CS 354 Shadows

CS 354
Shadows
Mark Kilgard
University of Texas
March 20, 2012

CS 354 2

Today’s material
 In-class quiz
 On GPU architecture lecture
 Lecture topic
 Shadow Algorithms
 Course status
 Mid-term graded, but not yet recorded
 Project #2 on texturing, shading, & lighting is
coming

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My Office Hours
 Tuesday, before class
 Painter (PAI) 5.35
 8:45 a.m. to 9:15
 Thursday, after class
 ACE 6.302
 11:00 a.m. to 12

 Randy’s office hours
 Monday & Wednesday
 11 a.m. to 12:00
 Painter (PAI) 5.33

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Last time, this time
 Last lecture, we
 Took the mid-term
 This lecture
 Shadow generation algorithms
 How can we efficiently determine when and
how much light is occluded by other objects
during shading?

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On a sheet of paper
Daily Quiz • Write your EID, name, and date
• Write #1, #2 followed by its answer

 Multiple choice: The effective  Multiple choice: Programmable
memory bandwidth of a tessellation is good for
graphics processor can be
higher than its raw memory a) displacement mapping
bandwidth due to:
b) per-pixel lighting
a) more multiply-add
operations per clock c) increasing the appearance of
surface curvature
b) not showing pixels when
they are opaque d) feeding more triangles to the
graphics pipeline
c) domain-specific
compression techniques e) a, c, and d
d) off-loading work to the f) a, b, c, and d
network
g) b, c, and d

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Shadows
 Important visual cue
 All real world scenes have shadows
 Lack of shadows = big clue that an image is
computer generated!
 Occlusion from light’s point-of-view instead of
viewer’s
 Cue for light-object-object relationships
 Artistic effect
 Soft vs. hard feel, dramatic or spooky feel

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Shadows Provide
Cues About Depth
 Two scenes
 Difference is in shadows

Balls resting on ground Balls floating off surface

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Computed Shadows aren’t
Necessarily Realistic

Shadows of Past – Lyubomir Bukov

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Shadows in Gaming
Shading + Shadows = More Drama

+ Bump mapping
+ Specular

Only Shadows + Shading
Diffuse + Decal Combined

+ Shadows

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Ray Tracing
Approach to Shadows
 Shadows = global lighting effect
 Involves more than light + surface

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Ray Tracing Shadow Algorithm
 Cast primary rays from eye
 Determine surface intersection
 Then, cast a secondary (shadow) ray
 From surface
 To each light source

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Interactive
Lighting Models
 Typically lack shadow support
 So-called “local” lighting models ignore
occlusion of light sources that create
shadows
 Except trivial self-shadowing (i.e., clamping L•N)
 Global lighting models account for shadows
 Examples: radiosity, ray tracing
 But too expensive for interactive use

 Interactive shadow algorithms typically
operate independent of local lighting models

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Interactive Shadow
Simplications
 True shadows are expensive, cut corners
 Simple geometry tricks
 Projection
 Volume intersection

 Pre-compute static shadow results where
possible
 Make simplifying assumptions
 Treat area light sources as points
 Exploit hardware features such as stencil and
depth textures

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Interactive Shadow
Rendering Techniques
 Different approaches, different tradeoffs
 Shadow maps
 Planar projected shadows
 Stenciled shadow volumes
 Pre-computed shadow textures (light maps)

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Common Real-time
Shadow Techniques
Projected Shadow
planar volumes
shadows

Hybrid
approaches
Light maps

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Projective Texturing
Shadow Maps Visualized

Without Shadows Projected Shadow Map With Shadows

Light’s View Light’s View Depth

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Shadow Mapping
 Image-space shadow determination
 Lance Williams published the basic idea in 1978
 By coincidence, same year Jim Blinn invented bump
mapping (a great vintage year for graphics)
 Completely image-space algorithm
 means no knowledge of scene’s geometry is required
 must deal with aliasing artifacts
 Well known software rendering technique
 Pixar’s RenderMan uses the algorithm
 Leverages GPU hardware
 Depth buffering + texture mapping
 Multi-pass algorithm: render depth maps, then
project depth maps as textures for eye view

