Real-Time Shadows in Video Games

Amit Ofer 11-27-2016

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Table of Contents Abstract ........................................................................................................................................... 2

1. Introduction ................................................................................................................................ 2

1.1. Hard shadows vs. soft shadows ............................................................................................ 5

2.1. Projection shadows .................................................................................................................. 6

2.1.1. Planar shadows .................................................................................................................. 6

2.1.2. Shadow Textures ............................................................................................................... 9

2.2. Shadow mapping .................................................................................................................... 11

2.2.2. Omnidirectional shadows maps ...................................................................................... 15

2.3. Shadow volumes..................................................................................................................... 16

2.3.1. Naïve implementation ..................................................................................................... 17

2.3.2. Stencil Shadow Volumes ................................................................................................. 18

2.3.3. Silhouette-Based Shadow Volumes ................................................................................. 19

2.3.4. Level of Details ................................................................................................................ 19

3. Soft shadows techniques ........................................................................................................... 20

3.1. Image based approach ....................................................................................................... 20

3.1.1. Combination of several point based shadow images ...................................................... 20

3.1.2. Fixed sized penumbra filtering techniques ..................................................................... 21

3.1.3. Variable sized penumbra filtering techniques ................................................................ 21

3.2. Geometry based approach ................................................................................................. 22

4. Conclusion and further reading ................................................................................................. 24

5. References ................................................................................................................................. 25

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Abstract Shadows are an important part in video games and simulations, shadows contribute to realism

and help us comprehend spatial relationships between objects and where they are located

inside the scene. Furthermore, shadows can also be treated as artistic means and many movies

(and sometimes video games) exploit shadows to illustrate the presence of a person or an

object without revealing its actual appearance.

Although shadow algorithms and techniques have been researched for a few decades they still

remain a challenge for real time graphics, as new hardware is being develops games become

more realistic which demands better and quicker shadow techniques.

In this summary, I will explore and give a brief survey of the most common techniques in

shadow calculation for games and real time simulations; I will give explain the basics of 4

common shadows techniques used today: Planar shadows, Shadow Textures, Shadow maps and

shadow volumes; I will explore the differences between hard and soft shadows and discuss

some of the common approaches used to create real-time soft shadows.

1.Introduction

A shadow is defined as a dark area where light from a light source is blocked by an opaque

object.

Shadows are created when a surface blocks the light's path. The shadows caused by an ideal

point light source would be sharp but in the real world shadows have blurry edges, this is called

the penumbra. A penumbra arises because real world light sources cover some area and so

produce light rays that gaze the edges of an object at different angles.

Shadows play an important role in computer graphics. Besides dramatically improving image

realism they also provide the observer with visual cues that gives information about the viewed

scene such as the characters of the geometries, relative position of object, complexity of the

shadow occluders and receivers, shape and size of the light sources in the scene and more.

Shadows are an important component in computer graphics because they give the observer

important visual cues such as information about light sources and objects, depth perception and

light intensity.

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Figure 1: the exact same object in all 4 images looks as if it is found in different height thanks to the shape and position of the shadow.

Figure 2:demonstrate how the shadow can give us visual cues to where the light source is located in our scene.

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Figure 3: demonstrates how the shadow shape can give us visual cues about the shape of the surface the shadow is cast upon.

Unfortunately shadows computation is difficult, especially when considering the case of soft

shadows and when dealing with multiple light sources of different types.

Modern computer games and simulations demand fast real time shadow calculation so usually

fast and less accurate shadow techniques are more beneficial than the more accurate slow

techniques.

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1.1.Hard shadows vs. soft shadows Shadows that are produced from point light sources (sources that has no actual size but omit

light from a 3d point in space, e.g. point light or a basic spot light) are called hard shadows.

Hard shadows have crisply defined, sharp edges as opposed to soft shadows which are created

from light sources that contains size definition such as an area light and appear less distinct and

fade out towards the edges of the shadow area.

When talking about soft shadows we divide the shadow region into two sections called umbra

and penumbra, the umbra is the innermost and darkest part of the shadow where the light

source is completely blocked by the occluding body whereas the penumbra is the region in

which only a portion of the light source is obscured by the occluding body, the width of the

penumbra is determined by the size of the light and its distance from the shadow caster and

the receiving object. In hard shadows the umbra takes the entire shadow.

Using soft shadows can make a scene appear more realistic than a scene where only hard

shadows are used but getting accurate soft shadows can be complicated to achieve, especially

when talking about games and real time simulation where computation time is usually more

important than accuracy.

Usually to get the best results, the best approach would be to use soft shadows in conjunction

with hard shadows, and prefer method for less accurate but faster soft shadows in order to

allow the scene to be rendered as fast as possible.

*note that while shadows are important to achieve realism it is only one of many effects

simulated in a computer game and thus are allowed only a limited time for computation.

In the next section I will describe in detail the common techniques for producing hard shadows,

after that I will provide a brief description of the some of the common techniques used in video

games and real time simulations to achieve good looking semi accurate soft shadows.

Figure 4: shows the difference between hard shadows (left) and soft shadows (right)

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2.Basic Techniques

2.1.Projection shadows Projection shadows refers to a group of relatively simple techniques that can produce good

results but suffers from several shortcomings which makes them a bit out dated in recent

rendering engines, but are still worth mentioning.

