Shadows

1
Shadows

• Dinesh Manocha
• Computer Graphics
• COMP-770 lecture
• Spring 2009

2
What are Shadows?

• From Websters dictionary

Shad-ow (noun) partial darkness or obscurity
within a part of space from which rays from a
source of light are cut off by an interposed
opaque body
Is this definition sufficient?
3
What are Shadows?

• Does the occluder have to be opaque to have a
  shadow?
• transparency (no scattering)
• translucency (scattering)
• What about indirect light?
• reflection
• atmospheric scattering
• wave properties diffraction
• What about volumetric or atmospheric shadowing?
• changes in density

Is this still a shadow?
4
What are Shadows Really?
Volumes of space that receive no light or
lightthat has been attenuated through obscuration

• Is this definition sufficient?
• In practice, too general!
• We need some restrictions

5
Common Shadow Algorithm Restrictions

• No transparency or translucency!
• Limited forms can sometimes be handled
  efficiently
• Backwards ray-tracing has no trouble with these
  effects, but it is much more expensive than
  typical shadow algorithms
• No indirect light!
• More sophisticated global illumination algorithms
  handle this at great expense (radiosity,
  backwards ray-tracing)
• No atmospheric effects (vacuum)!
• No indirect scattering
• No shadowing from density changes
• No wave properties (geometric optics)!

6
What Do We Call Shadows?

• Regions not completelyvisible from a light
  source
• Assumptions
• Single light source
• Finite area light sources
• Opaque objects
• Two parts
• Umbra totally blocked from light
• Penumbra partially obscured

area light source
shadow
umbra
penumbra
7
Basic Types of Light Shadows
area, direct indirect
area, direct only
point, direct only
directional, direct only
SOFT SHADOWS
HARD or SHARP SHADOWS
simpler
more realistic
more realistic for small-scale scenes,
directional is realistic for scenes lit by
sunlight in space!
8
Goal of Shadow Algorithms
Ideally, for all surfaces, find the fraction of
lightthat is received from a particular light
source

• Shadow computation can be considered a global
  illumination problem
• this includes ray-tracing and radiosity!
• Most common shadow algorithms are restricted to
  direct light and point or directional light
  sources
• Area light sources are usually approximated by
  many point lights or by filtering techniques

9
Global Shadow Component inLocal Illumination
Model
Without shadows
With shadows

• Shadowi is the fraction of light received at the
  surface
• For point lights, 0 (shadowed) or 1 (lit)
• For area lights, value in 0,1
• Ambient term approximates indirect light

10
What else does this say?

• Multiple lights are not really difficult
  (conceptually)
• Complex multi-light effects are many single-light
  problems summed together!
• Superposition property of illumination model ()
• This works for shadows as well!
• Focus on single-source shadow computation
• Generalization is simple, but efficiency may be
  improved

11
Characteristics of Shadow Algorithms

• Light-source types
• Directional
• Point
• Area
• Light transfer types
• Direct vs. indirect
• Opaque only
• Transparency / translucency
• Atmospheric effects
• Geometry types
• Polygons
• Higher-order surfaces

12
Characteristics of Shadow Algorithms

• Computational precision (like visibility
  algorithms)
• Object precision (geometry-based, continuous)
• Image precision (image-based, discrete)
• Computational complexity
• Running-time
• Speedups from static viewer, lights, scene
• Amount of user intervention (object sorting)
• Numerical degeneracies

13
Characteristics of Shadow Algorithms

• When shadows are computed
• During rendering of fully-lit scene (additive)
• After rendering of fully-lit scene
  (subtractive)not correct, but fast and often
  good enough
• Types of shadow/object interaction
• Between shadow-casting object and receiving
  object
• Object self-shadowing
• General shadow casting

14
Taxonomy of Shadow Algorithms

• Object-based
• Local illumination model (Warnock69,Gouraud71,Pho
  ng75)
• Area subdivision (Nishita74,Atherton78)
• Planar projection (Blinn88)
• Radiosity (Goral84,Cohen85,Nishita85)
• Lloyd (2004)
• Image-based
• Shadow-maps (Williams78,Hourcade85,Reeves87,
  Stamminger/Drettakis02, Lloyd 07)
• Projective textures (Segal92)
• Hybrid
• Scan-line approach (Appel68,Bouknight70)
• Ray-tracing (Appel68,Goldstein71,Whitted80,Cook84)
  