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Shadow Mapping
References
 Important SIGGRAPH papers
 Lance Williams, “Casting Curved
Shadows on Curved Surfaces,”
SIGGRAPH 78
 William Reeves, David Salesin, and Robert Cook
(Pixar), “Rendering antialiased shadows with depth
maps,” SIGGRAPH 87
 Mark Segal, et. al. (SGI), “Fast Shadows and Lighting
Effects Using Texture Mapping,” SIGGRAPH 92
 OpenGL extensions
 ARB_shadow, ARB_depth_texture
 Standardized in OpenGL 1.4 (2002)

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Shadow Map Example
 Pixar’s Luxo Jr. – state-of-the-art for 1986
 Running in real-time – GeForce3 in Japan, 2001

3 light sources =
3 depth map
renders per frame

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Shadow Maps for Fine
Shadows

Chain-link fence is
shadow volume
nightmare!

Chain-link fence’s
shadow appears on
truck & ground with
shadow maps

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The Shadow Mapping
Concept (1)
 Depth testing from the light’s point-of-view
 Two pass algorithm
 First, render depth buffer from the light’s
point-of-view
 the result is a “depth map” or “shadow map”
 essentially a 2D function indicating the depth of

the closest pixels to the light
 This depth map is used in the second pass

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The Shadow Mapping
Concept (2)
 Shadow determination with the depth map
 Second, render scene from the eye’s point-of-
view
 For each rasterized fragment
 determine fragment’s XYZ position relative to the
light
 this light position should be setup to match the

frustum used to create the depth map
 compare the depth value at light position XY in the

depth map to fragment’s light position Z

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The Shadow Mapping
Concept (3)
 The Shadow Map Comparison
 Two values
 A = Z value from depth map at fragment’s light XY
position
 B = Z value of fragment’s XYZ light position

 If B is greater than A, then there must be
something closer to the light than the
fragment
 then the fragment is shadowed
 If A and B are approximately equal, the
fragment is lit

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Shadow Mapping
with a picture in 2D
 The A < B shadowed fragment case
depth map image plane

depth map Z = A
light
source
eye
position

eye view image plane,
aka the frame buffer
fragment’s
light Z = B

25

Shadow Mapping
CS 354

 The A ≅ B unshadowed fragment case
depth map image plane

depth map Z = A
light
source
eye
position

eye view image plane,
aka the frame buffer
fragment’s
light Z = B

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Shadow Mapping
 Note image precision mismatch!

The depth map
could be at a
different resolution
from the framebuffer

This mismatch can
lead to artifacts

27

Avoiding Artifacts with
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Depth Map Bias
 OpenGL supports glPolygonOffset that provides window-space depth bias
 Used during shadow map construction
 How much polygon offset bias depends

Too little bias, Too much bias, shadow
everything begins to starts too far back
shadow

Just right

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Visualizing the Shadow
Mapping Technique (1)
 A fairly complex scene with shadows

the point
light source

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 Compare with and without shadows

with shadows without shadows

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 The scene from the light’s point-of-view

FYI: from the
eye’s point-of-view
again

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 The depth buffer from the light’s point-of-view

FYI: from the
light’s point-of-view
again

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 Projecting the depth map onto the eye’s view

FYI: depth map for
again

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Shadow Map Eye Linear
Texture Coordinate Transform
glTexGen automatically
xe xo applies this when modelview
Eye matrix contains just the eye
ye view Modeling yo view transform
ze
= (look at) matrix zo
matrix
we wo

s 1/2 1/2 Inverse xe
Light Light
t 1/2 1/2 frustum view
eye ye
r
= (projection) (look at)
view
ze
1/2 1/2 (look at)
matrix matrix
q matrix we
1

Supply this combined transform to glTexGen or shader

CS 354 34

Projective Texturing
 Mimic perspective divide but for texture
 (s,t,r,q) → (s/q,t/q,r/q)
 Light’s view frustum needs perspective
 An intuition for projective texturing
 The slide projector analogy

Source: Wolfgang Heidrich [99]

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 Projecting the depth map onto the eye’s view

FYI: depth map for
again

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 Projecting light’s planar distance onto eye’s view
 Essentially r/q in the [0,1] range
 Analogous to window-space depth for depth buffering

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 Comparing light distance to light depth map

Green is where
the light planar
distance and Non-green is
the light depth where shadows
map are should be
approximately
equal