These techniques are still relevant when artistic freedom such as changing the shape, color and

texture of the shadow is more important that physical accuracy.

2.1.1.Planar shadows "Planar shadows" is a technique used for faking simple shadows where an object casts its

shadow onto a planar surface. This technique is useful for creating a simple and fast hard

shadow.

Figure 5:Planar projected shadows can be used to produce shadows on planar receievers by projecting the polygons of the caster onto the plane and drawing it with a dark color.

In this technique, a second copy of our 3d object will be rendered by projecting it onto a plane

and giving it a dark color with no illumination. Such a projection can be easily described with

using a simple projection matrix:

We will describe our plane using the equation: 𝑛 ×𝑥 + 𝑑 = 0, we would like to find the matrix

M such that 𝑣′ = 𝑀𝑣, where v' is the projection of vertex v onto the plane. Projecting a vertex

onto a plane is similar to computing the intersection between a ray and a plane; we will shoot

our ray from the light position l onto the plane, thus:

𝑟(𝑡) = 𝑙 + 𝑡𝑑 And 𝑑 = 𝑣 − 𝑙

By taking that expressions and substituting it for x in the plane equation we get:

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𝑛 ×(𝑙 + 𝑡𝑑) + 𝑑 = 0 => 𝑡 = −𝑛×𝑙+𝑑

𝑛×𝑑

Thus the intersection point will be:

𝑣′ = 𝑟(𝑡) = 𝑙 − 𝑛×𝑙 + 𝑑

𝑛 ×(𝑣 − 𝑙)(𝑣 − 𝑙) =

(𝑛 ×(𝑣 − 𝑙)) − (𝑛×𝑙 + 𝑑)(𝑣 + 𝑙)

𝑛×(𝑣 − 𝑙)

= (𝑛×𝑙 + 𝑑)𝑣 − (𝑛×𝑣 + 𝑑)𝑙

𝑛×𝑙 − 𝑛×𝑣

Now in order to get the matrix for we will use the fact that we can utilize homogenous

coordinates for the division by putting the denominator in the w-component of v' so that:

𝑣′𝑥 = (𝑛×𝑙)𝑣𝑥 − (𝑛𝑥𝑣𝑥 + 𝑛𝑦𝑣𝑦 + 𝑛𝑧𝑣𝑧 + 𝑑)𝑙𝑥

𝑣′𝑦 = (𝑛×𝑙)𝑣𝑦 − (𝑛𝑥𝑣𝑥 + 𝑛𝑦𝑣𝑦 + 𝑛𝑧𝑣𝑧 + 𝑑)𝑙𝑦

𝑣′𝑧 = (𝑛×𝑙)𝑣𝑧 − (𝑛𝑥𝑣𝑥 + 𝑛𝑦𝑣𝑦 + 𝑛𝑧𝑣𝑧 + 𝑑)𝑙𝑧

𝑣′𝑦 = (𝑛×𝑙) − (𝑛𝑥𝑣𝑥 + 𝑛𝑦𝑣𝑦 + 𝑛𝑧𝑣𝑧)

And since for homogenous coordinates (x,y,z,w) = (x/w,y/w,z/w,1) we can write the matrix as:

𝑀 =

[ 𝑛𝑙 + 𝑑 − 𝑛𝑥𝑙𝑥 −𝑛𝑦𝑙𝑥 −𝑛𝑧𝑙𝑥 −𝑑𝑙𝑥

−𝑛𝑥𝑙𝑦 𝑛𝑙 + 𝑑 − 𝑛𝑦𝑙𝑦 −𝑛𝑧𝑙𝑦 −𝑑𝑙𝑦−𝑛𝑥𝑙𝑧 −𝑛𝑦𝑙𝑧 𝑛𝑙 + 𝑑 − 𝑛𝑧𝑙𝑧 −𝑑𝑙𝑧−𝑛𝑥 −𝑛𝑦 −𝑛𝑧 𝑛𝑙 ]

After we have calculated the projection matrix for the shadow, we can easily render the shadow

by applying the matrix to each of the shadow caster's vertices in the vertex shader before

applying the camera matrix (that is used for calculating the position of the actual geometry).

Although this technique is simple and straightforward it does come with a few problems, though

these problems can easily be fixed. One of the problems with planar shadows is the case where

the light source is located between the ground plane and the shadow caster, in this scenario the

shadow caster will not be able to cast its shadow onto the ground but the projection matrix

would still lead to points on the receiving plane. This issue can be solved by adding a simple test.

For a single vertex (projected onto the receiving plane) we can simply test if its w component is

negative, for a triangle we test each of its vertices. In the more complicated scenario where at

least one of the vertices have at least one positive w component and one negative we can

interpolate w and test it per fragment.

Another problem with this technique happens because the projection will deliver a point on the

ground plane which will make the shadow projection and the ground plane coincide at the same

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depth location in space, This would lead to a problem known as z-fighting, that is since z

buffering usually keeps the pixels that are nearest to the observer, imprecisions will lead to a

random choice between the shadow projection and the ground plane.

The problem can easily be solved by one the following methods:

First drawing the ground plane then disabling culling and depth test when projecting the

shadows and finally rendering the rest of the scene with standard settings and depth

testing.

Lifting the shadow projection above the ground plane by giving him a small amount of

offset will also solve the problem but this requires choosing the right offset value which

can be tricky.

