CS 354Shadows

Mark KilgardUniversity of TexasMarch 20, 2012

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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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Daily Quiz1. Multiple choice: The effective

memory bandwidth of a graphics processor can be higher than its raw memory bandwidth due to:

a) more multiply-add operations per clock

b) not showing pixels when they are opaque

c) domain-specific compression techniques

d) off-loading work to the network

2. Multiple choice: Programmable tessellation is good for

a) displacement mapping

b) per-pixel lighting

c) increasing the appearance of surface curvature

d) feeding more triangles to the graphics pipeline

e) a, c, and d

f) a, b, c, and d

g) b, c, and d

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

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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 ProvideCues 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 GamingShading + Shadows = More Drama

OnlyDiffuse + Decal

+ Shadows

+ Bump mapping+ Specular

Shadows + Shading Combined

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Ray TracingApproach 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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InteractiveLighting 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 LN)

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 ShadowSimplications

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 ShadowRendering 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-timeShadow Techniques

Shadowvolumesvolumes

Light maps

Projectedplanarshadows

Hybridapproaches

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Projective TexturingShadow Maps Visualized

Without Shadows With ShadowsProjected Shadow Map

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 MappingReferences

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’s shadow appears on truck & ground with shadow maps

Chain-link fence is shadow volume nightmare!

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The Shadow MappingConcept (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 MappingConcept (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 MappingConcept (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 Mappingwith a picture in 2D

lightsource

eyeposition

depth map Z = A

fragment’slight Z = B

depth map image plane

eye view image plane,aka the frame buffer

The A < B shadowed fragment case

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Shadow Mappingwith a picture in 2D

lightsource

eyeposition

depth map Z = A

fragment’slight Z = B

depth map image plane

eye view image plane,aka the frame buffer

The A B unshadowed fragment case

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Shadow Mappingwith a picture in 2D

Note image precision mismatch!

The depth mapThe depth mapcould be at acould be at adifferent resolutiondifferent resolutionfrom the framebufferfrom the framebuffer

This mismatch canThis mismatch canlead to artifactslead to artifacts

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Avoiding Artifacts withDepth 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 little bias,everything begins toeverything begins toshadowshadow

Too much bias, shadowToo much bias, shadowstarts too far backstarts too far back

Just rightJust right

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Visualizing the ShadowMapping Technique (1)

A fairly complex scene with shadows

the pointlight source

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Visualizing the ShadowMapping Technique (2)

Compare with and without shadows

with shadows without shadows

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Visualizing the ShadowMapping Technique (3)

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

FYI: from theeye’s point-of-viewagain

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Visualizing the ShadowMapping Technique (4)

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

FYI: from thelight’s point-of-viewagain

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Visualizing the ShadowMapping Technique (5)

Projecting the depth map onto the eye’s view

FYI: depth map forlight’s point-of-viewagain

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Shadow Map Eye LinearTexture Coordinate Transform

1/21/2

1/21/2

1/21/2

11

1/21/2

1/21/2

1/21/2LightLight

frustumfrustum(projection)(projection)

matrixmatrix

LightLightviewview

(look at)(look at)matrixmatrix

InverseInverseeyeeyeviewview

(look at)(look at)matrixmatrix

EyeEyeviewview

(look at)(look at)matrixmatrix

ModelingModelingmatrixmatrix

xxoo

yyoo

zzoo

wwoo

xxee

yyee

zzee

wwee

==

==xxee

yyee

zzee

wwee

ssttrrqq

glTexGen automatically applies this when modelview matrix contains just the eye

view transform

Supply this combined transform to glTexGen or shader

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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]Source: Wolfgang Heidrich [99]

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Visualizing the ShadowMapping Technique (5)

Projecting the depth map onto the eye’s view

FYI: depth map forlight’s point-of-viewagain

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Visualizing the ShadowMapping Technique (6)

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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Visualizing the ShadowMapping Technique (7)

Comparing light distance to light depth map

Green is where the light planar

distance and the light depth

map are approximately

equal

Non-green is where shadows should be

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Visualizing the ShadowMapping Technique (8)

Scene with shadows

Notice how specular

highlights never appear

in shadows

Notice how curved surfaces cast shadows on 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 toinfinitely thin floor

Could be fixed bygiving floor thickness

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Shadow Map Precision Artifacts

Resolution of rendered depth map determines shadow mapping precision

sufficientshadow map resolution

low-resolutionshadow map blockiness

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Four Images ofDueling Frusta Case

Eye’sView

Light’sView

Eye’s View with projectionof color-codedmipmap levelsfrom light:Red = minificationBlue = magnification

Light’s View withre-projectionof above imagefrom the eye

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Interpretation of the Imagesof the Dueling Frusta Case

Eye’sView

Light’sView

Region that is smallest in the light’s view is a region that is very large in the eye’s view. This implies that it would require a very high-resolution shadow map to avoid obvious blocky shadow edge artifacts.

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Dueling Frusta Blocky Shadow Edge Artifacts

Light position out here pointing towards the viewer.

Blocky shadow edge artifacts.

Notice that shadow edge is well defined in the distance.

