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Perspective Shadow Maps
Marc StammingerREVES/INRIA, Sophia-Antipolis, France
now at: Bauhaus-Universität, Weimar, Germany
George DrettakisREVES/INRIA, Sophia-Antipolis, France
Generate shadow
Hard shadows algorithms-Which are binary.
For example, shadow volumes ,depth buffer,ray tracing
Soft shadows algorithms-Also display the
penumbra area around the central umbra shadow.
For example, radiosity
Generate shadow
Ray Tracing Radiosity
Generate shadow
Kevin Weiler and Peter Atherton, Siggraph ‘1977– Hidden Surface Removal Using Polygon Area
Sorting
Franklin C., Siggraph ‘1977– Shadow Algorithms for Computer
Graphics
Traditional Shadow Maps
Williams, Siggraph ‘1978– render scene from light source– shadowing by depth comparison
Adaptive shadow maps
T.Lokovic E.Vearch , Siggraph ‘2000– Deep Shadow Maps
Randima F. Sebastian F. Kavita B., Siggraph ‘2001– Adaptive Shadow Maps– Replace the flat ahsdow map with an
adaptive,hierarchical representation.
Adaptive shadow maps
drawback:
By using multiple shadow maps,several rendering passes are required,and due to the more involved data structures,the methods no longer map to hardware.
Adaptive shadow maps
Introduction Method used to generate shadows: 1.clipping 2.shadow volumes These methods often suffer from robustness
problems due to the geometric computations required,and may also involve a significant rendering overhead.
Such algorithms are usually a preprocess,and are thus best suited to static scenes.
Introduction The paper by Lance Williams (Casting Curved
Shadows on Curved Surfaces) 1978 --“Shadow map“
Shadow Maps
The algorithm1.The depth values for the objects closest to
the source are stored to the depth map for each point.
2.As each point is generated into the obsevers view,it is transformed into the light source’s coordinate system and tested for visibility.
Result
shadow map aliasing
View frustum is for obsever
Light frustum is for light source
shadow map aliasing
NN
shadow map aliasing
N
α α
L/2
ds rs
1
shadow map aliasing
ds
rs
(L/2) * cosα
1
cos
1**
rs
cos*
1rsdsl
lds
cos
1**
rs
cos*
1rsdsl
lds
cos
1**
rs
cos*
1rsdsl
lds
shadow map aliasing
N
d
L/2β β
1
rs
cos
1**
ri
cos*
1ridl
ld
shadow map aliasing
cos
1**ridl
cos
1**rsdsl
cos
cos*
*
cos
1**
cos
1**
ri
rsdsdridrsds
shadow map aliasing
For an orthogonal view, d is proportional to ds*rs.
For directional light sources ,d is only dependent of ds/ri.
If d>di , shadow map aliasing happens.
shadow map aliasing
rs/ri is not close to a constant. cosβ /cosα become large. When the light rays are almost
parallel to a surface.
Situations
shadow map aliasing
prone to aliasingwhen zooming intoshadow boundaries
single shadow map pixel
shadow map aliasing
perspective aliasingparallel light
okay aliasedaliased okay
shadow map aliasing
perspective aliasing– smooth transition
alia
sed
o
vers
ampl
ed
shadow map aliasing
projection aliasing
parallel light
shadow map aliasing
projection aliasing– very local
alia
sed
o
vers
ampl
ed
Perspective shadow maps
Step
1. Mapping the scene to post-perspective space.
2. Generating a standard shadow map by rendering a view from the transformed light source to the unit cube.
perspective transformation
World space
Observer
f
n
(Camera distance)
perspective transformation
post
-pers
pect
ive
w
orl
d s
pace
perspective shadow map
standard shadow map
perspective shadow map
shadow map
imag
e
perspective shadow map
standard shadow map
perspective shadow map
alia
sed
o
vers
ampl
ed
perspective shadow map
shadow map in post-perspective space
just another shadow map projection
reduces perspective aliasing regeneration per frame necessary
parallel light transformation
post
-pers
pect
ive
w
orl
d s
pace
parallel light transformation
1. Directional light sources can be considered as point lights at infinity plane.
2. The infinity plane is at: z=(f + n) / (f - n)
3. A directional light source from behind is mapped to a “inverted” point light source.
4. A directional light parallel to the image plane remains at infinity.
point light transformationpost
-pers
pect
ive
w
orl
d s
pace
front back
point light transformation
Point light on the plane through the view point which is perpendicular to the view direction ,become directional.
discussion
best case:– parallel light in
post-perspectivespace
– no new perspectivedistortion
post
-pers
pect
ive
w
orl
d s
pace
discussion
non-optimal case:– point light
close tofrustum
worst case:– becomes
uniformshadow map p
ost
-pers
pect
ive
w
orl
d s
pace
discussion
A common problem in shadow maps is the bias necessary to avoid self-occlusion or surface acne.
This problem is increased for perspective shadow maps ,because objects are scaled non-uniformly.
Including all objects Casting Shadows
The shadow map must contain all objects within that frustum plus all potential occluders outside the frustum that can cast a shadow onto any visible object.
shadow map window
geometric method to include all necessary objects
Including all objects Casting Shadows
In World Space
Including all objects Casting Shadows
In Post-perspective Space
Including all objects Casting Shadows
When a line intersects the camera plane, where the intersection point is mapped to infinity.
Moving the center of projection back, so that we are behind the furthermost point which can cast a shadow into the view frustum.
This camera point displacement is only for the shadow map generation , not for rendering the image.
Point Rendering
Point Rendering is particularly well suited for natural objects.
For the generation of uniform shadow maps point rendering loses most of its benefits.
Perspective Shadow Map fits nicely with the point rendering.
results
results
first implementation on an Xbox game developer kit
courtesy of Thatcher Ulrich
results
results
results
No shadows Uniform shadow map
results
Perspective shadow map
conclusion
perspective shadow maps– shadow map in post-perspective space– just another shadow map matrix– non-uniform shadow map resolution– needs recomputation per frame– minimal overhead for dynamic scenes
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