Figure 6 - left: Artifacts caused by z-fighting in planar shadows + shadow extending off the surface; Right: fixing z-fighting by extending the shadow geometry off the ground

Last, another 2 issues might arise, the first when the projected shadow includes multiple

overlapping triangles which will make standard alpha blending with the plane's color look bad

(darker when the triangles overlap) and the second issue is when the projected shadow goes

beyond the edges of the plane (see figure 5).

Fortunately, these issues can be solved by using the stencil buffer, we fill the stencil buffer with

a special value for the ground plane, then we only render the projected shadow in pixels that

has this special stencil value and then we set this value to zero. Doing so will clip the projected

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shadow where it does not lie on the plane and will take care of the darker shadow artifact

causes by overlapping triangles.

This technique also save us the need to lift the shadow above the ground plane (to avoid z-

fighting) as we can use this value to avoid rendering the floor over the shadow region.

2.1.2.Shadow Textures The biggest disadvantage of the previous technique is that it's only relevant to rendering

shadows on planes; fortunately, it is possible to extend the projection shadows method to work

on curved surfaces by using the planar shadow image as a texture projected onto the receiving

objects.

This technique is known as shadow texture or shadow map, not to be confused with the shadow

mapping method I will present later on.

Figure 7:Shadow Textures - a shadow image is used as a projective texture to cast shadows onto the surface.

In order to explain how this technique works we'll look at a rather simple scenario where we

have a single point light, a shadow receiving object and a set of occluders between the light and

the receiving object.

We are going to place our camera at the light source pointing towards the shadow receiving

object, from that point of view we are going to render a binary image of the scene where each

pixel is initially set to white and all of the shadow casters are drawn black, this image will be

used later on to test whether a point lies in the shadow or not.

Since a point p lies in shadow if the open segment between p and the light source l intersects

the scene, we can use the observation that each segment project to a single point for the

camera at the light source that we used to create the binary texture.

Therefore we can use a single texture lookup while rendering the receiving object to test for

shadows; if the pixel containing the segment was filled when we rendered our binary texture it

must be in shadow.

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We can divide this algorithm into two main steps:

1. We render the shadows casters into a shadow texture

2. We render the shadow receivers using the shadow texture.

For step 1 we need to calculate the camera matrix that we will use for projecting the shadow

casters onto the shadow texture.

This is pretty straight forward; we define the camera matrix as 𝑀𝑐 = 𝑀𝑝 ∗ 𝑀𝑣 where Mp is

either a parallel or perspective matrix and Mv is a matrix that transforms a vertex from world

space into camera space, which is simply a matter of placing the world origin at the camera's

position and aligning the view direction with the normal of the shadow projection plane (the

view direction is along the negative z axis for a right handed coordinate system).

For step 2 we need to calculate the matrix used for getting the shadow texture coordinates. In

the vertex shader we use to render the shadow receievers the texture coordinates into the

shadow texture should be calculated as 𝑣′ = (𝑀𝑝 ∗ 𝑀𝑣)𝑣 where Mp and Mv are the same

projection and view matrices we calculated for the previous step, this calculation will produce

texture coordinates in the range of [−1,1]2 which we will need to shift to the more

conventional texture space [0,1]2 this can easily be done by calculating 𝑣′′ =(𝑣′

𝑥𝑦+1)

2 or by

creating another matrix for the shift so that 𝑣′ = (𝑀𝑡 ∗ 𝑀𝑝 ∗ 𝑀𝑣)𝑣 where Mt is the following

matrix:

𝑀𝑡 = (

0.5 0 0 0.50 0.5 0 0.50 0 0.5 0.50 0 0 1

)

Texture coordinates that fall outside [0,1]2 represent unshadowed areas. This should be

checked in the fragment shader.

The major drawback of this technique is the fact that blockers and receivers need to be

separated which requires a shadow texture per block and makes shelf shadowing impossible to

handle. Same as the shadow projection technique the receiving object should not lie between

behind the light source otherwise the shadow texture might be erroneously applied, again this

situation can be handled by simply testing the w coordinate for its sign.

Although this technique is rather simple in inaccurate it does provide a major advantage where

the appearance of the shadow is more important than its accuracy; Since we are using a texture

it is possible to create it in advanced and then have it edited offline by artists which can add

interesting artistic effects. For example, we can apply a filtering mask to the texture in order to

produce fake soft shadows.

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2.2.Shadow mapping The shadow texture technique that was described in the previous section is a simplified version

of one of the most famous technique for calculating shadows in real time in today's rendering

and game engines.

The main difference between shadow mapping and shadow textures is the fact that shadow

mapping doesn't need to separate occluders from receivers and is therefore capable of handling

self-shadowing. The shadow mapping technique was first introduced in [Williams78], its main

principle is that the light sees all the lit surfaces of the scene, therefore every unseen surface

must lay in shadow.

In order to determine which surfaces are visible to the light the algorithm first creates an image

of the scene from the lights position, where each pixel in this image holds the depth of the

visible surface (its distance from the light), this image is known as the shadow map.

The creation of such image uses the same mechanism used for rendering depth maps in order to

determine a surface's visibility during standard rendering; therefore it's supported by graphics

hardware.