• Backwards ray-tracing (Arvo86)
• Shadow-volumes (Crow77,Bergeron86,Chin89)

15
Good Surveys of Shadow Algorithms

• Early complete surveys found in (Crow77 Woo90)
• Recent survey on hard shadows Lloyd 2007 (Ph.D.
  thesis)
• Recent survey on soft shadows Laine 2007 (Ph.D.
  thesis)

16
Survey of Shadow Algorithms

• Focus is on the following algorithms
• Local illumination
• Ray-tracing
• Planar projection
• Shadow volumes
• Projective textures
• Shadow-maps
• Will briefly mention
• Scan-line approach
• Area subdivision
• Backwards ray-tracing
• Radiosity

17
Local Illumination Shadows

• Backfacing polygons are in shadow (only lit by
  ambient)
• Point/directional light sources only
• Partial self-shadowing
• like backface culling is a partial visibility
  solution
• Very fast (often implemented in hardware)
• General surface types in almost any rendering
  system!

18
Local Illumination Shadows

• Typically, not considered a shadow algorithm
• Just handles shadows of the most restrictive form
• Dramatically improves the look of other
  restricted algorithms

19
Local Illumination Shadows

• Properties
• Point or directional light sources
• Direct light
• Opaque objects
• All types of geometry (depends on rendering
  system)
• Object precision
• Fast, local computation (single pass)
• Only handles limited self-shadowing
• convenient since many algorithms do not handle
  any self-shadowing
• Computed during normal rendering pass
• Simplest algorithm to implement

20
Ray-tracing Shadows

• Only interested in shadow-ray tracing (shadow
  feelers)
• For a point P in space, determine if it is shadow
  with respect to a single point light source L by
  intersecting line segment PL (shadow feeler) with
  the environment
• If line segment intersects object, then P is in
  shadow, otherwise, point P is illuminated by
  light source L

L
shadow feeler(edge PL)
P
21
Ray-tracing Shadows

• Arguably, the simplest general algorithm
• Can even handle area light sources
• point-sample area source distributed ray-tracing
  (Cook84)

Li
Area light Li
P
P
Shadowi 0
Shadowi 2/5
22
Ray-tracing Shadows
Sounds great, whats the problem?

• Slow
• Intersection tests are (relatively) expensive
• May be sped up with standard ray-tracing
  acceleration techniques
• Shadow feeler may incorrectly intersect object
  touching P
• Depth bias
• Object tagging
• Dont intersect shadow feeler with object
  touching P
• Works only for objects not requiring
  self-shadowing

23
Ray-tracing Shadows

• How do we use the shadow feelers?
• 2 different rendering methods
• Standard ray-casting with shadow feelers
• Hardware Z-buffered rendering with shadow feelers

24
Ray-tracing Shadows
Ray-casting with shadow feelers
Light

• For each pixel
• Trace ray from eye through pixel center
• Compute closest object intersection point P along
  ray
• Calc Shadowi for point by performing shadow
  feeler intersection test
• Calc illumination at point P

Eye
25
Ray-tracing Shadows
Z-buffering with shadow feelers

• Render the scene into the depth-buffer (no need
  compute color)
• For each pixel, determine if in shadow
• unproject the screen space pixel point to
  transform into eye space
• Perform shadow feeler test with light in eye
  space to compute Shadowi
• Store Shadowi for each pixel
• Light the scene using per-pixel Shadowi values

Light
Eye
26
Ray-tracing Shadows

• Z-buffering with shadow feelers

How do we use per-pixel Shadowi values to light
the scene?

• Method 1 compute lighting at each pixel in
  software
• Deferred shading
• Requires object surface info (normal, materials)
• Could use more complex lighting model

27
Ray-tracing Shadows

• Z-buffering with shadow feelers

How do we use per-pixel Shadowi values to light
the scene?

