Shadow Rendering Techniques

A point is in the shadow of a light source if it can not be “seen” by the light source, i.e. the line segment that connects the point and the light source intersects other objects.

A point that is in the shadow of a light source is not illuminated by the light source.

Direct Projection Method

Projection Plane

Light Source

Object

Projected Shadow

P (x, y, z)

P' (x', y', z')

PL (xL, yL, zL)

NP' + D = 0

uLL )( PPPP

)( L

LDu

PPN

PN

Shadow Map Method

xL

zL

Shadow Map

Shadow Map: Texture that stores depth values when the scene is rendered from the perspective of a light source.

xv

zv

zL

P0 (View Point)

PL (Light Source)

xL

1) Render the scene from the perspective of the light source. Save depth buffer content as shadow map.

2) Render the scene from the original view point. For each point in the scene, transform its position into light source local coordinates and use the transformed position as texture coordinates (s, t, r).

3) Sample shadow map using (s, t) coordinates, compare the result with r coordinate. If it’s less than r, then the point is in the shadow, otherwise it’s not in the shadow.

Shadow rendering procedure using shadow map

Shadow Volume Method

Light Source

Object to cast shadow

Shadow Volume

Object Outline

Shadow Volume: An enclosed region of space that is formed by extruding object outline from the light source.

Z-Pass Shadow Volume Algorithm

Light Source

1. For each point in the scene, connect a line segment from this point to the view point;

2. Count the number of front facing and back facing shadow volume faces this line segment intersects: nf and nb;

3. If nf = nb the point is illuminated, otherwise it is in the shadow.

View Point

Illuminated

Illuminated

Shadowed

Shadow Volume

Object Outline

Z-Path algorithm generates incorrect results when the view point itself is in the shadow.

Z-Fail Shadow Volume Algorithm

Light Source

1. For each point in the scene, cast a ray from this point to infinity that runs away from the view point;

2. Count the number of front facing and back facing shadow volume faces this ray intersects: nf and nb;

3. If nf = nb the point is illuminated, otherwise it is in the shadow.

View Point

Illuminated

Illuminated

Shadowed

Shadow Volume

Object Outline

Z-Fail algorithm generates correct results when the view point itself is in the shadow.

Generate Shadow Volume Faces

Orientation of a polygon surface with respect to light source

P

PL

N

L

Polygon Surface

Light Source

PL Light source positionP A point on polygon surfaceL = PL P Direction to light vectorN Polygon surface normal

NL > 0, The polygon surface faces toward the light source (front facing)NL 0, The polygon surface faces away from the light source (back facing)

Determine object outlines with respect to light source

Polygon Surfaces

Light Source

Polygon Edge

For each polygon edge:1. Find the two polygon surfaces that share this edge.2. Determine the orientations of these two surfaces with respect

to the light source.3. If one is facing toward the light and the other is facing away

from the light, then this polygon edge is an outline.

Extrude a point away from light source

P

P'

PL

uLL )( PPPP

d

PL Light source positionP Point to be extrudedP' Extruded pointd Extrusion distance

d PPL

du

PP 1

Shadow Volume Generation Algorithm

Front Face (unchanged)

Light Source

Outline Edge

1. All polygon surfaces that face toward the light source form the top cap of the shadow volume.

2. For all polygon surfaces that face away from the light source, extrude their vertices and the new extruded polygons form the bottom cap of the shadow volume.

3. Find all polygon edges that are outlines and extrude these outlines into quadrilaterals. These quadrilaterals form the side of the shadow volume.

Back Face (extruded)

Quadrilateral (Extruded from

Outline)

Shadow Volume Using Stencil Buffer

1. Render the scene with all light sources turned off.2. Clear Stencil Buffer3. Turn off depth buffer and color buffer writes.4. Render all shadow volume faces facing away from the viewer. Increase s

tencil buffer value by one for each point that fails the depth test. 5. Render all shadow volume faces facing towards the viewer. Decease sten

cil buffer value by one for each point that fails the depth test. 6. Turn on depth buffer and color buffer writes.7. Render the scene again with light source turned on and only where the st

encil buffer value is zero. 8. Repeat 2, 3, 4, 5, 6, 7 for each light source.

Radiosity Illumination Model

Use physical laws that govern radiant energy transfer between objects.

Radiant Energy Terms

Total Radiant Energy E

Radiant Flux (Radiant Power): Radiant energy transmitted per unit time dt

dE

Radiosity : Radiant flux per unit area of a surfacedA

dB

Intensity : Radiant flux in a certain radiant direction per unit solid angle per unit projected area cosd

dBI

: Angle between radiant direction and surface normal

Radiosity for Lambertian Reflector

x

y

N

d

dB

Radiant Direction

hemispherehemisphere

dIdBB cos

ddd sin

IddIB 2/

0

2

0

sincos

constantI

Form Factor

Form Factor Fjk: Fractional amount of radiant energy from surface j that reaches surface k.

Surface j

Surface kNj

ddBj

Nk

dAj

dAk

j

k

r

2

cos

r

dAd kk

2,

coscoscos

r

dA

I

dI

B

dB

dAB

dAdBF kkj

j

jj

j

j

jj

jjdAdA kj

j kA A

jkkj

jjk dAdA

rAF

2

coscos1

Properties of form factors

kjkjkj FAFA

0jjFFor planar surface and convex surface

Basic Radiosity Model

• The object surfaces must form an enclosed space that has no energy exchange with outside world.