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 Scene with shadows

Notice how Notice how
specular curved
highlights surfaces cast
never appear shadows on
in shadows each other

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More Examples
 Smooth surfaces with object self-
shadowing

Note object self-shadowing

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More Examples
 Complex objects all shadow

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Shadow Mapping Artifacts
 Even the floor casts shadow, but…

Note shadow
leakage due to
infinitely thin
floor

Could be fixed by
giving floor
thickness

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Shadow Map Precision Artifacts
 Resolution of rendered depth map determines
shadow mapping precision

low-resolution sufficient
shadow map blockiness shadow map resolution

CS 354 43

Four Images of
Dueling Frusta Case
Eye’s View with
projection
of color-coded
Eye’s mipmap levels
View from light:
Red = minification
Blue = magnification

Light’s Light’s View with
View re-projection
of above image
from the eye

CS 354 44

Interpretation of the Images
of the Dueling Frusta Case
Region that is smallest in
the light’s view is a region
Eye’s
that is very large in the
View
eye’s view. This implies
that it would require a very
high-resolution shadow
map to avoid obvious
blocky shadow edge
artifacts.
Light’s
View

CS 354 45

Dueling Frusta Blocky
Shadow Edge Artifacts
Notice that
shadow edge
is well defined
in the
distance. Light position
out here pointing
towards the
viewer.

Blocky
shadow edge
artifacts.

CS 354 46

Shadow Acne
 Ambiguous shadow map comparisons cause very
unsightly artifacts
 Moiré patterns form; animates poorly

“shadow acne” polygon offset
depth comparison is provides sufficient depth offset
ambiguous for unambiguous depth
comparisons

CS 354 47

Planar Projected
Shadows
 So-called “fake” shadows
 Uses projective geometry trick
 Flattens 3D model into ground plane
 Shadow effect only can be applied to planes
 Supports either positional or directional lights

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Projected Planar Shadow
Example

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Projected Planar
Shadows
 Classic computer graphics trick
 Given
 Ground plane equation, Ax + By + Cz + D = 0
 Light position (x, y, z, w)

 Construct projective transform that “squishes”
vertices into ground plane based on light
position
 Concatenate this with view transform
 Rendering 3D object creates shadow-like pile
of polygons in ground plane

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Projected Planar
Shadow Matrix
 4x4 Projective Matrix

P - Lx A -Ly A -Lz A -Lw A
-Lx B P - Ly B -Lz B -Lw B
-Lx C -Ly C P - Lz C -Lw C
-Lx D -Ly D -Lz D P - Lw D

where P = Lx A + Ly B + Lz C + Lw D

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Careful about Reverse Projection
 Projection can cast a shadow of an object “behind” the
light w.r.t. the plane
 Make sure occluders are between light and ground plane

Good Bad, reverse projection

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Projected Planar
Shadow Issues
 Shadow must be cast on infinite planes
 Stencil can limit shadow to finite planar region
 “Pile of polygons” creates Z-fighting artifacts
 Polygon offset fixes this, but disturbs Z values
 Stencil testing is better solution

 Difficult to blend shadow with ground texture
 Just blending creates “double blends”
 But stencil testing can eliminate “double blends”

 Specular highlights can show in shadow

CS 354 53

Planar Projected
Shadow Artifacts
Bad Good

extends off
ground region

Z fighting double blending

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Quick Tutorial on
Stencil Testing
 An extra test for fine-grain pixel control
 Standard OpenGL and Direct3D feature
 Per-pixel test similar to depth buffering
 Tests fragment against pixel’s stencil value, rejects
fragments that fail
 Also, can modify pixel’s stencil buffer value based on stencil/
depth test results
 Hardware accelerates stencil testing
 Typically allocated with depth buffer
 8-bit stencil value paired with 24-bit depth value
 Invented by Kurt Akeley and Jim Foran (SGI)

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Stencil Testing in the
Fragment Pipeline
Fragment Pixel
+ Scissor Alpha
Ownership
Test Test
Associated Test
Data

Depth Stencil
Test Test

Blending Dithering Logic Frame
Op buffer

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Stencil Testing
 Similar to Depth Testing but
 Compares current reference value to pixel’s
stencil buffer value
 Same comparison functions as depth test:
 NEVER, ALWAYS
 LESS, LEQUAL
 GREATER, GEQUAL
 EQUAL, NOTEQUAL
 Stencil bit mask controls comparison
 (( ref & mask ) op ( svalue & mask )