• Method 2 use graphics hardware
• For point lights
• Shadowi values either 0 or 1
• Use stencil buffer, stencil values Shadowi
  values
• Re-render scene with the corresponding light on
  using graphics hardware but use stencil test to
  only write into lit pixels (stencil1). Should
  perform additive blending and ambient-lit scene
  should be rendered in depth computation pass.
• For area lights
• Shadowi values continuous in 0,1
• Multiple-passes and modulation blending
• Pixel Contribution Ambienti
  Shadowi(DiffuseiSpeculari)

28
Ray-tracing Shadows
Properties

• Point, directional, and area light sources
• Direct light (may be generalized to indirect)
• Opaque (thin-film transparency easily handled)
• All types of geometry (just need edge
  intersection test)
• Hybrid object-precision (line intersection),
  image-precision for generating pixel rays
• Slow, but many acceleration techniques are
  available
• General shadow algorithm
• Computed during illumination (additive, but
  subtractive is possible)
• Simple to implement

29
Planar Projection Shadows

• Shadows cast by objects onto planar surfaces
• Brute force project shadow casting objects onto
  the plane and draw projected object as a shadow

Directional light(parallel projection)
Point light(perspective projection)
30
Planar Projection Shadows

• Not sufficient
• co-planar polygons (Z-fighting) depth bias
• requires clipping to relevant portion of plane
  shadow receiver stenciling

31
Planar Projection Shadowsbetter approach,
subtractive strategy

• Render scene fully lit by single light
• For each planar shadow receiver
• Render receivers stencil pixels covered
• Render projected shadow casters in a shadow color
  with depth testing on, depth biasing (offset from
  plane), modulation blending, and stenciling (to
  write only on receiver and to avoid double pixel
  writing)
• Receiver stencil value1, only write where
  stencil equals 1, change to zero after modulating
  pixel

Texture is visible in shadow
32
Planar Projection Shadowsproblems with
subtractive strategy

• Called subtractive because it begins with
  full-lighting and removes light in shadows
  (modulates)
• Can be more efficient than additive (avoids
  passes)
• Not as accurate as additive. Doesnt follow
  lighting model
• Specular and diffuse components in shadow
• Modulates ambient term
• Shadow color is chosen by user

as opposed to the correct version
33
Planar Projection Shadowseven better approach,
additive strategy

• Draw ambient lit shadow receiving scene (global
  and all lights local ambient)
• For each light sourceFor each planar receiver
• Render receiver stencil pixels covered
• Render projected shadow casters into stenciled
  receiver area depth testing on, depth biasing,
  stencil pixels covered by shadow
• Re-render receivers lit by single light source
  (no ambient light) depth-test set to EQUAL,
  additive blending, write only into stenciled
  areas on receiver and not in shadow
• Draw shadow casting scene full-lighting

34
Planar Projection ShadowsProperties

• Point or directional light sources
• Direct light
• Opaque objects (could fake transparency using
  subtractive)
• Polygonal shadow casting objects, planar
  receivers
• Object precision
• Number of passes Lnum lights, Pnum planar
  receivers
• subtractive 1 fully lit pass, LP special
  passes (no lighting)
• additive 1 ambient lit pass, 2LP receiver
  passes, LP caster passes

35
Planar Projection ShadowsProperties

• Can take advantage of static components
• static objects lights precompute silhouette
  polygon from light source
• static objects viewer precompute first pass
  over entire scene
• Visibility from light is handled by user(must
  choose casters and receivers)
• No self-shadowing (relies on local illumination)
• Both subtractive and additive strategies
  presented
• Conceptually simple, surprisingly difficult to
  get right
• gives techniques needed to handle more
  sophisticated multi-pass methods

36
Shadow VolumesWhat are they?
Volume of space in shadow of a single occluder
with respect to a point light source OR Volume of
space swept out by extruding an occluding polygon
away from a point light source along the
projector rays originating at the point light and
passing through the vertices of the polygon
point light
occluding triangle
3D shadow volume
37
Shadow VolumesHow do you use them?

• Parity test to see if a point P on a visible
  surface is in shadow
• Initialize parity to 0
• Shoot ray from eye to point P
• Each time a shadow-volume boundary is crossed,
  invert the parity
• if parity0, P is in shadowif parity1, P is lit
• What are some potential problems?

point light
eye
0
occluder
0
0
1
1
0
parity0
parity1
parity0
38
Shadow VolumesProblems with Parity Test
Eye inside of shadow volume
Self-shadowing of visible occluders
Multiple overlapping shadow volumes
0
0
0
0
1
0
1
1
0
0

• Incorrectly shadows pts(reversed parity)
• Should a point on the occluder flip the
  parity?(consistent if not flipped)

• Point on the occluder should not flip the parity
• Touching boundary is not counted as a crossing

• Incorrectly shadows pts (incorrect parity)
• Is paritys binary condition sufficient?