After we have obtained the so called shadow map the second step of the algorithm would be to

render the scene from the actual viewpoint, in the fragment shader stage each fragment

position p is transformed into light clip space so that 𝑝𝐿𝐶 = (𝑝𝑥𝐿𝐶 , 𝑝𝑦

𝐿𝐶 , 𝑝𝑧𝐿𝐶) where (𝑝𝑥

𝐿𝐶 , 𝑝𝑦𝐿𝐶) are

the coordinates in the shadow map to where p would project when viewed from the light's

position and 𝑝𝑧𝐿𝐶 is the distance between the fragment and the light.

In order to determine if the fragment is seen from the light (and therefore is lit), all we need to

do is test if 𝑝𝑧𝐿𝐶 is smaller the value stored in the shadow map at (𝑝𝑥

𝐿𝐶 , 𝑝𝑦𝐿𝐶), otherwise the

fragment must be hidden from the light by some other surface that's closer to the light source

and therefore lie in shadow.

*we should note the fact that the depth map is not accessed directly with light clip-space

position 𝑝𝐿𝐶 but with its according shadow texture coordinates 𝑝𝑠 which can be derived

according to the same matrix 𝑀𝑡 we used earlier to calculate the texture coordinates in the

range of [0,1]2.

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Figure 8:Shadow mapping technique.

The biggest advantage in using the shadow mapping technique is the fact that it works great

with almost any input as long as depth values can be produced and since both steps of the

algorithm involves standard rasterization gives the technique a huge potential for graphics

hardware acceleration.

Although this technique is very powerful and very common in modern rendering and game

engine it does have a few problems that should be addressed when used including imprecisions

due to the depth test step, aliasing artifacts caused from the pixel representation of the shadow

maps, and last the need for special treatment for omnidirectional light sources.

2.2.1.Disadvantages of shadow mapping

When implementing the shadow mapping technique there are two main issues that must be

addressed.

2.2.1.1.Depth bias

In order to test if a point is farther away than the reference in the shadow map some tolerance

threshold is required for the comparison. Otherwise due to the limited shadow map resolution

and other numerical issues the shadow will include unwanted artifacts that are commonly

referred to as z-fighting or shadow acne.

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Figure 9: shadow acne.

The explanation to this issue is that if the shadow map had infinite resolution, the shadow

testing would be a matter of checking if the point is represented in the shadow map, however

with a discrete shadow map resolution, sampled points from the eye position are compared to

an image consisting of pixels, each of these pixel's value is defined by the world sample

corresponding to that pixel's center. When querying a view sample, it usually will not project

exactly to the same location as was sampled in the shadow map and therefore will be compared

to the average between nearest neighbors. This leads to problems when the view sample is

farther from the source than the corresponding value in the shadow map because unwanted

shadows can occur.

In order to deal with the shadow acne issue a threshold needs to be added in the form of a

depth bias that will offset the light samples slightly from the light source.

Although this might sound simple, it is in fact more problematic than it seems as the greater the

slope of the surface is the bigger the change in depth value between adjacent samples which

means that a larger value of depth bias is required in order to avoid the surface incorrectly

shadowing itself.

Furthermore, if the depth bias is too large it might lead to light leaking at contact shadows,

causing the shadow to look disconnected from the caster, a problem usually referred to as Peter

Panning.

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Figure 10: Peter panning artifact.

The standard approach is to use two parameters for the bias, one constant and the other one

depends on the slope of the triangle as seen from the light source.

2.2.1.2.Shadow map aliasing

A major drawback of using an image based scene representation for calculating the shadows is

that the shadow map texture is limited in resolution and therefore result in aliasing.

Aliasing in the shadow map means that the shadow created using the shadow map will reflect

the discretization of the texture in the form of pixels. Consequently, the edges of the shadow

will contain visible stair stepping artifacts.

Figure 11: Aliasing artifacts; Left - without anti-aliasing; right - with anti-aliasing.

The reason for this is that several view samples on a receiver object might be projected onto the

same texel in the shadow map, hence will receive the same shadow response. As soon as the

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object projects onto the next texel the shadow response might change drastically causing the

stair stepping artifacts mentioned above.

The best approach to dealing with these artifacts is to increase the shadow map resolution and

usually in modern games shadow map resolution exceeds the window size; 4096 and 8192 are

common choices. By using such large textures the chance of two view samples to fall into the

same texel is reduced.

Another solution is to create a shadow map per object and to adapt the shadow map resolution.

Although this solution is useful for creating high quality shadows it is considered more

complicated as it requires specialized scene structures and separated rendering passes.

Another common technique for dealing with aliasing in shadow maps is called "Percentage

Closer Filtering" or in short PCF. The basic principle of PCF is that instead of sampling one texel

in the shadow map in order to determine if a pixel is in shadow we also sample the texel's

neighbors and return a float in the range [0, 1] that reflects the weighted average of these

samples. We can use this result as the shadow factor for the pixel and by that makes the shadow

borders much smoother.

This technique is so common that a hardware implementation already exists in modern GPUs

and is also a base for a soft shadows technique I will describe later.

2.2.2.Omnidirectional shadows maps The technique that was presented in the previous section uses rendering for producing the

shadow map, therefore it is necessary to specify a light frustum which implies that the

technique is aiming at spot lights, which has a specific direction and a light radius.

What if we want to use the same technique to produce shadows from a point light?

