Photorealism: Ray TracingHuamin Wang

(whmin@cc.gatech.edu)

Georgia TechNov 11, 2008

Quiz 1

Quiz 2

Henrik Wann Jensen, 1992

quiz

"Boreal" by Norbert Kern (2004)

"Christmas Baubles" by Jaime Vives Piqueres (2005)

quiz

"The Wet Bird" by Gilles Tran (2001)

CONTENT• Basics of ray tracing

• Monte Carlo integration

• Distributed ray tracing– Soft shadow– Glossy surface– Fuzzy glass– Depth of field– Motion blur

• Conclusion

Basics of ray tracing

Camera

Image Plane

Light 0

Light 1 Object 0Object 1

E

L(E)?

Light Transport

ObjectObject

EI

L(I)L(E)

N

( )( )

( )R

L EF I E

L I ( ) ( ) ( )RL E F I E L I

p

Phong modelAn example of Reflectance

( ) ( ) ( )kR a d sF I E S S N I S R I

EIL(I)

L(E)

N

Rp

Light Transport

EL(E)

N

( ) ( ) ( )RL E F I E L I

p

( ) ( ) ( )RL E F I E L I dI

Light Transport in Basic Ray Tracing

EI

L(E)?

N

( ) ( )RF I E L I

R

( ) ( )RF R E L R

T

( ) ( )TF T E L T 2 2( ) ( )RF I E L I

direct illumination

Mirror (indirect) Glass (indirect)

L(I1)L(In)

L(R)

L(T)

( ) ( ) ( )RL E F I E L I dI

known

Basics of ray tracing

L(E)1.p=Intersection(E);2. if p==NULL return backgrd;3.

4. R=Reflection(E, N);5. 6. T=Refraction(E, N);7. 8. return l;

Camera

Image Plane

Light 0

Light 1 Object 0Object 1

N

( , ) ( ) ( );i R i ii

l g p I F I E L I

I0

pE

I1

g(p,I1)=0

R

T

g(p,I0)=1

( ) ( );Rl F R E L R

( ) ( );Tl F T E L T

Result of Basic Ray Tracing

Huamin Wang et al, 2005

1 2 3 1 2 3

2 3 1 1 2 3

3 1 2 1 2 3

( ) / ( )

( ) / ( )

( ) / ( )

s area PP P area PP P

s area PP P area PP P

s area PPP area PP P

…area of a triangle…

1 2 3

1 2 3 1 2 3

1 2 3

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3

, ,x x x

y y y

z z z

x y z y z x z x y

z y x y x z x z y

P P P

area P P P P P P

P P P

P P P P P P P P P

P P P P P P P P P

P2=(P2.x, P2.y, P2.z)

P1=(P1.x, P1.y, P1.z)

P3=(P3.x, P3.y, P3.z)

Ray-Implicit Surface IntersectionImplicit Surface: f(P)=0Ray: P=O+tDSolution t: f(O+tD)=0

Example (Sphere):

C

r

2 2 2 2( ) ( ) ( ) ( ) 0x x y y z zf P P C P C P C r

2 2 2 2( ) ( ) ( ) 0x x x y y y z z zO tD C O tD C O tD C r

2 0at bt c 2, 42

bt b ac

a

Review: Basics of ray tracing

E

Camera

IntersectionIntersection

IntersectionIntersection

R

IntersectionIntersection

T

IntersectionIntersection

R

IntersectionIntersection

R

IntersectionIntersection

T

L

L

L

L

L

L

L

Result of Basic Ray Tracing

A rendering result: max_depth=16

Limitations of Basic Ray Tracing

Image Plane

Light 1 Object 0Object 1

N

pE

R

T 1. Light Source2. Indirect Illumination3. Lens Camera4. Pixel Intergration5. ….

CONTENT• Basics of ray tracing

• Monte Carlo integration

• Distributed ray tracing– Soft shadow– Glossy surface– Fuzzy glass– Depth of field– Motion blur

• Conclusion

Monte Carlo Integration

• What’s the integral of ?

a b

( )( ) ( ) ( ) ( )

b i

a

f Xf x dx f x b a b a

N

( ), [ , ]f x x a b

f

x1X

1f

2X

2f

3X

3f

4X

4f

5X

5f

6X

6f

7X

7f

8X

8f

1

( )( )

N

ii

f Xf x

N

Monte Carlo Integration

• What’s the integral of ?( ),f

ΩΩ

( )f

1

( )( )

N

ii

ff

N

( )( ) ( ) if

f d fN

Monte Carlo Integration

• What’s the integral of ?( ),f

ΩΩ

( )f

1

( )( )

N

ii

ff

N

( )( ) ( ) if

f d fN

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a rectangle?

a

b

(0,0)

(a,b)

()

()

x Rand a

y Rand b

p=(x,y)

dydx

dydx

dydx

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a sphere?

() 2

()

Rand

Rand

WRONG!d

d

d r rd

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a sphere?

http://www.cs.utah.edu/~thiago/cs7650/hw5/

d

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a sphere?

() 2

2 () 1

arccos( )

Rand

h Rand

h

h

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a sphere?

http://www.cs.utah.edu/~thiago/cs7650/hw5/

2 rh2 rh2 rh2 rh

2 rh

Monte Carlo Integration

• Given a 1D uniform random function Rand() from 0 to 1, How to uniformly sample a region?