39
Shadow VolumesSolutions to Parity Test Problems
Eye inside of shadow volume
Self-shadowing of visible occluders
Multiple overlapping shadow volumes
0
1
1
1
-1
-1
1
1
0
0
1
1
2
0

• Init parity to be 0 when starting outside and 1
  when inside
• Do not flip parity when viewing the in-side of
  an occluder

• Do not flip parity when viewing out-side of an
  occluder either

• Binary parity value is not sufficient, we need a
  general counter for boundary crossings 1
  entering a shadow volume, -1 exiting

40
Shadow VolumesA More General Solution

• Determine if point P is in shadow
• Init boundary crossing counter to number of
  shadow volumes containing the eye pointWhy?
  Because ray must leave this many shadow volumes
  to reach a lit point
• Along ray, increment counter each time a shadow
  volume is entered, decrement each time one is
  exited
• If the counter is gt0, P is in shadow
• Special case when P is on an occluder
• Do not increment or decrement counter
• Point on boundary does not count as a crossing

41
Shadow VolumesMore Examples

• Can you calculate the final boundary count for
  these visible points?

42
Shadow VolumesMore Examples

• Can you calculate the final boundary count for
  these visible points?

1
0
1
1
1
1
-1
1
1
-1
1
1
-1
-1
0
2
0
0
43
Shadow VolumesHow do we use this information to
find shadow pixels?

• Could just use ray-casting (ray through each
  pixel)
• Too slow, possibly more primitives to intersect
  with
• Could use silhouette of complex objects to
  simplify shadow volumes

0
0
1

-

-

1

-
0

-
-




-
-


-

0

-


-

1
2
0
1
44
Shadow VolumesUsing Standard Graphics Hardware

• Simple observations
• For convex occluders, shadows volumes form convex
  shape.
• Enter through front-facing shadow-volume
  boundariesExit through back-facing

0
0
1

-

-

1

-
0

-
-




-
-


-

0

-


-

45
Shadow VolumesUsing Standard Graphics Hardware

• Use standard Z-buffered rendering and the stencil
  buffer (8 bits) to calculate boundary count for
  each pixel
• Create shadow volumes for each occluding object
  (should be convex)
• Render the ambient lit scene, keep the depth
  values
• For each light source
• Initialize stencil values to number of volumes
  containing the eye point
• Still using the Z-buffer depth test (strictly
  less-than), but no depth update
• Render the front-facing shadow-volume boundary
  polygons, increment stencil values for all pixels
  covered by the polygons that pass the depth test
• Render the back-facing boundary polygons, but
  decrement the stencil.
• Pixels with stencil value of zero are lit,
  re-render the scene with lighting on (no ambient,
  depth-test should be set to equal).

46
Shadow VolumesUsing Standard Graphics Hardware
step-by-step

• Create shadow volumes
• Initialize stencil buffer valuesto of volumes
  containing eye

per-pixel stencil values initially 0
47
Shadow VolumesUsing Standard Graphics Hardware
step-by-step

• Render the ambient lit scene
• Store the Z-buffer
• Set depth-test to strictly less-than

48
Shadow VolumesUsing Standard Graphics Hardware
step-by-step

• Render front-facing shadow-volume boundary
  polygons
• Why front faces first? Unsigned stencil values
• Increment stencil values for pixels covered that
  pass depth-test

49
Shadow VolumesUsing Standard Graphics Hardware
step-by-step

• Render back-facing shadow-volume boundary
  polygons
• Decrement stencil values for pixels covered that
  pass depth-test

50
Shadow VolumesUsing Standard Graphics Hardware
step-by-step

• Pixels with stencil value of zero are lit
• Set depth-test to strictly equals
• Re-render lit scene with no ambient into lit
  pixels

51
Shadow VolumesMore Potential Problems

• Lots o geometry!
• Only create on shadow-casting objects
  (approximation)
• Use only silhouettes
• Lots o fill!
• Reduce geometry
• Have a good max distance
• Clip to view-volume
• Near-plane clipping

52
Shadow VolumesProperties

• Point or directional light sources
• Direct light
• Opaque objects (could fake transparency using
  subtractive)
• Restricted to polygonal objects (could be
  generalized)
• Hybrid object precision in creation of
  shadow-volumes, image-precision per-pixel stencil
  evaluation
• Number of passes Lnum lights, Nnumber of tris
• additive 1 ambient lit, 3NL shadow-volume, 1
  fully lit
• subtractive 1 fully lit, 3NL shadow-volume, 1
  image pass (modulation)
• Could be made faster by silhouette
  simplification, and by hand-picking shadow
  casters and receivers

