Author: Romain Vergne (website)
Please cite my name and add a link to my web page if you use this course

Image synthesis and OpenGL: shadows

Quick links to:

Importance of shadows
Definition
Shadow volumes
Shadow map
Perspective Shadow Map
Cascaded Shadow map
Fixed soft shadows and filtering
Extended Soft Shadows
Sources

Importance of shadows

Shadows can surprisingly affect perceived object positions

Images from [Mamassian et al. 1998]. Watch the demo here.

Definition

\[
L(\mathbf{p} \rightarrow \mathbf{e}) =
\rho_a L_a +
\sum_{k}
\rho(\mathbf{p}, \mathbf{e}, \pmb{\ell}_k) \
(\mathbf{n}\cdot\pmb{\ell}_k) \
V(\mathbf{p},\pmb{\ell}) \ L(\mathbf{p} \leftarrow \pmb{\ell}_k)
\]

Visibility term \( V \) at a point \( \mathbf{p} \)

0 if the light source is hidden at point \( \mathbf{p} \)
1 if the light source is visible at point \( \mathbf{p} \)
Shadows ~= surfaces for which light sources are not visible

Shadow volumes

A punctual source divides space in two: shadowed and lighted regions
shadow volume = boundary between these regions

Algorithm

Render the scene with depth ambient lighting attributes
From a light source, calculate silhouettes of all occluders
Extrude silhouettes away from the light
Render the shadow volume: from the camera, test front and back shadow volume faces and update the stencil buffer
Do a light pass using the stencil buffer
Repeat steps 2-5 for all lights

Dealing with soft shadows

Compute shadow volumes for a few light positions
Compare shadow faces for the different positions

Shadow volumes in Doom 3

+ precise
+ directional / punctual light sources
- highly dependent on the scene geometry

necessitates manifold meshes
lots of triangles : lots of silhouette extrusions

Further reading on shadow volumes

Shadow map

Algorithm

From the light point of view

render the scene
store depth in a buffer (the shadow map) using render to texture (FBO)

via an orthographic projection with a directional light
via a perspective projection with a spot light
via a perspective projection in a cube map for a point light

From the camera point of view

render the scene
compute lighting
project/convert vertex position in the light coordinate system
compare vertex depth with the one stored in the shadow map
if the vertex is farther, then it is in the shadow

left: final rendering from the camera. Middle: rendering from the light source. Right: depth map obtained from the light source (shadow map)

Shadow map (depth from light)

Basic shadow mapping

Issues

Shadow acne effect

Solution 1: use a bias when comparing depths (but may produce other artifacts)
Solution 2: do not use thin geometry. Draw back faces first (generate shadow maps), and front faces next to render and compare

Aliasing

Perspective Shadow Map

A solution consists in increasing the resolution of the shadow map near the camera (where the problem is the most important and visible)

Images taken here

Cascaded Shadow map

Use several shadow maps at different resolutions depending on camera frustum

A simple example here

Fixed soft shadows and filtering

Percentage Closer Filtering (PCF)

Bilinear interpolation on the result of the comparison test
Warning: different from comparing the result of the bilinear interpolation on the depth map

Better but still a lot of aliasing

Does not generate soft shadows
May introduces artifacts

Variance / Convolution / Exponential Shadow Maps

Solution: approximate shadow test by a linear function that can be prefiltered
Goal: blur the shadow map to generate realistic soft shadows


VSM: based on mean and variance depth values May produce light bleeding effects But better solutions proposed [Lauritzen 07/08]	CSM: based on 1D fourier expansion May produce bleeding and ringing Quite slow	ESM: based on an exponential approximation May produce small artifacts But resolved by [Salvi08] Fast