The common way to deal with omnidirectional light sources is to create six light frustums

around the light source (each frustum represents a side in the cube that blocks that light source)

that together covers the entire sphere of directions.

According to [Wan07] a six-face spherical map can provide better utilization of resolution rather

than using a simple cube map, such a map can be thought of as a cube that is "inflated" to a

spherical shape such that each side of the map is a dome instead of flat.

Using six light frustums means that our scene's geometry has to be processed 6 times which

introduce a significant penalty in computation time.

Using Geometry shaders allows performing the required projection on a cube map in a single

pass but it doesn't prevent the geometry from being duplicated for each cube face.

It's worth mentioning that some techniques have been suggested to improve this method such

as using a parabolic map instead of a cube [Heidrich98] which enables the extraction of the

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entire field with only two rendering passes, however cube maps remains the norm today due to

its simplicity.

2.3.Shadow volumes The shadow mapping technique we have seen in the previous section was based on an image

representation of the scene, which led to several problems caused by approximating the scene

in image space.

In this section we will introduce a different type of shadow technique that works directly in

object space thus does not suffer from the same problems as the previous technique did.

Instead of transforming our scene elements into a set of pixels our shadows will be described by

creating new geometric elements in our scene called shadow volumes (hence the name).

Since these volumes are being constructed accurately from the scene geometry it’s considered a

good method for creating accurate hard shadows, however this comes at an increased

computation cost.

The shadow volumes algorithm was first introduced by Frank Crow in 1977 [Crow77] and have

been evolving and maturing ever since, it was first named volumetric shadows, a name which

nowadays reserved for shadow algorithms that creates shadows in fog, clouds and smoke.

The basic concept in the shadow volume algorithm is that we extend our scene geometry in

order to create a new geometry that represents our shadows. For each triangle in our scene that

potentially cast a shadow on the scene we will define a shadow region, which will be define by

the triangle itself and by three quads that extends to infinity. Each of these quads is defined by

two of the triangle's vertices and by extruding these two vertices to infinity along the line from

the light source to the vertex.

Each of these quads along with the triangle itself form the triangle's shadow volume, the

triangle is usually referred to as the "near cap" as it adds a cap to the shadow volume.

We can now determine that a point lies in shadow if it is located within one or more of these

shadow volumes.

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Figure 12: Shadow volumes technique.

Although the basic idea for this algorithm sounds rather simple, an efficient algorithm for this

technique is not so trivial to implement, thus requires a discussion about optimizing our

computation.

2.3.1.Naïve implementation The basic principle of the naïve approach is that each triangle in our occluder model will be

extended in the light's direction and will create a shadow volume, then when rendering the

shadow, all view samples will be tested against all shadow volumes (that is against each volume

that was produced earlier from each of the triangle that belongs to the occluder's model) in

order to determine if the sample is in shadow.

This method is not feasible for rendering complex scenes with where the number of polygons in

each model is high and high frame rate is critical (which is the case in video games and real time

simulations).

Although more efficient methods will be described later, I will give a brief explanation on how

the basic shadow volume can be created as this technique will also be useful in the more

advanced algorithms.

In order to extrude the shadow volumes to infinity, homogeneous coordinates can be used,

given a vertex in homogeneous coordinates, p:= ( 𝑝𝑥 , 𝑝𝑦, 𝑝𝑧, 1) we need to move it to infinity

along the line from the positional light l: = ( 𝑙𝑥 , 𝑙𝑦, 𝑙𝑧 , 1).

Using homogeneous coordinates, any point on a line between those two points can be

described by 𝛼𝑙 + 𝛽𝑝 with 𝛼, 𝛽 ∈ 𝑅. Consequently, the particular point 𝑝 − 𝑙 = (𝑝𝑥 − 𝑙𝑥, 𝑝𝑦 −

𝑙𝑦, 𝑝𝑧 − 𝑙𝑧, 0) lies on the line that corresponds to the direction into which the vertex should be

extruded. This point also lies in infinity since its w coordinate is 0. In order to create the

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extruded shadow volume quad for an edge defined by two vertices v1, v2 we need to output the

vertices v1, v2, v1 - l, v2 – l. (the w-component will be equal to one for the first two vertices and

zero for the latter two that are extruded to infinity.

When using a directional light the process is even simpler as the two vertices at infinity are

located at the same position (and the quad becomes a triangle). The light itself describes the

direction into which the vertices should be extruded and these points simply become

( −𝑙𝑥 , −𝑙𝑦, −𝑙𝑧, 0).

The shadow volume quads should be oriented so that their plane equation have the interior of

the shadow volume on the inside and the exterior on the outside. In order to create a quad with

the right orientation we first need to figure out on which side of the triangle plane the light

source is located (which can be done using cross product).

2.3.2.Stencil Shadow Volumes It wasn't until 1991, with Heidmann's stencil shadows [Heidmann91] that shadow volumes

techniques became feasible for real-time dynamic scenes. The major benefit was that the

geometric computations (intersections and containment tests) were no longer used but instead,

we mapped to the existing z buffer and stencil buffer operations.

In order to simplify the explanation, we will assume that the eye position is located in light and

not shadow, we also make the assumption that the scene geometry is watertight (no holes) and

thus satisfies Jordan condition [Jordan87].