53
Shadow VolumesProperties

• Can take advantage of static components
• static objects lights precompute shadow
  volumes from light sources
• static objects viewer precompute first pass
  over entire scene
• General shadow algorithm, but could be restricted
  for more speed
• Both subtractive and additive strategies presented

54
Projective Texture ShadowsWhat are Projective
Textures?

• Texture-maps that are mapped to a surface through
  a projective transformation of the vertices into
  the textures camera space

55
Projective Texture ShadowsHow do we use them to
create shadows?

• Project a modulation image of the shadow casting
  objects from the lights point-of-view onto the
  shadow receiving objects

Lights point-of-view
Shadow projective texture (modulation image or
light-map)
Eyes point-of-view, projective texture applied
to ground-plane(self-shadowing is from another
algorithm)
56
Projective Texture ShadowsMore details

• Fast, subtractive method
• For each light source
• Create a light camera that encloses shadowed area
• Render shadow casting objects into lights view
• only need to create a light map (1 in light, 0 in
  shadow)
• Create projective texture from lights view
• Render fully-lit shadow receiving objects with
  applied modulation projective-textures (need
  additive blending for all light sources except
  first one)
• Render fully-lit shadow casting objects

57
Projective Texture ShadowsMore examples
Cast shadows from complex objects onto complex
objects in only 2 passes over shadow casters and
1 pass over receivers (for 1 light)
Lighting for shadowed objects are computed
independently for each light source and summed
into a final image
Colored light sources. Lit areas are modulated by
value of 1 and shadow areas can be any ambient
modulation color
58
Projective Texture ShadowsProblems

• Does not use visibility information from the
  lights view
• Objects must be depth-sorted
• Parts of an object that are not visible from the
  light also have the projective texture applied
  (ambient light appears darker on shadows
  receiving objects)
• Receiving objects may already be textured
• Typically, only one texture can be applied to an
  object at a time

59
Projective Texture ShadowsSolutions well, sort
of...

• Does not use visibility information from the
  lights view
• User selects shadow casters and receivers
• Casters can be receivers, receivers can be
  casters
• Must create and apply projective textures in
  front-to-back order from the light
• Darker ambient lighting is accepted. Finding
  these regions requires a more general shadow
  algorithm
• Receiving objects may already be textured
• Use two passes first to apply base texture,
  second apply projective texture with modulation
  blending
• Use multi-texture this is what it is for! Avoids
  passes over the geometry!

60
Projective Texture ShadowsProperties

• Point or directional light sources
• Direct light (fake transparency, with different
  modulation colors)
• All types of geometry (depends on the rendering
  system)
• Image precision (image-based)
• For each light, 2 passes over shadow-casting
  objects (1 to create modulation image, 1 with
  full lighting), 1 pass over shadow receiving
  object (fully-lit w/ projective texture)
• More passes will be required for shadow-casting
  objects that are already textured
• Benefits mostly from static scene (precompute
  shadow textures)
• User must partition objects into casters and
  receivers (casters could be receivers and vice
  versa)

61
Projective Texture ShadowsHow do we apply
projective textures?

• All points on the textured surface must be mapped
  into the textures camera space (projective
  transformation)
• Position on textures camera viewplane window
  maps into the 2D texture-map

How can this be done efficiently?Slight
modification to perspectively-correct
texture-mapping
62
Projective Texture ShadowsPerspectively-incorrect
Texture-mapping

• Relies on interpolating screen-space values along
  projected edge
• Vertices after perspective transformation and
  perspective divide(x,y,z,w)?(x/w,y/w,z/w,1)

63
Projective Texture ShadowsPerspectively-correct
Texture-mapping

• Add 3D homogeneous coordinate to texture-coords
  (s,t,1)
• Divide all vertex components by w after
  perspective transformation
• Interpolate all values, including 1/w
• Obtain perspectively-correct texture-coords
  (s,t) by applying another homogeneous
  normalization (divide interpolated s/w and t/w
  terms by interpolated 1/w term)

Final perspectively-correct values, by
normalizing homogeneous texture-coords
64
Projective Texture ShadowsProjective
Texture-mapping