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Stencil Operations
 Way stencil buffer values are controlled
 Stencil side effects of
 Stencil test fails
 Depth test fails
 Depth test passes
 Possible operations
 Increment, Decrement (saturates)
 Increment Wrap, Decrement Wrap (a.k.a. modulo)
 Keep, Replace, Zero, Invert

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OpenGL API
 Stencil function
 Controls when stencil test passes or fails
 glStencilFunc(GLenum stencil_function,
GLint reference_value,
GLuint read_mask)
 Stencil operations
 Controls how the stencil buffer is updated
 glStencilOp(GLenum stencil_fail,
GLenum depth_fail,
GLenum depth_pass)
 Stencil mask
 Controls bit-mask for writing stencil
 glStencilMask(GLuint write_mask)
 Also two-sided stencil API
 Provides different stencil operations for front- and back-facing polygons
 glStencilFuncSeparate, glStencilOpSeparate, glStencilMaskSeparate

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The Shadow Volume
Concept
 Volumetric shadows, not just planar
 A single point light source splits the world in two
 shadowed regions
 unshadowed regions
 A shadow volume is the boundary between these
shadowed and unshadowed regions
 First described by [Crow 77]
 Professor at University of Texas!
 Discrete framebuffer support
 Shadow count in the framebuffer from Fournier and
Dr. Fussell (1988)
 Translates natrually to the stencil buffer…

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Visualizing
Shadow Volumes
 Occluder and light projects a shadow volume

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Shadow Volume
Result
 Objects within the volume are shadowed

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Shadow Volume
Algorithm
 High-level view of the algorithm
 Given the scene and a light source position,
determine the shadow volume (harder than it
sounds)
 Render the scene in two passes
 Draw scene with the light enabled,
updating only fragments in unshadowed region
 Draw scene with the light disabled,

updated only fragments in shadowed region
 But how to control update of regions?

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2D Cutaway of a
Shadow Volume
surface outside
shadowing shadow volume
object (illuminated)
light
source shadow
volume
(infinite extent)

eye
position surface inside
partially
shadowed shadow volume
object (shadowed)

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Tagging Pixels as
Shadowed or Unshadowed
 Using stencil testing
 High-level algorithm does not say how to update
only either pixels in or out of the shadow volume!
 The stenciling approach
 Clear stencil buffer to zero and depth buffer to 1.0
 Render scene to leave depth buffer with closest Zs
 Render shadow volume into frame buffer with depth
testing but without updating color and depth, but inverting
a stencil bit
 This leaves stencil bit set within shadow!

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Stencil Inverting of
Shadow Volume
 Why it works
shadowing
light object
source
two inverts, left zero

one invert, left one

eye zero inverts, left zero
position

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Visualizing Stenciled
Shadow Volume Tagging
Shadowed scene Stencil buffer

red = stencil value of 1
green = stencil value of 0

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Computing
Shadow Volumes
 Harder than you might think
 Easy for a single triangle, just project out
three infinite polygons from the triangle,
opposite the light position
 But shadow volume polygons should not
intersect each other for invert trick to work
 This makes things hard
 For complex objects, projecting object’s 2D
silhouette is a good approximation (flat
objects are easy)
 Static shadow volumes can be pre-compiled

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For Shadow Volumes
With Intersecting Polygons
 Use a stencil enter/leave counting approach
 Draw shadow volume twice using face culling
 1st pass: render front faces and increment when
depth test passes
 2nd pass: render back faces and decrement when

depth test passes
 This two-pass way is more expensive than
invert
 And burns more fill rate drawing shadow
volumes
 Inverting is better if no polygon intersections

CS 354 69

Why Eye-to-Object Stencil
Counting Approach Works

Light Shadowing object
source

zero +1

zero

Example in 2D
+2 +2
Eye +1
+3
position

CS 354 70

Illuminated,
Behind Shadow Volumes (Zpass)

source

zero +1

zero

+ + + - - - Unshadowed
object
+2 +2
Eye +1
+3
position

Shadow Volume Count = +1+1+1-1-1-1 = 0

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Shadowed, Nested in Shadow
Volumes (Zpass)
source

zero +1

zero

+ + + -

+2 +2 Shadowed
Eye +1 object
+3
position

Shadow Volume Count = +1+1+1-1 = 2

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Illuminated, In Front of Shadow
Volumes (Zpass)
source

zero +1

zero

+2 +2 Shadowed
Eye +1 object
+3
position

Shadow Volume Count = 0 (no depth tests pass)