According to Jordan's theorem we can test whether a point lies inside or outside a shadow

volume by simply testing the number of intersections along the rays from the eye point to each

view sample, we count the number of times a ray enters versus exits a shadow volume, more

precisely we increase\decrease a counter every time the ray enters\exits a shadow volume.

Based on our previous assumption that the eye is located outside the shadow region, the final

count indicates the number of shadow volumes containing the view sample, a count different

than zero implies that the view sample lies in shadow.

Heidmann suggested to use a more GPU friendly computation than actually testing rays

explicitly against shadow volumes. Heidmann observed that a ray always enters a shadow

volume through a front facing polygon and leaves through a back facing polygon. Since each ray

is defined by a pixel in the image, one could implicitly test whether a ray enters a shadow

volume by simply drawing its front faces. All of the pixels that are covered by the drawn quad

will effectively enter the volume. Rendering all the back-facing quads will determine pixels

whose associated rays would leave the volume.

Heidmann suggested using the stencil buffer in order to implement these counters by rendering

all of the shadow volume quads and incrementing/decrementing the stencil values for front and

back facing polygons, since it represents entering/exiting shadow volumes.

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In order to deal with shadow volumes that lie between the camera and the view sample

standard z-culling is used, where the depth buffer contains the shadow receiving scene, and any

updates to the z-buffer are disabled when rasterizing the quads. This way the stencil buffer will

contain the correct counter per pixel after having rendered all quads.

To summarize, the algorithm includes the following steps:

1. First pass – the scene is rendered from the viewport to create the z-buffer and the

ambient lighting will also be calculated in this step and saved to a second buffer.

2. Second pass – in this step the z-buffer and color buffer writing is disabled and we render

all front facing shadow volume quads to the stencil buffer. Only when a shadow volume

quad passes the depth test the counter in the stencil buffer is incremented. In the next

step, all back facing shadow volume quads are rendering, this time decrementing the

stencil buffer for quads that passes the depth test.

3. Third pass – in the final pass, the scene is rendered again, this time adding the specular

and diffuse lighting contribution into the color buffer while using the stencil buffer from

the previous stage as a mask to discard any pixel in shadow.

This type of stencil updates presented here are usually referred to as "z-pass algorithm" and it’s

a much more efficient and practical approach than the naïve implementation presented earlier.

However, there are several basic improvements that can be made and also there's a need to

address the assumptions we made earlier about the location of the eye (see z-fail algorithm

[Bilodeau99] or Carmack's reverse [Carmack00]) and the scene being watertight. But these

topics are beyond the scope of these summary and can be explored more thoroughly in the

sources and articles found in the reference section.

2.3.3.Silhouette-Based Shadow Volumes For watertight models, a good optimization technique one can use, is to omit the inner quads of

the shadow volume as these does not contribute to determine whether a point lies in shadow or

light. Instead of using all of the model's edges to create the shadow volumes, a different

approach can be taken. The shadow volume can be built using only the model's silhouette edges

as seen from the light, these edges will be extruded in the lights direction to create the shadow

volume. The silhouette edges can be found by searching for shared edges between one triangle

that is front facing and one triangle that is back facing the light source.

2.3.4.Level of Details Another possible technique that can be used in order to increase performance is to use a

simpler approximation to the model, one which contains less polygons so that the volumes can

be generated fast. This also opens up the possibility of using different LOD objects for shadow

volumes depending on the model's distance from the camera. E.g. use a simpler model when

the object is far and use a complex model when the object is near the viewer's eye.

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3.Soft shadows techniques As mentioned earlier, soft shadows are important to achieve high realism in scenes and are the

result of using an area light (which has a clear size and shape as opposed to a point light that has

no size).

Figure 13: Hard shadows vs. soft shadows.

In this section I will give a brief introduction to how soft shadows can be created and describe

briefly some of the most common techniques used today. Soft shadows techniques are divided

into two types of algorithms, ones that are based on an image-based approach and are built

upon the shadow mapping algorithm and ones that are based on an object-based approach and

are built upon the shadow volume algorithm.

3.1.Image based approach Shadow mapping is the most used technique used today to create shadows it is also the most

active on shadow researching in the last years, unfortunately the standard shadow mapping

algorithm is unable to generate shadows with penumbra as it cannot handle area lights,

therefore shadow mapping needs to be extended in order to support the creation of soft

shadows, and as we will see in this section most of the common soft shadows techniques are an

extension of the shadow mapping algorithm.

3.1.1.Combination of several point based shadow images The simplest image based technique used to create soft shadow maps is to use several sample

points to simulate the area light. Each of these sample points will used to create a shadow map

(a binary occlusion map), additive blending will be used to accumulate the contribution of each

light and the softness of the shadow will be determined by the number of sample points used.

The biggest advantage of this method is that it simple to implement and can achieve good

results and when enough samples are used the shadow will contain more information that

shadows achieved with other image based technique thus will appear to be more physically

accurate.

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The drawback of using this method is that this method is relatively slow as the rendering time

will increase linearly with the number of samples used to approximate the area light and when

too few samples are used unwanted artifacts will be introduced.

3.1.2.Fixed sized penumbra filtering techniques The following techniques can be used to blur the shadow in order to a soft-shadow-life

appearance, the results these techniques can achieve are pretty good but the drawback is that

the resulting penumbra is fixed sized thus does not reflect the occluding object's distance from

the shadow receiving object.