• Assume each surface is either a Lambertian reflector, a emitter, or a combination of both.

• Divide each surface into small surface polygons (surface patches) and calculate form factors.

• Solve radiosity equations.

Bi Radiosity of surface iEi Energy emission rate per unit area of surface ii Reflectivity of surface ii = 1, 2, 3, …, n

Radiosity equations

n

jjkjkkk FBEB

1

k = 1, 2, 3, …, n

11

n

kjkF

k = 1, 2, 3, …, nkkj

jkjkkkkk EFBBF

)1(

nnnnnnnnn

n

n

E

E

E

B

B

B

FFF

FFF

FFF

2

1

2

1

21

22222212

11121111

1

1

1

or

Solve the above equations for Bi

Ray-Tracing Methods

Basic Ray-Tracing Algorithm

Projection Reference

Point

Pixel Center

Pixel Ray

Projection Plane

1. Cast pixel ray from projection reference point through pixel center.2. Each time a pixel ray intersects an object surface, it splits into two

secondary rays: a reflection ray and a refraction ray. (No refraction ray for opaque object.)

3. Repeat step 2 for each pixel ray. Each intersected surface is added to a binary ray-tracing tree.

4. A pixel ray is terminated when the ray intersects no surfaces, intersects a light source that is not a reflecting surface, or the ray-tracing tree reaches maximum allowable depth.

Ray Casting Procedure

S1

S2

S3

S4

R1 T1

R2R3

T3

R4

Projection Reference

Point

S1

S2S3

S4

T1R1

R2

R3 T3

R4

Paths of pixel rays Ray-tracing tree

Pixel Intensity Calculation

The ray-tracing tree is processed in bottom-up order. (Trace each pixel ray backward.)

• For each pixel ray at the bottom of the tree, its intensity is assigned a background intensity value if it does not intersect a light source. Otherwise the intensity is assigned to the light source intensity.

• At each surface intersection, the intensities from reflection ray, refraction ray and intensity contributions from all the light sources are accumulated for the parent ray.

• Pixel ray intensity is attenuated by the distance it travels.• The pixel intensity is obtained at the root of the tree.

N

R

L

V

H

Light Source

Incoming ray

Reflected ray

Shadow ray

Refracted ray

T

u

u Unit vector in pixel ray directionV Unit vector in direction to viewerR Unit vector in reflected ray directionT Unit vector in refracted ray direction

N Surface normalL Unit vector in shadow ray direction

(direction to light source)H Halfway vector

IR

IT

I

TtRs

n

l

nlss

ldd

la

lriaae IkIkIkIkffIkII

l

1

)()( HNLN

VL

VLH

NuNuR )2( uNTr

iri

r

i

coscos

uV

kt: Transparency coefficient

otherwise,1

objectsother intersects sourcelight ray toshadow If,0 ii

Advantage of Ray-Tracing Algorithm

Ray-tracing can produce highly realistic scenes. It automatically detects visible surfaces, renders shadows, transparency effects and generates perspective projection views.

Disadvantage of Ray-Tracing Algorithm

Ray-tracing calculation is highly complex and takes considerable more time to complete than basic illumination and shading models. It is not yet implemented in hardware and is not suitable for real time rendering (simulations, games, etc.) at this time.

Most calculation time of ray-tracing algorithm is spent on ray-surface intersection calculations

Methods to Speed up Ray-Tracing Calculations

Bounding Volume

Enclose a group of objects within a bounding volume (sphere or box). If a pixel ray does not intersect the surface of the bounding volume, then it does not intersect the objects inside the bounding volume.

Bounding Sphere Bounding Box

Bounding Volume Tree

Enclose several smaller bounding volumes with a larger bounding volume to form a hierarchical tree structure. The intersection test is done by processing the tree in top-down order.

Space Subdivision Methods

• Obtain bounding box for the entire scene• Divide the bounding box into a number of sub regions (cells).

Sub regions are usually rectangular solids.• Each cell is associated with a list of objects it contains.• For each pixel ray, trace the cells it intersects and only perform

intersection tests for objects within these cells.

Pixel ray

Pixel ray

Distributed Ray-TracingUse stochastic sampling method that randomly distributes rays according to various parameters.

Jittering

• Divide a pixel area into regular grid of subpixels.

• Generate jittered positions by randomly perturbing the center of each subpixel by a small amount.

Anti-aliasing Effect

Fire subpixel rays through the jittered subpixel positions and average the intensity of these rays to obtain pixel intensity.

Out-of-focus Effect

Place a lens in front of projection plane. Distribute subpixel rays through aperture area of the lens.

Projection Reference

Point

Projection Plane

Object Plane

Lens

Gloss Effect

Gloss: Specular highlight that is blurred.

Distribute reflection rays around the specular reflection direction.

N

R

Incoming ray Reflected rays

u

Translucency Effect

Translucency: Light passing through the material is scattered so that objects behind the material appear blurred.

Distribute refraction rays around the ideal refraction direction.

N

T

Incoming ray

Refracted rays

u

Soft Shadows under Extended Light Source

Extended Light Source

Object

UmbraPenumbra Penumbra

Umbra: Completely dark region

Penumbra: Partially illuminated region

Motion Blur Effect

Distribute rays over time.

Motion Blur: Moving objects appear blurred on film.

Distribute shadow rays over the area of the light source.

N

L

Shadow rays

Extended Light Source