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Shadow Rendering Shadow Rendering Techniques: Hard and Techniques: Hard and

SoftSoftAuthor: Jamiur RahmanAuthor: Jamiur Rahman

Supervisor: Mushfiqur RoufSupervisor: Mushfiqur RoufDepartment of CSEDepartment of CSE

BRAC UniversityBRAC University

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ChaptersChapters Shadows: Hard and SoftShadows: Hard and Soft Hard Shadow Rendering TechniquesHard Shadow Rendering Techniques Soft Shadow Rendering TechniquesSoft Shadow Rendering Techniques Recent Works Recent Works

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ShadowsShadows A point is in shadow if the light got blocked A point is in shadow if the light got blocked

between the light source and point between the light source and point Light Source

Viewer

Point is in shadow

Occluder

Point is lit

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ShadowsShadows Terminology: Umbra and PenumbraTerminology: Umbra and Penumbra

(area) light source

receiver shadow

occluder

umbra

penumbra• umbra – fully shadowed region• penumbra – partially shadowed region

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““Hard” and “Soft” Hard” and “Soft” ShadowsShadows

Depends on the type of light sourcesPoint or Directional (“Hard Shadows”, umbra)

Area (“Soft Shadows”, umbra, penumbra), more difficult problem

point directional area

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““Hard” and “Soft” Hard” and “Soft” ShadowsShadows

Hard shadow Soft shadow – point light source – area light source

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Hard Shadow Hard Shadow RenderingRendering

Techniques Techniques

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Planar ShadowsPlanar Shadows The simplest algorithm – shadowing The simplest algorithm – shadowing

occurs when objects cast shadows on occurs when objects cast shadows on planar surfaces (projection shadows)planar surfaces (projection shadows)

shadow

lighty

y=0

shadow

lighty

n.x + d =0

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Planar ShadowsPlanar Shadows Special case: the shadow receiver is Special case: the shadow receiver is

an axis plane an axis plane Just project all the polygon vertices to Just project all the polygon vertices to

thatthat plane and form shadow polygonsplane and form shadow polygons

shadow

lighty

y=0

v

p

Given: - Light position l- Plane position y = 0- Vertex position v

Calculate: p

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Planar ShadowsPlanar Shadows We can use similar triangles to solve We can use similar triangles to solve

pp

shadow

lighty

y=0

v

px

px-lx ly

vx-lx ly-vy=

px = ly vx – lx vy

ly - vy

l

• Same principle applied to different axis planes

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Planar ShadowsPlanar Shadows Basic algorithmBasic algorithm

Render scene (full lighting)Render scene (full lighting) For each receiver polygonFor each receiver polygon

Compute projection matrix Compute projection matrix MM Mult with actual transformation Mult with actual transformation

(modelview)(modelview) Render selected (occluder) geometryRender selected (occluder) geometry

Darken/BlackDarken/Black

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Shadow VolumesShadow Volumes [Crow77][Crow77] Shadow algorithms for computer Shadow algorithms for computer

graphics graphics Compute regions of shadow in 3DCompute regions of shadow in 3D

Object-space algorithmObject-space algorithm Cast shadows onto arbitrary receiver Cast shadows onto arbitrary receiver

geometrygeometry(polygons)(polygons)

From the School of Leonardo Da Vinci

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Shadow VolumesShadow Volumes Extend occluder polygons to form Extend occluder polygons to form

semi-infinite volumessemi-infinite volumes Light source is Light source is center-of-projectioncenter-of-projection Everything behind occluder is in Everything behind occluder is in

shadowshadow Test if point is in at leastTest if point is in at least

one volume !one volume ! Extend to reach outsideExtend to reach outside

of view frustum of view frustum

Light Source

Shadow Region

Occluder

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Shadow VolumesShadow Volumes Shadow Volumes illustrated (2D)Shadow Volumes illustrated (2D)

shadowingobject

shadowvolume(infinite extent)

partiallyshadowed object

lightsource

eyeposition surface inside

shadow volume(shadowed)

surface outsideshadow volume(illuminated)

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Shadow VolumesShadow Volumes Shadow volume generationShadow volume generation

Trivial wayTrivial way One volume for each polygonOne volume for each polygon

BetterBetter Silhouette-based approachSilhouette-based approach

Goal: one shadow volumeGoal: one shadow volume Selected occluders onlySelected occluders only

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Shadow VolumesShadow Volumes Use stencil buffer as counter Use stencil buffer as counter

1. Render scene (ambient color)1. Render scene (ambient color)

2. Render front-facing parts of shadow volumes2. Render front-facing parts of shadow volumes with stencil operation with stencil operation incrementincrement (enter) (enter)

3. Render back-facing parts of shadow volumes3. Render back-facing parts of shadow volumes with stencil operation with stencil operation decrementdecrement (exit) (exit)

4. Render scene (fully lit) 4. Render scene (fully lit) with stencil test with stencil test equal zeroequal zero

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Shadow MapsShadow Maps• [Williams78][Williams78]

Casting curved shadows on curved Casting curved shadows on curved surfacessurfaces Image-space algorithmImage-space algorithm Well suited for hardware Well suited for hardware

implementationimplementation

Real-Time Luxo Jr. …uses three dynamic shadow maps (OpenGL, GeForce3)

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Shadow MapShadow Map Basic idea: objects that are not Basic idea: objects that are not

visible to the light are in shadow visible to the light are in shadow How to determine whether an object How to determine whether an object

are visible to the eye? are visible to the eye? Use z-buffer algorithm, but now the Use z-buffer algorithm, but now the

“eye” is light, i.e., the scene is rendered “eye” is light, i.e., the scene is rendered from light’s point of viewfrom light’s point of view