PCF (Percentage Closer Filtering) – We mentioned PCF earlier as a technique to handle

shadow map aliasing, this technique is also commonly used to create a fixed sized

penumbra soft shadows

VSM (Variance Shadow Maps) – Introduced by Donnelly and Lauritzen [Donnelly06], this

technique uses statistics to facilitate precomputation of shadow-map filtering. The basic

idea of this technique is to replace the standard shadow map query with an analysis of

the distribution of depth values and employs variance and Chebyshev’s inequality to

determine the amount of shadowing over an arbitrary filter kernel thus allowing the

shadow maps to be pre-filtered and create very fast soft shadows with large filter

kernels.

CSM (Convolution Shadow Maps) – Introduced in [Annen07] and is the first approach

that allows filter precomputation based on a linear signal theory framework by using

Fourier expansion to derive suitable basis functions for the approximations of the

shadow comparison function.

ESM (Exponential Shadow Maps) – Introduced in [Annen08b] and [Salvi08], this

technique is based on the CSM technique but instead of using Fourier expansion it uses

simple exponential which voids much of the storage requirements that the CSM method

has.

3.1.3.Variable sized penumbra filtering techniques The following techniques are different than the ones mentioned before as they take into

account the distance between the object and therefore the penumbra width is of variable size.

PCSS (Percentage Closer Soft Shadows) – one of the most common techniques for image

based soft shadows, this technique is based on the PCF technique and will be discussed

in details later.

PCSS + VSM\CSM – a combination of the PCSS technique with either VSM or CSM

techniques mentioned in the previous section.

Backprojection – refers to a group of algorithms initially introduced in [Atty06], the basic

idea in these techniques is to obtain a shadow map from the light source's center and

reconstruct potential occluders in world space from it. These occluders are then back-

projected from the currently considered receiver point p onto the light's plane to

estimate the visible fraction of the light area. These techniques mainly differ in the type

of occluder approximation that is employed, the way the computation is organized and

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how the occluded light area is derived. These choices influence the performance of the

technique, its generality, robustness and visual quality.

3.1.3.1.PCSS explained

The basic idea of the PCSS technique is to calculate the penumbra width and use it when

filtering the shadow map to achieve soft shadows. There are 3 parts in this technique:

Blocker search – first we need to calculate the shadow region 𝑅𝑆 that contains samples of

the relevant occluders. The shadow region is defined by the intersection of the light-

receiver-point pyramid (where the light source is the base and the point p is the apex) with

the shadow-map's near plane, the region is then searched for blockers which are simply

identified by performing a standard shadow map test, meaning all shadow map entries that

are closer to the light source than p are considered as blockers.

Figure 14: Illustration of the blocker search step.

Penumbra-width estimation – in the second part of the algorithm we need to calculate the

penumbra width, we make the simplifying assumption that there is only one occluder that is

furthermore planar and parallel to the area light's plane. For this plane, we use the average

depth of all the blockers that we found in the blocker search phase, we mark it with 𝑍𝑎𝑣𝑔.

We also make the assumption that point p belongs to a planar receiver that is also parallel

to the planar occluder, the penumbra width is then calculated using the formula:

𝑊𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎 = 𝑝𝑧 − 𝑧𝑎𝑣𝑔

𝑧𝑎𝑣𝑔𝑤𝑙𝑖𝑔ℎ𝑡

Filtering – now that we have the penumbra width we can use it to derive a suitable PCF

window by projecting the penumbra width onto the shadow-map's near plane using the

equation:

𝑤𝑓 = 𝑧𝑛𝑒𝑎𝑟

𝑝𝑧𝑤𝑝𝑒𝑛𝑢𝑚𝑏𝑟𝑎

After that the shadow map can be queried and filtered according to the window size.

3.2.Geometry based approach Although Geometry based algorithms for soft shadows are less commonly used and less

researched than the shadow mapping based algorithms when considering a shadowing

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technique one should also consider one of the following geometry based algorithms (based on

the shadow volume technique introduced earlier:

Using several point samples to simulate an area light – same as with shadow mapping,

one can use multiple sampling points to generate shadow volumes and combine them

into a soft shadow using additive blending.

Soft shadow volumes – The idea of this methods is the concept of using "Penumbra

wedges" [Akenine-Moller02, Assarsson04]. The basic idea behind this technique is to

encapsulate the penumbra regions by geometrically creating a wedge from each

silhouette edge, where the wedge encloses the penumbra cast by the corresponding

edge. Shadow-receiving points that lie inside the penumbra wedge receive a shadow

value based on interpolation between the inner and outer wedge borders. Borders are

not allowed to overlap otherwise artifacts will appear (Although a later technique

suggested in [Assarsson03a] suggest a way to remove this limitation).

The benefit of using these types of techniques is that the resulting shadow is very

pleasing and does not suffer from discretization artifacts or undesirable discontinuities.

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4.Conclusion and further reading Although real-time shadow computation is not an easy task we've seen several basic techniques

that are not too difficult to implement and can achieve very nice results. We've also seen a few

more advanced techniques that will allow us to solve some of the problems encountered in the

more simpler techniques such as aliasing issues and the need for soft shadows. Shadow

techniques are still actively researched around the world and new techniques and algorithms

that allows to achieve more accurate shadows in a shorter time keep emerging and will keep

improving as hardware becomes better and faster and games that strive for realism will require

better techniques.