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Shadow Volume
Issues
 Practical considerations [Bergeron 86]
 If eye is in shadow volume, need to
determine this and flip enabled & disabled
lighting passes
 Shadow volume only as good as its
tessellation
 Shadows tend to magnify limited tessellation of
curved surfaces
 Open models and non-planar polygons
 Must cap the shadow volume’s intersection
with the near clipping plane

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Problem Created by
Near Clip Plane (Zpass)
Missed shadow volume
intersection due to near
clip plane clipping; leads
to mistaken count Far clip
plane

zero

+1
+1
+2
zero
+3
+2

Near clip
plane

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Alternative Approach: Zfail

 Render scene to initialize depth buffer
 Depth values indicate the closest visible
fragments
 Use a stencil enter/leave counting
approach
 Draw shadow volume twice using face
culling
 1st pass: render back faces and increment when
depth test fails
 2nd pass: render front faces and decrement when
depth test fails

CS 354 76

Illuminated,
Behind Shadow Volumes (Zfail)

source

zero +1

zero

Unshadowed
object
+2 +2
Eye +1
+3
position

Shadow Volume Count = 0 (zero depth tests fail)

CS 354 77

Shadowed, Nested in
Shadow Volumes (Zfail)
source

zero +1

zero

+ +

+2 +2 Shadowed
Eye +1 object
+3
position

Shadow Volume Count = +1+1 = 2

CS 354 78

Illuminated, In Front of Shadow
Volumes (Zfail)

source

zero +1

zero

- - - + + +

+2 +2 Shadowed
Eye +1 object
+3
position

Shadow Volume Count = -1-1-1+1+1+1 = 0

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Problem Created by
Far Clip Plane (Zfail)
Far clip
plane

Missed shadow volume
intersection due to far
clip plane clipping;
zero
leads to mistaken count

+1

zero
+1 +2
+2
+3
Near clip
plane

CS 354 80

Problem Solved by
Eliminating Far Clip

zero

+1

+1 +2
+2
+3
Near clip
plane

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Avoiding Far Plane Clipping
 Usual practice for perspective GL projection
matrix
 Use glFrustum (or gluPerspective)
 Requires two values for near & far clip planes
 Near plane’s distance from the eye
 Far plane’s distance from the eye
 Assumes a finite far plane distance
 Alternative projection matrix
 Still requires near plane’s distance from the eye
 But assume far plane is at infinity
 What is the limit of the projection matrix when
the far plane distance goes to infinity?

CS 354 82

Standard glFrustum Projection
Matrix
 2 × Near Right + Left 
 Right − Left 0 0 
Right − Left
 
 2 × Near Top + Bottom 
0 0
P= Top − Bottom Top − Bottom 
 Far + Near 2 × Far × Near 
 0 0 − − 
 Far − Near Far − Near 

 0 0 −1 0 


 Only third row depends on Far and Near

CS 354 83

Limit of glFrustum Matrix as
Far Plane is Moved to Infinity
 Right − Left 0 0 
Right − Left
 
2 × Near Top + Bottom
lim P = Pinf = 0 0 
Far →∞  Top − Bottom Top − Bottom 
 0 0 −1 − 2 × Near 
 

 0 0 −1 0 


 First, second, and fourth rows are the same as
in P
 But third row no longer depends on Far
 Effectively, Far equals ∞

84

Verifying Pinf Will Not Clip
CS 354

Infinitely Far Away Vertices (1)
 What is the most distant possible vertex in
front of the eye?
 Ok to use homogeneous coordinates
 OpenGL convention looks down the negative Z
axis
 So most distant vertex is (0,0,-D,0) where D>0

 Transform (0,0,-D,0) to window space
 Is such a vertex clipped by Pinf?
 No, it is not clipped, as explained on the next
slide

