Anti-aliasing and Continuity using Trapezoidal Shadow Maps

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Anti-aliasing and ContinuityusingTrapezoidal
Shadow Maps

• Speaker Tobias Martin
• Co-Author Tiow-Seng Tan
• National University of Singapore

Standard Shadow Maps
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Content

• Shadows in Computer Graphics
• Standard Shadow Maps (SSM)
• Problems with SSM
• Problem 1 Aliasing/Resolution
• Problem 2 Polygon Offset
• Problem 3 Continuity
• Trapezoidal Shadow Maps
• Conclusion

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Shadows in Computer Graphics

• Why?
• Spatial relationship between objects is better
  perceivable
• Realism is enhanced
• Our Requirements
• Robust shadows in real-time

(Screenshots taken from shadowcast.exe by Mark
J. Kilgard, NVIDIA)
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Standard Shadow Maps (SSM)

• 1. Shadow Map Generation
• Transform scene into post-perspective space (PPS)
  of light, i.e. vL PL ? CL ? W ? v
• Render scene from this space
• Copy depth buffer into shadow map
• 2. Shadow Determination
• Render scene in eyes PPS and perform shadow test
  per-fragment
• Fragment is in shadow iff zp gt shadowmapxp, yp,
  where xp, yp and zp is fragment in PPS of light

(Screenshots taken from shadowcast.exe by Mark
J. Kilgard, NVIDIA)
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Standard Shadow Maps (SSM)

• Problem 1 Resolution ProblemJagged shadow
  boundary appears due to low resolution in shadow
  map
• ? Trivial solutionIncrease shadow map size to
  increase resolution improve quality

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Standard Shadow Maps (SSM)

• Problem 2 Polygon OffsetDue to finite
  precision, surfaces can cast wrong shadows on
  themselves
• ?Practical Solution Adding offset to depth
  values to move shadow slightly away from light

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Current Solutions

• Problem 3 Continuity (1)
• Straightforward approximation can result in
  shadow discontinuities
• e.g. in Perspective Shadow Maps (PSM)Stamminger
  and Drettakis 2002
• e.g. in the Bounding Box Approximation (BB)
  Brabec et al. 2002

Frame i 1
Frame i
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Current Solutions

• Problem 3 Continuity (2)
• What happens if shadow map depends on dynamic
  scene geometry?

light
light
scenes bounding box
eye
eye
scenes bounding box
n frames later
?expanded hull contains shadow occluders
?shadow map quality worsened
?tight hull contains shadow occluders ?good
shadow map quality
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Trapezoidal Shadow Maps (TSM)

• Solution to Problem 1 (Resolution)
• Shadow map generation focuses on area potentially
  visible to the eye
• Solution to Problem 2 (Polygon Offset)
• Depth values are preserved, so that problem is
  not worsened
• Solution to Problem 3 (Continuity)
• Frame coherent technique resulting in a
  continuous change in shadow map resolution

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Trapezoidal Shadow Maps (TSM)
PPSof light
NT
A
trapezoidal space
Shadow map resolution is increased
Shadow aliasing is reduced
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Trapezoidal Shadow Maps (TSM)

• Solution to Problem 1
• SSM algorithm is slightly modified
• Calculate shadow map in the trapezoidal space,
  and perform the shadow test there as well,
  i.e.vT NT ? PL ? CL ? W ? v
• ?Except for the calculation of NT the algorithm
  can completely be mapped to graphics hardware!

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Trapezoidal Shadow Maps (TSM)

• Side effect of the trapezoidal transformation

(b)
(a)
Non-uniform distribution
Uniform distribution

• a) Approximation of an eye's frustum with a
  trapezoid
• b) Applying NT may lead to severe polygon offset
  problems
• ? Different distribution of z-values require
  different offsets

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Trapezoidal Shadow Maps (TSM)

• Solution to (worsened) Problem 2
• Apply NT only to the x- and y-values
• Maintain z in PPS of light
• ? Store (xT , yT , zL) in the shadow map

Simply applying NT
Applying modified NT
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Trapezoidal Shadow Maps (TSM)

• 1st pass (Shadow Map Generation)
• Vertex stage
• vT NT ? PL ? CL ? W ? v
• vL PL ? CL ? W ? v
• Fragment stage
• shadowmapxT, yT zL instead of zT
• ?Use additional texture coordinate vL and replace
  zT with zL per fragment

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Trapezoidal Shadow Maps (TSM)

• 2nd pass (Shadow Determination)
• Vertex stage
• vE PE ? CE ? W ? v
• vT NT ? PL ? CL ? W ? v
• vL PL ? CL ? W ? v
• Fragment stage
• Fragment in shadow iff zL gt shadowmapxT, yT
• ? Use additional texture coordinate vL and use zL
  for shadow map comparison

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Trapezoidal Shadow Maps (TSM)

• Solution to Problem 3
• Base and Top Lines

Center Line
2D-Convex Hull
Base Top Line
l
lt
lb
CHE

• Center line governs the choices of top and base
  line ? top and base line transit smoothly from
  frame to frame

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Trapezoidal Shadow Maps (TSM)

• Side Lines 80 rule governs the choices

0
Focus region of the eye
80 line
Trapezoidal approximation in L
Trapezoidal space due to 80 rule
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Trapezoidal Shadow Maps (TSM)
q

• Calculate NT that pL is mapped to 80 line in T
• Calculate q using 1D perspective projection

map to y1
?
lt
map to y?
?
pL
?
map to y-1
E
lb
l

• (Minus signs in the proceedings got eaten up by
  the printer)

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Trapezoidal Shadow Maps (TSM)
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Trapezoidal Shadow Maps (TSM)

• Indication for Continuity
• Plot of the total area covered by focus region in
  shadow map
• Change in frustum are color encoded

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Trapezoidal Shadow Maps (TSM)
light
light
light

• General case
• Eyes frustum E is not completely within then
  lights frustum L
• Algorithm can be easily adjusted
• Singularities are avoided

eye
eye
eye
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Results

• Fantasy World
• BB vs. PSM vs. TSM
• Urban Model
• PSM vs. TSM

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Conclusion

• TSM addresses
• Resolution Problem
• Polygon Offset Problem
• Continuity Problem
• following the 3 principles
• Effectiveness of 80 rule
• Simplicity which is difficult to achieve
• Continuity rather than correctness
• Q and A

TSM
http//www.comp.nus.edu.sg/tants/tsm.html
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Literature

• BRABEC, S., ANNEN T., AND SEIDEL, H. 2002.
  Practical Shadow Mapping. Journal of Graphics
  Tools 7(4), 918.
• CROW, F. C. 1977. Shadow Algorithms for Computer
  Graphics. In
• Proceedings of SIGGRAPH 1977, 242248.
• STAMMINGER, M., AND DRETTAKIS, G. 2002.
  Perspective Shadow Maps.
• WILLIAMS, L. 1978. Casting curved shadows on
  curved surfaces. In
• Proceedings of SIGGRAPH 1978, 270274.
• WOO, A., POULIN, P., AND FOURNIER, A. 1990. A
  survey of shadow algorithms. IEEE Computer
  Graphics and Applications, 10(6), 1332.