomposed
Single object
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Per-Tile Split Test

• As such, we can only avoid stencil updates
• Still the same number of pixels processed ?
• Solution low-res split test in e.g. 88 pixel
  tiles
• Safe, since we are just choosing between Z-Pass
  and Z-Fail
• Then use either zmin or zmax from low-resolution
  Z buffer for early Z culling
• Instead of (zpixel vs. zsplit) we thus have
  (ztile vs. zsplit)

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Hardware Modifications

• What do we need?
• Compute the result of the split test for each
  rasterized tile
• 3 MULs and 3 ADDs per tile
• Low precision is OK
• We are just choosing between Z-Pass and Z-Fail
• Both work, so the image will always be correct

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Hardware Modifications, part 2

• Low-res rasterizer needs to have the split plane
• Proposition split plane is given to the low-res
  rasterizer by the vertex shader
• Thus, split plane would not be a part of the
  rendering state (unlike depth bounds)
• No state changes would be required when changing
  the split plane
• Split planes could be fed to GPU via auxiliary
  vertex streams

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Results

• Split-plane shadow volumes compared against
  Z-Pass and Z-Fail, both with depth bounds
• Statistics gathered from animation sequences,
  1024768 resolution
• Per-tile split test and early culling done in 88
  pixel tiles

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Knight
Ratios between comparison algorithms and
split-plane shadow volumes
Z-Pass vs. SPSV Z-Fail vs. SPSV
Non-culled tiles 2.87 2.70
Pixels processed 3.00 2.88
Pixels updated 3.51 3.42
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16Knights
Ratios between comparison algorithms and
split-plane shadow volumes
Z-Pass vs. SPSV Z-Fail vs. SPSV
Non-culled tiles 2.49 2.18
Pixels processed 2.93 2.35
Pixels updated 3.43 2.35
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Tree
Ratios between comparison algorithms and
split-plane shadow volumes
Z-Pass vs. SPSV Z-Fail vs. SPSV
Non-culled tiles 2.44 1.83
Pixels processed 2.76 1.87
Pixels updated 3.27 2.07
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Tree-Decomposed
Ratios between comparison algorithms and
split-plane shadow volumes
Z-Pass vs. SPSV Z-Fail vs. SPSV
Non-culled tiles 03.78 03.73
Pixels processed 05.26 04.79
Pixels updated 14.09 12.30
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Per-Frame Pixel Processing Counts
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Per-Frame Pixel Processing Counts
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Discussion

• The method can be applied whenever we need to
  identify pixels inside a polyhedral volume
• Shadow volumes being the most prominent
  application
• Only small hardware modifications required
• Two-stage implementation might also be feasible
• 1. render the split test results into 1-bit
  low-res buffer
• 2. render shadow volume, fetching the results
  from buffer
• Could use any kind of split surface or other
  heuristics

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Future Work

• Better understanding of how the split planes
  should be constructed new algorithms for that!
• The two methods in the paper are just a starting
  point
• Automatic shadow caster decomposition
• Trade-off between better split planes vs. more
  silhouettes
• Perhaps even dynamic on-the-fly decomposition
  based on light and camera positions?

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Thank You!

• Questions
• Thanks go to
• 3Dr group at HUT, especially Timo Aila, for
  discussions
• National Technology Agency of Finland, Bitboys,
  Hybrid Graphics, Nokia and Remedy Entertainment
  for the cash