This particular z-buffer for the eye is This particular z-buffer for the eye is called called shadow mapshadow map

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Shadow MapsShadow Maps Basic AlgorithmBasic Algorithm

Render scene as seen from light Render scene as seen from light sourcesource

Save back depth buffer (2D shadow Save back depth buffer (2D shadow map)map)

Render scene from viewer’s positionRender scene from viewer’s position Transform pixel coordinates to light Transform pixel coordinates to light

source spacesource space Compare z with z value stored in shadow Compare z with z value stored in shadow

mapmap Pixel is in shadow if z(light) < z(viewer) Pixel is in shadow if z(light) < z(viewer)

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Shadow MapsShadow Maps

Shadow map

Final scene

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1st Pass

View from light Depth Buffer (shadow map)

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2nd Pass

Visible surface depth

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2nd Pass

Non-green in shadow Final Image

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Soft Shadow TechniquesSoft Shadow Techniques

Sampling the Light SourceSampling the Light Source Soft Shadow Maps Soft Shadow Maps [Heidrich00][Heidrich00]

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Sampling the Light SourceSampling the Light Source Use arbitrary hard shadow Use arbitrary hard shadow

algorithmalgorithm Select point sample on area light Select point sample on area light

sourcesource Render hard shadowsRender hard shadows Sum up weighted result Sum up weighted result

(e.g. accumulation buffer)(e.g. accumulation buffer)

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Sampling the Light SourceSampling the Light Source Ground plane shadow textureGround plane shadow texture

1. Initialize FB (white)1. Initialize FB (white)

2. For each sample point do2. For each sample point do

2a. Render scene2a. Render scene

2b. Subtract 1/N from FB2b. Subtract 1/N from FB only once for each only once for each pixel (stencil) ! pixel (stencil) !

Image from ATI Developer’s Site

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Sampling the Light SourceSampling the Light Source

Image from ATI Developer’s Site

ResultResult

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Soft Shadow MapsSoft Shadow Maps [Heidrich00] [Heidrich00] Soft shadow maps for linear Soft shadow maps for linear

lights lights

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Soft Shadow MapsSoft Shadow Maps[Heidrich00] [Heidrich00] Soft penumbra regions for linear light Soft penumbra regions for linear light

sourcessources Based on “traditional” shadow map Based on “traditional” shadow map

algorithmalgorithm Suitable for hardware and software Suitable for hardware and software

renderingrendering Very small number of light source Very small number of light source

samplessamples Soft shadows at real-time / interactive Soft shadows at real-time / interactive

frame ratesframe rates

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Soft Shadow MapsSoft Shadow Maps Visibility of light sourceVisibility of light source

100% to 0% for [p1,p2]100% to 0% for [p1,p2] 0% for [p2,q2]0% for [p2,q2] 0% to 100% for [q2,q1]0% to 100% for [q2,q1]

IdeaIdea NormalNormal shadow maps for shadow maps for

umbra and completely litumbra and completely litregionsregions

Linear interpolation of Linear interpolation of visibility for penumbra visibility for penumbra regionsregions

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Soft Shadow MapsSoft Shadow Maps Linear interpolation of visibilityLinear interpolation of visibility

Rational function:Rational function:

Approximation:Approximation:

valid because large valid because large penumbra regions whenpenumbra regions when

ReceiverReceiver

Light SourceLight Source

OccluderOccluder

tmxy 11

snxy 22

smxnxtxx

22

21

21 xstx

mn

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Soft Shadow MapsSoft Shadow Maps Visibility map:Visibility map:

Additional shadow map channel Additional shadow map channel (percentage visibility)(percentage visibility)

Two-channel shadow map for each sample Two-channel shadow map for each sample point point

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Soft Shadow MapsSoft Shadow Maps Generating the visibility mapGenerating the visibility map

Triangulate depth discontinuities (shadow Triangulate depth discontinuities (shadow map)map)

Warp resulting skin polygons to other viewWarp resulting skin polygons to other view

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Soft Shadow MapsSoft Shadow Maps Generating the visibility mapGenerating the visibility map

Render skin polygons to visibility mapRender skin polygons to visibility map Gouraud-shading (linear interpolation)Gouraud-shading (linear interpolation)

““White” for vertices on receiverWhite” for vertices on receiver ““Black” for vertices on occluderBlack” for vertices on occluder

Completely lit regionsCompletely lit regions Default visibility 0.5Default visibility 0.5

Completely shadowed regionsCompletely shadowed regions First shadow map channel First shadow map channel

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Soft Shadow MapsSoft Shadow Maps

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Soft Shadow MapsSoft Shadow Maps

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Recent WorksRecent Works

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Real-Time Hair Simulation and Real-Time Hair Simulation and Visualisation for GamesVisualisation for Games

Lund University Graphics Group (LUGG) in cooperation with Digital Illusions CE AB, Stockholm (An EA Company)

With self shadow Without self shadow

“Deep Shadow Maps” by Tom

Lokovic Eric Veach, Pixar Animation Studios

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AcknowledgmentsAcknowledgments “Shadow Techniques for Interactive and Real-

Time Applications” By Stefan Brabec ,MPI, Germany (PhD thesis)

“Alias-Free Shadow Maps” By Timo Aila and Samuli Laine, Helsinki University of Technology/TML and Hybrid Graphics Ltd., Finland

“Shadow Mapping and Shadow Volumes: Recent Developments in Real-Time Shadow Rendering”

By University of British Columbia, Canada “Deep Shadow Maps” Tom Lokovic and Eric

Veach, Pixar Animation Studios Lund University Graphics Group (LUGG), Sweden

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Thank you !Thank you !