• Texture-coords become 4D just like vertex
  coords(x,y,z,w)?(s,t,r,q)
• Full 4x4 matrix transformation is applied to
  texture-coords
• Projective transformations also allowed, another
  perspective divide is needed for texture-coords
• Vertices homogeneous space to screen-space
• (x,y,z,w)?(x/w,y/w,z/w)
• Texture-coords homogeneous space to
  texture-space
• (s,t,r,q) ?(s/q,t/q,r/q)
• Requires another per-vertex transformation, but
  per-pixel work is same as in perspectively-correct
  texture-mapping (Segal92)

65
Projective Texture ShadowsProjective
Texture-mapping

• Given vertex v, corresponding texture-coords t,
  and two 4x4 matrix transformations M and T (M
  composite modeling, viewing, and projection
  transformations, and T texture-coords
  transformation matrix)
• Each vertex represented as Mv, Tt x y z
  w s t r q
• Transformed into screen space through a
  perspective divide of all components by w
• x y z w s t r q ? x/w y/w z/w s/w t/w r/w
  q/w
• All values are linearly interpolated along edge
  (across polygon face)
• Perform per-pixel homogeneous normalization of
  texture-coords by dividing interpolated q/w value
• x y z s t r x/w y/w z/w (s/w)/(q/w)
  (t/w)/(q/w) (r/w)/(q/w)
• Same as perspectively-correct texture-mapping,
  but instead of dividing by interpolated 1/w,
  divide by interpolated q/w (Segal92)

66
Projective Texture ShadowsProjective
Texture-mapping
Final perspectively-correct values, by
normalizing homogeneous texture-coords
67
Projective Texture ShadowsProjective
Texture-mapping

• So how do we actually use this to apply the
  shadow texture?
• Use the vertexs original coords as the
  texture-coords
• Texture transformationT LightProjectionLightV
  iewing NormalModeling

68
Shadow-Mapsfor accelerating ray-traced shadow
feelers
Light

• Previously, shadow feelers had to be intersected
  against all objects in the scene
• What if we knew the nearest intersection point
  for all rays leaving the light?
• The depth-buffer of the rendered scene from a
  camera at the light would give us a discretized
  version of this
• This depth-buffer is called a shadow-map
• Instead of intersecting rays with objects, we
  intersect the ray with the light viewplane, and
  lookup up the nearest depth value.
• If the lights depth value at this point is less
  than the depth to the eye-ray nearest
  intersection point, then this point is in shadow!

Light-ray nearest intersection point
Eye
L
E
Eye-ray nearest intersection point
If L is closer to the light than E, then E is in
shadow
69
Shadow-Mapsfor accelerating ray-traced shadow
feelers

• Cool, we can really speed up ray-traced shadows
  now!
• Render from eye view to accelerate first-hit
  ray-casting
• Render from light view to store first-hits from
  light
• For each pixel-ray in the eyes view, we can
  project the first hit point into the lights view
  and check if anything is intersecting the shadow
  feeler with a simple table lookup!
• The shadow-map is discretized, but we can just
  use the nearest value.
• What are the potential problems?

70
Shadow-MapsProblems with Ray-traced Shadow Maps

• Still too slow
• requires many per-pixel operations
• does not take advantage of pixel coherence in eye
  view
• Still has self-shadowing problem
• need a depth bias
• Discretization error
• Using the nearest depth value to the projected
  point, may not be sufficient
• How can we filter the depth-values? The standard
  way does not really make sense here.

71
Shadow-Mapsfaster way standard shadow-map
approach

• Not normally used as a ray-tracing acceleration
  technique, normally used in a standard Z-buffered
  graphics system
• Two methods presented (Williams78)
• Subtractive post-processing on final lit image
  (like full-scene image warping)
• Additive as implemented in graphics hardware
  (OpenGL extension on InfiniteReality)

72
Shadow-Mapsillustration of basic idea
Shadow-map from light 1
Shadow-map from light 2
Final view
73
Shadow-MapsSubtractive

• Render fully-lit scene
• Create shadow-map render depth from lights view
• For each pixel in final image
• Project point at each pixel from eye screen-space
  into light screen-space (keep eye-point depth De)
• Look up light depth value Dl
• Compare depth values, if DlltDe eye-point is in
  shadow
• Modulate, if point is in shadow

74
Shadow-MapsSubtractive advantages

• Constant time shadow computation!
• just like full-scene image-warping eye view
  pixels are warped to light view and then a depth
  comparison is performed
• Only a 2-pass algorithm
• 1 eye pass, 1 light pass (and 1 constant time
  image-warping pass)
• Deferred shading (for shadow computation)

Zhang98 presents a similar approach using a
forward-mapping (from light to eye, reverses this
whole process)
75
Shadow-MapsSubtractive disadvantages

• Not as accurate as additive (same reasons)
• Specular and diffuse components in shadow
• Modulates ambient term
• Has standard shadow-map problems
• Self-shadowing depth-bias needed
• Depth sampling error how do we accurately
  reconstruct depth values from a point-sampling?

