shadow - marriesadvancedgraphics.marries.nl/lectures/03_shadows.pdf · variance shadow maps use...

Advanced Graphics 2012-2013 Advanced Graphics 2012-2013

Advanced Graphics

Shadow

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Advanced Graphics 2012-2013

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Important for depth perception

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Overview

Recap of basic techniques Various problems

– Filtering – Varying penumbra – Light source types

• Point light source • Directional light source

– Volumetric shadow – Subsurface scattering

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Shadow Volumes

Shadow volumes

– Rarely used anymore

– Extrude geometry

– Use stencil buffer to mark shadowed areas

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Shadow Volumes

Creates extremely sharp shadows – Usually not preferred

Bad worst-case performance – Why?

• Extreme overdraw

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Shadow Maps

Render scene depth from light source

– Store in shadow map

– Compare distancez from light source with shadow map depth

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Unshadowed: Shadow map depth == distancez(point, light)

Shadowed: Shadow map depth < distancez(point, light)

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Shadow Maps

Shadow map stores z coordinate in the view space of the light source

– Not the distance

We also need to compare it to the view space z coordinate in the shadow map test – We call this distancez

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Shadow Maps

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Shadow Acne

Shadow map has a finite resolution

– Discretization artifacts

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Shadow Acne

Solve by applying an offset (bias)

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Shadow Acne

Hard to pick a bias for every situation

Too much bias can cause “Peter Panning”

– Because everything seems to float

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FILTERING Shadow

Filtering

Varying penumbra

Light source types

Volumetric shadow

Subsurface scattering


Aliasing

Shadow map resolution must be high

– To prevent aliasing

– Can we interpolate the shadow map?

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What happens when we interpolate the shadow map? – We want the result to be half-shadowed – But it is fully shadowed

Shadow test is

– distancez > average(shadowmap)

But it should be – average(distancez > shadowmap)

Shadow Map Interpolation

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Percentage Closer Filtering

Percentage Closer Filtering (PCF)

– Execute the shadow test multiple times

• average(distancez > shadowmap)

Hardware supported in DX10+

– HLSL SampleCmp function (instead of Sample)

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Shadow boundary is still blocky – Increase filter radius

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Increasing the filter radius requires a lot of samples

– Need 64 samples in this case

– Bandwidth bottleneck


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2x2 samples 4x4 samples 8x8 samples

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Randomize the sample locations

– Less samples

– Introduces noise

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Pre-Filtering

Sample from a downscaled shadow map – Do the filtering (averaging) in advance

• Create mipmaps

– But we (still) can’t use the interpolated values

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Mipmaps:

Magnified:


Variance Shadow Maps

Stores a depth description which can be filtered – Based on probability theory

A shadow map is not probabilistic – But it does have a distribution

The variance describes the width of the distribution

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𝜇-𝜎 𝜇 𝜇+𝜎

Distributions – Mean 𝜇 = 𝐸 𝑥 (expected value) – Variance 𝜎2 = 𝐸 𝑥2 − 𝐸 𝑥 2 – First moment 𝑀1 = 𝐸 𝑥 – Second moment 𝑀2 = 𝐸 𝑥2


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Shadow distribution looks more like a cumulative distribution

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area ≥ 𝑡

𝑃(𝑥 = 𝑡) 𝑃(𝑥 ≥ 𝑡)

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𝑡 𝑡



Use Chebychev’s inequality

– Works with unknown distribution type

– Provides an upper bound for 𝑃 𝑥 ≥ 𝑡

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In this context

– 𝑃 𝑥 ≥ 𝑡 is the fraction this position is lit

– 𝑡 is the distancez from this position to the light source

– 𝜇 and 𝜎2 describe the shadow map depth distribution

• Calculated using 𝐸 𝑥 and 𝐸 𝑥2 , where 𝑥 is the depth value

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We store the depth value 𝑥 and the squared depth value 𝑥2 – Interpolation averages the depth, giving 𝐸 𝑥 and 𝐸 𝑥2


Example

– Interpolate 𝑀1 and 𝑀2 – Calculate 𝜇 and 𝜎2 – Calculate 𝑃 𝑥 ≥ 𝑡

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depth = 0.5

depth = 0.6

𝑀1 = 0.5 𝑀2 = 0.25

𝑀1 = 0.6 𝑀2 = 0.36

𝜇 = 𝐸 𝑥

𝜎2 = 𝐸 𝑥2 − 𝐸 𝑥 2

𝑀1 = 𝐸 𝑥

𝑀2 = 𝐸 𝑥2

𝜇

𝜎2 𝑃 𝑥 ≥ 𝑡

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Proof

Proof for this simple case:

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𝑝 is the interpolation parameter 𝑑1 and 𝑑2 are the depths

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Works for all kinds of linear filtering – Linear interpolation

– Mipmaps

– Blurring

We only need to store 𝑀1 and 𝑀2 (depth and depth2)