85

Verifying Pinf Will Not Clip
CS 354

Infinitely Far Away Vertices (2)
 Transform eye-space (0,0,-D,0) to clip-space
0 0
 xc   xc   Right − Left Right − Left   0 
 y  y   2 × Near Top + Bottom
  0 
 c  =  c =  0 0   
− D   zc   Top − Bottom Top − Bottom  − D 
     0 0 −1 − 2 × Near   
 − D   wc     0 

 0 0 −1 0 


 Then, assuming glDepthRange(0,1), transform clip-
space position to window-space position
zc −D
z w = 0.5 × + 0.5 = 0.5 × + 0.5 = 1
wc −D
 So ∞ in front of eye transforms to the maximum
window-space Z value, but is still within the valid depth
range (i.e., not clipped)

CS 354 86

Robust Shadow Volumes sans
Near (or Far) Plane Capping
 Use Zfail Stenciling Approach
 Must render geometry to close shadow volume extrusion
on the model and at infinity (explained later)
 Use the Pinf Projection Matrix
 No worries about far plane clipping
 Losses some depth buffer precision (but not much)

 Draw the infinite vertices of the shadow volume
using homogeneous coordinates (w=0)

CS 354 87

Visualize Net Stencil Rendering
 Non-zero stencil state marks shadowed pixels
w.r.t. the light source

Fully shaded scene Final stencil state

CS 354 88

Stencil Volume
Rendering Animation

CS 354 89

Shadow Volumes Add “Invisible”
Geometric Complexity

Visible geometry

Scene with multiple light sources Shadow volume
geometry
Abducted game images courtesy
Joe Riedel at Contraband Entertainment

CS 354 90

Examples of Possible Silhouette
Edges for Quake2 Models
An object viewed from the
same basic direction that
the light is shining on the
object has an identifiable
light-view silhouette

An object’s light-view
silhouette appears quite
jumbled when viewed form
a point-of-view that does
not correspond well with
the light’s point-of-view

CS 354 91

Multiple Lights and
Shadow Volumes
 Requires still more rendering passes,
but can work!

Shadows from different
light sources overlap
correctly

CS 354 92

Shadow Volumes from
Area Light Sources
 Make soft shadows
 Shadow volumes work for point light sources
 Area light sources are common and make
soft shadows
 Model an area light source as a collection of
point light sources [Brotman & Badler 84]
 Use accumulation buffer or additive blending
to accumulate soft shadow
 Linear cost per shadow volume sample

CS 354 93

Area Light Sources Cast Soft
Shadows
area light
source

umbra

CS 354 94

Soft Shadow Example
 Eight samples (more would be better)

Note the banding
artifacts

CS 354 95

Combined
Shadow Approaches
 Two Approaches at Once
just logo shadow volume

logo lacks shadow
on the teapot

just planar projected
teapot lacks
shadows
shadow
on the floor
combined
approach

CS 354 96

Pre-computed
Shadow Textures
 Lightmaps are static shadow textures
 Compute lightmaps off-line with radiosity
solver
 local lighting models evaluated on tight grid can
work well too
 Lightmaps with soft shadows can be built
faster with convolution approach, accelerated
using the Fast Fourier Transform [Soler &
Silion 98]
 Pre-computed shadow textures work well for
building interior with lots of diffuse surfaces

CS 354 97

Light maps can encode
Static Pre-computed Shadows
decal only

×
(modulate)

light maps only

=
* Id Software’s Quake 2
combined scene circa 1997

CS 354 98

Rendering
Soft Shadow Textures
 Fast soft shadows [Heckbert & Herf 96]
 Render a shadow texture
 For each shadowed polygon, project all light-source-
occluding polygons into the shadowed polygon’s plane
* Similar to projected planar shadows
* Model area light sources as multiple jittered points
* Use additive blending to accumulate all contributions
 Copy resulting image to the shadow texture
 Draw polygon in final scene with shadow texture

CS 354 99

Rendered
Soft Shadow Texture Example
 Shadow Texture and Final Result

Shadow texture, accumulation Final resulting scene, shadow
of nine jittered occluder texture modulated with
projections wooden floor

CS 354 100

Next Class
 Mid-term
 Return graded mid-term
 Review class statistics
 Project 2 assigned
 On texturing, shading, & lighting
 Study GLSL
 Next lecture
 Scene graphs
 How do applications organize data structures for
efficient rendering of scenes?

CS 354 Shadows

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