76
Shadow-MapsAdditive

• Create shadow-map render depth from lights view
• Use shadow-map as a projective texture!
• While scan-converting triangles
• apply shadow-map projective texture
• instead of modulating with looked-up depth value
  Dl, compare the value against the r-value (De) of
  the transformed point on the triangle
• Compare De to Dl , if DlltDe eye-point is in shadow

Basically, scan-converting triangle in both eye
and light spaces simultaneously and performing a
depth comparison in light space against
previously stored depth values
77
Shadow-MapsAdditive advantages

• Easily implemented in hardware
• only a slight change to the standard
  perspectively-correct texture-mapping hardware
  add an r-component compare op
• Fastest, most general implementation to date!
• As fast as projective textures, but general!

78
Shadow-MapsAdditive disadvantages

• Computes shadows on a per-primitive basis
• All pixels covered by all primitives must go
  through shadowing and lighting operation whether
  visible or not (no deferred shading)
• Still has standard shadow-mapping problems
• Self-shadowing
• Depth sampling error

79
Shadow-MapsSolving main problems self-shadowing

• Use a depth bias during the transformation into
  light space
• Add a z translation towards the light source
  after transformation from eye to light
• OR
• Add z-translation towards eye before transforming
  into light space
• OR
• Translate eye-space point along surface normal
  before transforming into light space

80
Shadow-Maps

• Solving main problems depth sampling
• Could just use the nearest sample, but how would
  you anti-alias depth?

81
Shadow-MapsDepth sampling normal filtering

• Averaging depth doesnt really make sense
  (unrelated to surface, especially at shadow
  boundaries!)
• Still a binary result, (no anti-aliased softer
  shadows)

82
Shadow-MapsDepth sampling percentage closer
filtering (Reeves87)

• Could average binary results of all depth map
  pixels covered
• Soft anti-aliased shadows
• Very similar to point-sampling across an area
  light source in ray-traced shadow computation

83
Shadow-MapsHow do you choose the samples?
Quadrilateral represents the area covered by a
pixels projection onto a polygon after being
projected into the shadow-map
84
Scanline Algorithmsclassic by Bouknight and
Kelley

• Project edges of shadow casting triangles onto
  receivers
• Use shadow-volume-like parity test during
  scanline rasterization

85
Area-Subdivision Algorithmsbased on
Atherton-Weiler clipping

• Find actual visible polygon fragments
  (geometrically) through generalized clipping
  algorithm
• Create model composed of shadowed and lit
  polygons
• Render as surface detail polygons

86
Area-Subdivision Algorithmsbased on
Atherton-Weiler clipping
87
Multiple Light Sourcesfor any single-light
algorithm

• Accumulate all fully-lit single-light images into
  a single image through a summing blend op
  (standard accumulation buffer or blending
  operations)
• Global ambient lit scene should be added in
  separately
• Very easy to implement
• Could be inefficient for some algorithms
• Use higher accuracy of accumulation buffer
  (usually 12-bit per color component)

88
Area light Sourcesfor any point-light algorithm

• Soft or fuzzy shadows (penumbra)
• Some algorithms have some natural support for
  these
• For restricted algorithms, we can always sample
  the area light source with many point light
  sources jitter and accumulate
• Very expensive many high quality passes to
  obtain something fuzzy
• Not really feasible in most interactive
  applications
• Convolution and image -based methods are usually
  more efficient here