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One major disadvantage

– Can cause light bleeding

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Light Bleeding

Back to our example

– Investigate what happens when we vary the sampling depth 𝑡

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depth = 0.5

depth = 0.6

𝑀1 = 0.5 𝑀2 = 0.25

𝑀1 = 0.6 𝑀2 = 0.36

𝜇 = 𝐸 𝑥

𝜎2 = 𝐸 𝑥2 − 𝐸 𝑥 2

𝑀1 = 𝐸 𝑥

𝑀2 = 𝐸 𝑥2

1

0.55 0.6

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Light Bleeding

Work-around

– Light bleeding areas are always partially shadowed

• Never fully lit

– Remap shadow range

• For example: values 0-0.5 are considered fully shadowed

Use multiple layers of variance shadow maps

– Layered Variance Shadow Maps, Lauritzen and McCool, 2008.

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Numerical Stability

Variance calculation subtracts two large values – 𝜎2 = 𝐸 𝑥2 − 𝐸 𝑥 2 – The result (variance) is fairly small

• But important for our calculations

Catastrophic cancellation – Floats cannot retain small fractions for large values

• 1.0000000001 − 1 = 0

Floats (32 bit) are good enough in this case – But half floats (16 bit) can cause artifacts

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Very convenient to use probability theory

– Input is in range of our depth values (“expected” values)

– Output is in 0-1 range (probability)

– Only requires to store two values (depth and depth2)

– Can be averaged however we want

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VARYING PENUMBRA Shadow

Filtering

Varying penumbra

Light source types

Volumetric shadow



Umbra

Penumbra

Caused by area light sources

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Penumbra


Penumbra

Larger depending on the distance to occluder

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Hard Soft Correct

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Percentage Closer Soft Shadows

Vary shadow softness depending on penumbra width Approximate penumbra width

– Assumes parallel light source, occluder and receiver

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𝑤𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎 =𝑑𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 − 𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟

𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟∙ 𝑤𝑙𝑖𝑔ℎ𝑡 𝑠𝑜𝑢𝑟𝑐𝑒

𝑤𝑙𝑖𝑔ℎ𝑡 𝑠𝑜𝑢𝑟𝑐𝑒

𝑤𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎

𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟

𝑑𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 − 𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟



Known variables

– 𝑑𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟

– 𝑤𝑙𝑖𝑔ℎ𝑡 𝑠𝑜𝑢𝑟𝑐𝑒

Unknown variables

– 𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟 • Read from the shadow map, but where?

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Search for occluders in a region

– Region depends on

• 𝑑𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟

• 𝑤𝑙𝑖𝑔ℎ𝑡 𝑠𝑜𝑢𝑟𝑐𝑒

• shadow map near plane distance

– Use similar triangles again

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Light source

Shadow map

Receiver

Search region



Calculate 𝑑𝑜𝑐𝑐𝑙𝑢𝑑𝑒𝑟 by averaging the occluder depths

Search region can be relatively large – Semi-random sampling

• Still needs a lot of samples (at least 16)

– Can we use pre-filtering? • No, we need the average of the occluder depth (not the

average of all depths)

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Select Shadow Softness

Occluder depth is known

– Calculate 𝑤𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎

– Next step: select shadow softness

Select filter width based on 𝑤𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎

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For variance shadow maps – Use filter width size to select a mip-level – Interpolate between nearby values in the

mip-level

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Mipmapping

Lower resolution versions of the same texture

– Contains averaged values

– Easy to retrieve the average of a large surface

• With much less samples

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Mipmaps:

Magnified:



For variance shadow maps – Use filter width size to select a mip-level – Interpolate between nearby values in the

mip-level

However, this is just linear interpolation – Visible as boxy artifacts

We need better filtering

– The exact average of a certain region

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Summed-Area Table

Contains the sum of everything to the top-left

Allows us to retrieve the sum of an arbitrary rectangle

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2 1 3 1

4 0 1 2

2 2 1 0

0 3 4 3

2 3 6 7

6 7 11 14

8 11 16 19

8 14 23 29

Original

Summed-area table

2 1 3 1

4 0 1 2

2 2 1 0

0 3 4 3

2 3 6 7

6 7 11 14

8 11 16 19

8 14 23 29

= -

2 3 6 7

6 7 11 14

8 11 16 19

8 14 23 29


Summed-Area Table

Generating the SAT on the GPU – Similar to the sum example from lecture 1

For the 1D case (prefix sum):

More efficient methods available [Blelloch 1990]

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1 2 3 4 5 6 7 8



The summed-area table gives the sum

– Divide by the area for the average

Combination is called Summed-Area Variance Shadow Maps (SAVSM)

– When used with PCSS:

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LIGHT SOURCE TYPES Shadow

Filtering

Varying penumbra

Light source types

Volumetric shadow



Spotlight

Shadow maps can be used directly for spotlights

Shadow

Shadow map


Point Light

But what about (omnidirectional) point lights?