There are many topics relating to shadow techniques that I haven't touched in this summary, for

further reading I suggest going through some of the material and articles in the references

section.

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5.References Real time shadows 1st edition by Elmar Eisemann, Michael Schwarz, Ulf Assarsson,

Michael Wimmer, CRC Press 2011.

A survey of Real-Time Soft Shadows Algorithms, Jean-Marc Hasenfratz, Marc

Lapierre, ,Computer Graphics Forum, Volume 22, Number 4, page 753--774 - dec 2003

Variance Shadow Mapping by Kevin Myers, Nvidia January 2007

SIGGRAPH 2013 soft shadows course

Shadow Mapping and Shadow Volumes: Recent Developments in Real-Time,Shadow Rendering, University of British Columbia, CS514 Advanced Computer Graphics: Image Based Rendering, Instructor: Wolfgang Heidrich, Project Report, Andrew V. Nealen, Technische Universit¨at Darmstadt

Percentage-Closer Soft Shadows, Randima Fernando, NVIDIA Corporation

Real-time Soft Shadows in a Game Engine, Kasper Fauerby, Carsten Kjær, 14th December 2003

Real-Time Shadows, Eric Haines erich@acm.org, Tomas M¨ oller tompa@acm.org, [Excerpted and updated from the book ”Real-Time Rendering”, by Tomas M¨ oller and Eric. Haines, A.K. Peters, ISBN 1568811012. See http://www.realtimerendering.com/]

Penumbra Maps: Approximate Soft Shadows in Real-Time, Chris Wyman and Charles Hansen, School of Computing, University of Utah, Salt Lake City, Utah, USA

Fast, Practical and Robust Shadows, Morgan McGuire, John F. Hughes, and Kevin T. Egan, Brown University, Mark J. Kilgard and Cass Everitt, NVIDIA Corporation

http://roar11.com/2015/05/dealing-with-shadow-map-artifacts/

http://www.zachlynn.com/

http://www.peachpit.com/articles/article.aspx?p=486505&seqNum=6

[Akenine-Moller02] Akenine-Moller, T. and Assarsson, U. 2002. Approximate soft

shadows on arbitrary surfaces using penumbra wedges. In proceedings of Eurographics

Workshop on Rendering 2002, pp. 161-166.

[Annen07] Annen, T., Mertens, T., Bekaert, P., Seidel, H.-P., and Kautz, J. 2007

Convolution shadow maps. In Proceedings of Eurographics Symposium on Rendering

2007, pp. 51-60.

[Annen08b] Annen, T., Mertens, T., Seidel, H.-P, Flerackers, E., and Kautz, J. 2008.

Exponential Shadow maps. In Proceedings of Graphics interface 2008, pp. 155-161.

[Atty06] Atty , L. Holzschuch, N., Lapierre, M., Hasenfratz, J.-M., Hansen, C., and Sillion,

F. X. 2006. Soft shadow maps: Efficient sampling of light source visibility. Computer

Graphics Forum, 25,4, 725-741.

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[Assarsson03a] Assarsson, U. and Akenine-Moller, T. 2003. A geometry-based soft

shadow volume algorithm using graphics hardware. ACM Transactions on Graphics, 22,

3 (Proceedings of ACM SIGGRAPH 2003), 511-520.

[Assarsson04] Assarson, U. and Akenine-Moller, T. 2004.Occlusion culling and z-

fail for soft shadow volume algorithms. The visual compter, 20, 8-9.

[Bilodeau99] Bilodeu, W. and Songy, M. 1999. Real time shadows. Creativity 1999,

Creative Labs Inc. Sponsored game developer conferences, Los Angeles, California, and

Surrey, England.

[Carmack00] Carmack, J. 2000. Z-fail shadow volumes. Internet Forum.

[Crow77] Crow, F.C. 1977. Shadow algorithms for computer graphics. Computer

Graphics, 11, 2 (Proceeding of ACM SIGGRAPH 77), 242-248.

[Donnelly06] Donnelly, W. and Laurizen, A. 2006. Variance shadow maps. In Proceedings

of ACM SIGGRAPH symposium on Interactive 3D Graphics and Games 2006, pp. 161-165.

[Heidmann91] Heidmann, T. 1991. Real shadows real time. IRIS Universe, 18, 28-31.

[Jordan87] Jordan, C. 1887. Cours d'analyse. L'Ecole Polytechnique, pp. 587-594.

Available online at: http://maths.ed.ac.uk/~aar/jordan/jordan.pdf .

[Salvi08] Salvi, M. 2008. Rendering filtered shadows with exponential shadow

maps. In ShaderX6: Advanced Rendering Techniques (edited by W. Engel), pp.

257-274. Charles River Mdia, Hingham, MA. ISBN 978-1-58450-544-0.

[Williams78] Williams, L. 1978. Casting curved shadows on curved surfaces. Computer

Graphics, 12,3 (Proceedings of ACM SIGGRAPH 78),270-274.

[Wan07] Wan, L., Wong, T.-T., and Leung, C,-S. 2007, Isocube: Exploiting the cubemap

hardware. IEEE Transactions on Visualization and Computer Graphics, 13, 4, 720-731.