89
Backwards Ray-tracing

• Big topic sorry, no time

90
Radiosity

• Big topic sorry, no time

91
References

• Appel A. Some Techniques for Shading Machine
  Renderings of Solids, Proc AFIPS JSCC, Vol 32,
  1968, pgs 37-45.
• Arvo, J. Backward Ray Tracing, in A.H. Barr,
  ed., Developments in Ray 8-Tracing, Course Notes
  12 for SIGGRAPH 86, Dallas, TX, August 18-22,
  1986.
• Atherton, P.R., Weiler, K., and Greenberg, D.
  Polygon Shadow Generation, SIGGRAPH 78, pgs
  275-281.
• Bergeron, P. A General Version of Crows Shadow
  Volumes, CG A, 6(9), September 1986, pgs
  17-28.
• Blinn, Jim. Jim Blinns Corner Me and My (Fake)
  Shadow, IEEE CGA, vol 8, no 1, Jan 1988, pgs
  82-86.
• Bouknight, W.J. A Procedure for Generation of
  Three-Dimentional Half-Toned Computer Graphics
  Presentations, CACM, 13(9), September 1970, pgs
  527-536. Also in FREE80, pgs 292-301.
• Bouknight, W.J. and Kelly, K.C. An Algorithm for
  Producing Half-Tone Computer Graphics
  Presentations with Shadows and Movable Light
  Sources, SJCC, AFIPS Press, Montvale, NJ, 1970,
  pgs 1-10.
• Chin, N., and Feiner, S. Near Real-Time Shadow
  Generation Using BSP Trees, SIGGRAPH 89, pgs
  99-106.

92
References

• Cohen, M.F., and Greenberg, D.P. The Hemi-Cube
  A Radiosity Solution for Complex
  Environments,SIGGRAPH 85, pgs 31-40.
• Cook, R.L. Shade Trees, SIGGRAPH 84, pgs
  223-231.
• Cook, R.L., Porter, T., and Carpenter, L.
  Distributed Ray Tracing, SIGGRAPH 84, pgs
  127-145.
• Crow, Frank. Shadow Algorithms for Computer
  Graphics, SIGGRAPH 77.
• Goldstein, R.A.and Nagel, R. 3-D Visual
  Simulation, Simulation, 16(1), January 1971, pgs
  25-31.
• Goral, C.M., Torrance, K.E., Greenberg, D.P., and
  Gattaile, B. Modeling the Interaction of Light
  Between Diffuse Surfaces, SIGGRAPH 84 pgs
  213-222.
• Gouraud, H. Continuous Shading of Curved
  Surfaces, IEEE Trans. On Computers, C-20(6),
  June 1971, 623-629. Also in FREE80, pgs 302-308.
• Hourcade, J.C. and Nicolas, A. Algorithms for
  Antialiased Cast Shadows, Computers Grahpics
  9, 3 (1985), pgs 259-265.
• Nishita, T. and Nakamae, E. An Algorithm for
  Half-Tone Representation of Three-Dimensional
  Objects, Information Processing in Japan, Vol.
  14, 1974, pgs 93-99.
• Nishita, T., and Nakamae, E. Continuous Tone
  Representation of Three-Dimensional Objects
  Taking Account of Shadows and Interreflection,
  SIGGRAPH 85, pgs 23-30.

93
References

• Reeves, W.T., Salesin, D.H., and Cook, R.L.
  Rendering Antialiased Shadows with Depth Maps,
  SIGGRAPH 87, pgs 283-291.
• Segal, M., Korobkin, C., van Widenfelt, R.,
  Foran, J., and Haeberli, P. Fast Shadows and
  Lighting Effects Using Texture Mapping, Computer
  Graphics, 26, 2, July 1992, pgs 249-252.
• Warnock, J. A Hidden-Surface Algorithm for
  Computer Generated Half-Tone Pictures, Technical
  Report TR 4-15, NTIS AD-753 671, Computer Science
  Department, University of Utah, Salt Lake City,
  UT, June 1969.
• Whitted, T. An Improved Illumination Model for
  Shaded Display, CACM, 23(6), June 1980, pgs
  343-349.
• Williams, L. Casting Curved Shadows on Curved
  Surfaces, SIGGRAPH 78, pgs 270-274.
• Woo, Andrew, Pierre Poulin, and Alain Fournier.
  A Survey of Shadow Algorithms, IEEE CGA, Nov
  1990, pgs 13-32.
• Zhang, H. Forward Shadow Mapping, Rendering
  Techniques 98, Proceedings of the 9th
  Eurographics Rendering Workshop.

94
Acknowledgements

• Mark Kilgard (nVidia) for various pictures from
  presentation slides (www.opengl.org)
• Advanced OpenGL Rendering course notes
  (www.opengl.org)