– Where do we place the shadow map?

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?


Point Light

Use 6 shadow maps

– Each with a 90o field-of-view

– Store in a cubemap

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Point Light

Not very efficient – Can render to all faces simultaneous using geometry

shader • Is this faster? • Usually not in practice

– Can use dual paraboloid mapping

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Directional Light

Lights everything from the same direction

– Orthographic projection

– How to position the shadow map?

• Needs to cover everything visible

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Directional Light

Positioning the shadow map – Only needs to cover the view frustum

– Transform the frustum vertices to view space

of the directional light – Take min and max values – Create orthographic

projection

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Directional Light

Poor shadow map usage

– Wasted space

– Accuracy independent of camera distance

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Perspective Shadow Maps

Can we warp the shadow map? – Re-use the wasted space for nearby accuracy

Render the shadow map in Normalized Device Coordinate space – Directional light becomes an (inverted) point light!

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Perspective Shadow Maps

Can give good shadow quality

– Quality is highly view-dependent

– Many bad cases

• Occluders behind near plane

• Bad precision when view direction aligns with light direction

– Hard to get right for every case

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warp


Cascaded Shadow Maps

Simpler approach: use multiple shadow maps

– Cascade over frustum

– Subdivide the frustum in multiple sub-frusta

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Movement causes shadow edges to shimmer

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Snap shadow map to grid

– Only move whole pixels

– Needs additional space

• Grid cannot rotate

– Good solution

Does not solve shimmering when moving the light source

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VOLUMETRIC SHADOW Shadow 60

Filtering

Varying penumbra

Light source types

Volumetric shadow



Translucent Volumes

Uniform unbounded volumes

– Fog

Non-uniform bounded volumes

– Smoke/clouds

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Rendering Translucent Volumes

Translucency accumulates along the view ray

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– Directional light source

– Lighting is equal at every point

• Simple function of depth

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– Point light source

– Lighting varies

• How can we solve this?

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Keep it simple (for this lecture)

– Discretize the function

– Volume ray marching

• Sampling along the ray

• Blend the results

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Non-uniform bounded volumes

– For all light source types

– Use ray marching

• Sample translucency from 3D texture (for example)

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Volumetric Shadow

Volume being shadowed

Self-shadow of the volume

Volume affecting the environment

– Partial shadow

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Volumetric Shadow

General approach

– Test shadow for each ray march point

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Volumetric Shadow

Volume being shadowed – Most relevant for uniform unbounded shadows

– Use regular shadow map to test for shadow

Effect called crepuscular rays or god rays

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Volumetric Shadow

Volume being shadowed

Self-shadow of the volume

Volume affecting the environment

– Partial shadow

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Volumetric Shadow

Shadow cast by the translucent volume – Need the percentage of light at a point

Ray march to the light source? – Double work

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Deep Shadow Maps

Store opacity as a piecewise linear function – Simplify to reduce storage

Can sample percentage of light at each point – Extremely slow

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Opacity Shadow Maps

Store opacity per pixel – Depth is fixed

Layer multiple maps – Opacity is accumulated over the layers – Interpolate between the layers

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Hair shadows

Uses volumetric shadow

– Hairs are too small for regular shadow maps

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SUBSURFACE SCATTERING Shadow 75

Filtering

Varying penumbra

Light source types

Volumetric shadow



Subsurface Scattering

Volumetric rendering was single bounce

– Actually simplification

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Subsurface scattering occurs with multiple bounces

– Diffuses the light

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Can be observed in dense translucent materials

– For example: milk, marble, skin

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Problem can be very complex

– Especially for multi-layered materials (e.g. skin)

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Approximate effects on macro scale

– Partial translucency

– Diffusion

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Partial Translucency

Light decreases with distance travelled through the material – Use shadow map to calculate entrance depth

– Subtract from exit depth

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Diffusion

Diffuse (blur) the light over the surface – Only the light, not the color

– What to blur? • Light image rendered from the light source?

• Light image rendered from the camera?

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Texture-Space Diffusion

Perform the blur in texture-space – Tangent space with uv-mapping

Calculate lighting on a texture – Blur the lighting texture

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Rendering the lighting to a texture – Requires mindset switch

Render the model – But use the UV-coordinate as vertex position – The world position is used to calculate the lighting

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Blur the light texture

– Special blur kernel to simulate diffusion properties

• Depends on material

Requires a perfect UV-mapping • Impossible

• Correct for over/under stretching

• Correct for seams

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CONCLUSION Shadow 86

Filtering

Varying penumbra

Light source types

Volumetric shadow



Conclusion

Many different shadow techniques

– A lot can be combined

Cascaded Perspective Summed-Area Variance Shadow Maps with Percentage Closer Soft Shadows?

– No problem!

– CPSAVSM+PCSS

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