Shadow and Shadow Maps

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Shadow and Shadow Maps
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What kind of visual cues does shadow give?

• Object without shadow seem floating above the
  scene
• Shadow gives the depth information
• Shadow gives the information of the relative
  position of lights and objects in the scene

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What kind of visual cues does shadow give?

• Shadow increases scene realism
• Shadow makes the scene conceivable

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Some Shadow Algorithms

• Shodow Polygon (Blinn)
• Basically project polygon vertices to a flat
  plane
• Shadow Polygon Scanline (Appel Bouknight, Kelly)
• Shadow Volume (F. C. Crow)

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Some Shadow Algorithms

• Shodow Polygon (Blinn)
• Shadow Polygon Scanline (Appel Bouknight, Kelly)
• Figure out all the polygons involved in
  shadowing.
• Pair each polygon that cast shadow with each
  polygon that it casts shadow upon
• Process shadow at each scanline for those
  polygons
• Shadow Volume (F. C. Crow)

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Some Shadow Algorithms

• Shodow Polygon (Blinn)
• Shadow Polygon Scanline (Appel Bouknight, Kelly)
• Shadow Volume (F. C. Crow)

• Create a volume polygon for the intersection of
  view frustum and semi-infinite shadow volume
• Collision test for the shadow volume and polygons

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Shadow Algorithms

• Pros
• Precision
• Good for production / static scenes
• Cons
• Requires non-trivial data structures
• Requires large amount of memory
• Lack hardware support
• Too slow for interactive rendering

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• Shadow Map (L. Williams 1978)
• Render from the view point of the light source.
• Use the depth buffer as shadow map

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• Shadow Map (L. Williams 1978)
• Render from camera view point
• Project to light source and compare with shadow
  map
• If the depth are the same, its not under shadow
  (1)
• If the point is behind shadow map, its under
  shadow (2)

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• Shadow Map Aliasing
• Its all because of undersampling

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• Shadow Map Aliasing
• dsrs/ri becomes large ? perspective aliasing
• cos?/cos? becomes large ? projection aliasing

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• Shadow Map Aliasing
• dsrs/ri becomes large ? perspective aliasing
• cos?/cos? becomes large ? projection aliasing

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Shadow Map

• Pros
• Performance not constrained by number of polygons
• Shadow map z-buffer.
• Supported in todays graphic cards due to its
  simplicity
• Cons
• Aliasing!

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Adaptive Shadow Map (R. Fernando, S. Fernandez,
K. Bala, D.P. Greenberg 2001)

• Transform as usual
• Analyze shadow map base on depth. Try to reduce
  dsrs/ri and cos?/cos?

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Adaptive Shadow Map

• Refined shadow map by building an hierarchical
  refinement map

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Adaptive Shadow Map

• Pros
• Much better quality than uniform shadow map
• No manual intervention involved
• Uses mip-map feature on hardware
• Cons
• Still a software solution (analyzer, data
  structure etc)
• Interactive drawbacks need to refine a lot of
  data during interaction

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Perspective Shadow Map The Idea (Marc
Stamminger, Gorge Drettakis 2002)

• Apply perspective transformation to the scene
• View frustum is now a cube instead of a pyramided

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Perspective Shadow Map The Idea

• Now the size in this new scene is proportional to
  the final image
• We take the shadow map of the new scene instead
• The result is a shadow map with resolution same
  as the final image

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Uniform Shadow Map Shadow map has lower
resolution than image plane
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Perspective Shadow Map Shadow map has exactly
same resolution than image plane
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Is it really that easy?

• No! The light sources need perspective
  transformation too
• No! All objects casting shadow into view frustum
  must be included need an optimization plan for
  bounding box

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Perspective Shadow Map Light Sources

• Light sources need to be relocated before shadow
  map is taken
• Directional light in world space becomes point
  lights in post perspective space on infinity plane

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Perspective Shadow Map Light Sources

• Point lights are still point lights but not on
  the infinity plane
• Point lights on infinity plane in world space
  becomes directional light

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Perspective Shadow Map Objects

• What happens if a shadow in view frustum is cast
  by an object outside of view frustum?
• In post-perspective space, the objects that needs
  to cast shadow appear beyond infinity plane.
• Transformed objects beyond infinity plane appears
  inverted

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Perspective Shadow Map Objects

• Need to include more than just view frustum for
  perspective transformation
• M is all rays from light source to view frustum
  boundary
• The new world space to transform, H, is
  intersection of M, S(world space boundary) and
  light frustum

Now we have a little more than just view frustum
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Perspective Shadow Map Objects

• What about the inverted trees beyond infinity
  plane?
• Move the camera back in post perspective space so
  everything looks upright

• This solves the problem but we lose some
  resolution for taking a bigger picture

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Perspective Shadow Map

• Pros
• Everything uniform shadow map does, this can do
  much better
• Way faster than adaptive shadow map
• Takes full advantage of hardware supported shadow
  map
• Cons
• Transformations are not so trivial
• Slight computational overhead
• Occasional degradation when shadows are cast by
  objects behind camera (but always better than
  shadow map)

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Perspective Shadow Map Pictures
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Perspective Shadow Map Pictures
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Perspective Shadow Map Pictures
cs2.machineroom.org/ media/doom3-2.jpg
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References

• J. Teng. Institute of automation. Chinese Academy
  of Science liama.ia.ac.cn/meeting/Archives/shadow.
  ppt 2002
• F.C. Crow Shadow algorithms for computer
  graphics. ACM Press. 1977.
• L. Williams. Casting curved shadows on curved
  surface. Computer Graphics SIGGRAPH 1978
• R. Fernando, S. Fernndez, K. Bala, D.P.
  Greenberg. Adaptive shadow maps. SIGGRAPH 2001
• M. Stamminger, G. Drettakis. Perspective shadow
  maps. SIGGRAPH 2002

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http//www-sop.inria.fr/reves/publications/data/20
02/SD02/psm_divx.avi.gz