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Shadow Acne Ambiguous shadow map comparisons cause very

unsightly artifacts Moiré patterns form; animates poorly

polygon offsetprovides sufficient depth offset

for unambiguous depthcomparisons

“shadow acne”depth comparison is

ambiguous

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Planar ProjectedShadows

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 ShadowExample

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Projected PlanarShadows

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 PlanarShadow 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 PlanarShadow 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

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Planar ProjectedShadow Artifacts

Bad Good

extends offground region

Z fighting double blending

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Quick Tutorial onStencil 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 theFragment Pipeline

PixelOwnership

Test

StencilTest

DepthTest

Blending Dithering Logic Op

ScissorTest

AlphaTest

Frame buffer

Fragment+

AssociatedData

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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 VolumeConcept

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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VisualizingShadow Volumes

Occluder and light projects a shadow volume

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Shadow VolumeResult

Objects within the volume are shadowed

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Shadow VolumeAlgorithm

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 aShadow Volume

shadowingobject

shadowvolume(infinite extent)

partiallyshadowed object

lightsource

eyeposition surface inside

shadow volume(shadowed)

surface outsideshadow volume(illuminated)

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Tagging Pixels asShadowed 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 ofShadow Volume

Why it works

eyeposition

lightsource

shadowingobject

two inverts, left zero

one invert, left one

zero inverts, left zero

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Visualizing StenciledShadow Volume Tagging

Shadowed scene Stencil buffer

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

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ComputingShadow 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 VolumesWith 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

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Why Eye-to-Object Stencil Counting Approach Works

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Example in 2D

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Illuminated,Behind Shadow Volumes (Zpass)

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Unshadowedobject

+ ---+ +

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

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Shadowed, Nested in Shadow Volumes (Zpass)

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Shadowedobject

+ -+ +

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

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Illuminated, In Front of Shadow Volumes (Zpass)

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Shadowedobject

Shadow Volume Count = 0 (no depth tests pass)

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Shadow VolumeIssues

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 byNear Clip Plane (Zpass)

zero

zero

+1+1+2

+2+3

Near clipplane

Far clipplane

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

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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

Don’t update depth or color Afterward, pixel’s stencil is non-zero if pixel in

shadow, and zero if illuminated

Alternative Approach: Zfail

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Illuminated,Behind Shadow Volumes (Zfail)

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Unshadowedobject

Shadow Volume Count = 0 (zero depth tests fail)

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Shadowed, Nested inShadow Volumes (Zfail)

Shadowing objectLightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Shadow Volume Count = +1+1 = 2

+ +

Shadowedobject

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Illuminated, In Front of Shadow Volumes (Zfail)

Shadowing object Lightsource

Eyeposition

zero

zero

+1

+1+2 +2

+3

Shadowedobject

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

- +- - + +

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Problem Created byFar Clip Plane (Zfail)

zero

Near clipplane

Far clipplane

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

+1

+1 +2+2+3

zero

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Problem Solved byEliminating Far Clip

zero

+1

+1 +2+2+3

Near clipplane

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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 whenthe far plane distance goes to infinity?

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Standard glFrustum Projection Matrix

Only third row depends on Far and Near

0100

200

02

0

002

NearFarNearFar

NearFarNearFar

BottomTopBottomTop

BottomTopNear

LeftRightLeftRight

LeftRightNear

P

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Limit of glFrustum Matrix asFar Plane is Moved to Infinity

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

Effectively, Far equals ∞

01002100

020

002

lim

NearBottomTopBottomTop

BottomTopNear

LeftRightLeftRight

LeftRightNear

Far infPP

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Verifying Pinf Will Not ClipInfinitely 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

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Verifying Pinf Will Not ClipInfinitely Far Away Vertices (2)

Transform eye-space (0,0,-D,0) to clip-space

0

00

01002100

020

002

DNear

BottomTopBottomTop

BottomTopNear

LeftRightLeftRight

LeftRightNear

wzyx

DDyx

c

c

c

c

c

c

15.05.05.05.0

DD

wzzc

cw

Then, assuming glDepthRange(0,1), transform clip-space position to window-space position

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)

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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)

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Visualize Net Stencil Rendering

Non-zero stencil state marks shadowed pixels w.r.t. the light source

Fully shaded scene Final stencil state

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Stencil VolumeRendering Animation

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Shadow Volumes Add “Invisible” Geometric Complexity

Visible geometry

Shadow volume geometry

Scene with multiple light sources

Abducted game images courtesyJoe Riedel at Contraband Entertainment

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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

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Multiple Lights andShadow Volumes

Requires still more rendering passes,but can work!

Shadows from differentlight sources overlapcorrectly

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Shadow Volumes fromArea 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

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Area Light Sources Cast Soft Shadows

umbra

area lightsource

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Soft Shadow Example

Eight samples (more would be better)

Note the bandingartifacts

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CombinedShadow Approaches

Two Approaches at Oncejust logo shadow volume

combinedapproach

just planar projectedshadowsteapot lacks

shadowon the floor

logo lacks shadowon the teapot

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Pre-computedShadow 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

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Light maps can encodeStatic Pre-computed Shadows

(modulate)

=

light maps onlylight maps only

decal onlydecal only

combined scenecombined scene* Id Software’s Quake 2

circa 1997

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RenderingSoft 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

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RenderedSoft Shadow Texture Example

Shadow Texture and Final Result

Shadow texture, accumulationof nine jittered occluderprojections

Final resulting scene, shadowtexture modulated withwooden floor

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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?