(a,b)

(0,0)

()

()

x Rand a

y Rand b

While(1){

if ( (x,y) in Ω )break;

}

Rejection Method

p=(x,y)

Monte Carlo VS Riemann• Similar:

• The difference between MC and Riemann:

( )( , ) if X

f x y dxdyN

Monte Carlo VS Riemann

• The advantage of Monte Carlo

CONTENT• Basics of ray tracing

• Monte Carlo integration

• Distributed ray tracing– 1. Soft shadow– 2. Glossy surface– 3. Fuzzy glass– 4. Depth of field– 5. Motion blur

• Conclusion

1. Hard Shadow by Point Light

ObjectObject

EL(E)

N

( ) 1g I

p

Illuminated:Shadow: ( ) 0g I

( ) ( ) ( ) ( )RL E g I F I E L I

Genetti & Gordon, 1993

1. Soft Shadow by Area Light

ObjectObject

EL(E)

N

1. No Shadow2. Half Shadow (penumbra)3. Complete Shadow (umbra)

Genetti & Gordon, 1993

1. Area Light, distributed ray tracing

ObjectObject

EI

L(I)L(E)

N

ObjectObject

EL(E)

N

( ) ( ) ( ) ( )RL E g I F I E L I 1. For i=1:N2. Ii=Uniform_Sample(Ω); 3. 4. End;5.

( ) ( ) ( ) ( );i R i iL E g I F I E L I

p p

( ) ( ) ;L E L E N

1. Mathematical Validation

ΩΩ

( ) ( ) ( ) ( )rf I g I F I E L I

p

E: Eye

1

( )( ) ( )

( ) ( ) ( )

i

N

i R i ii

f IL E f I dI

N

g I F I E L IN

: Light

I

1. An Area Light ExampleCornell Box: 4 sampleshttp://www.cs.utah.edu/~thiago/cs7650/hw5/

1. An Area Light Examplehttp://www.cs.utah.edu/~thiago/cs7650/hw5/

Cornell Box: 10 samples

1. An Area Light Examplehttp://www.cs.utah.edu/~thiago/cs7650/hw5/

Cornell Box: 100 samples

Distributed Ray Tracing

• It was proposed by Cook, Porter and Carpenter in 1984.

• It is NOT ray tracing on a distributed system.

• It is a ray tracing method based on sampling rays randomly with certain distribution.

2. Glossy Surface Definition

Ideal Specular (mirror) Specular (glossy)

E R

L(E) L(R)

( ) ( ) ( )rL E F R E L R ( ) ( ) ( )rL E F R E L R dR

E

L(E) R

2. Glossy Surface, Distributed Ray Tracing

Mirror4 samples

E

L(E)

16 samples64 samples

( ) ( ) ( )rL E F R E L R dR

1. For i=1:N2.

Ri=Uniform_Sample(Ω);3. 4. End;5.

( ) ( ) ( );R i iL E F R E L R

( ) ( ) ;L E L E N

R

http://www.cse.ohio-state.edu/~xue/courses/782/final/dtr.html

2. Fuzzy Glass, Distributed Ray Tracing

Mirror

EL(E)

( ) ( ) ( )TL E F T E L T dT

4 samples16 samples

T

1. For i=1:N2.

Ti=Uniform_Sample(Ω);3. 4. End;5.

( ) ( ) ( );T i iL E F T E L T

( ) ( ) ;L E L E N

http://www.cse.ohio-state.edu/~xue/courses/782/final/dtr.html

3. An Fuzzy Glass Example

Different glasses rendered by distributing refracted rays, from left to right: ideal glass, fuzzy glass, more fuzzy glass.

4. The Pinhole Camera Model

Camera

Image P

lane E

Image Plane

Pinhole

The projection model in basic ray tracing

The pinhole camera model

Pixel

Pixel

Object

Object

4. Depth of Field: in-focus

Image Plane

lens

Focal plane

In-focus:

Pixel

Pixel

4. Depth of Field: out-of-focus

Image

lens

Out-of-focus:

Circle of Confusion

focal

object

Pixel

4. Depth of Field: out-of-focus

Image

lens

Out-of-focus:

Circle of Confusion

focalobject

Pixel

4. A Depth-of-Field Example

A rendered image illustrates the result at different depths.

http://www.pbrt.org/gallery

4. Depth-of-field, Distributed Ray Tracing

Image Plane lens

Image Plane

Pinhole

The pinhole camera model

The lens camera model

( ) ( )p L E E

Pixel p

Pixel p

( ) ( ') 'p L E dE

1

( ) ( ')N

i

p L EN

EE’

4. Depth-of-field, Distributed Ray Tracing

Image Plane Lens

Pixel p

How to efficiently find sample rays?

E’

E

Focus Plane

q

f

4. A Depth-of-Field Example

Scene rendered in POV-Ray 3.5 (http://www.povray.org)

5. Motion Blur, Distributed Ray Tracing

Camera

Image Plane

T0

ti

Tn

P(p)

( ) ( , )o

n

T

Tp p t dt

[ , ]i o nt T Tin which,

uniform distribution

0

1

( ) ( , )N

ni

i

T Tp p t

N

5. A Motion Blur Example

Motion Blur, by http://www.finalrender.com/

CONTENT• Basics of ray tracing

• Monte Carlo integration (uniform sampling)

• Distributed ray tracing– Glossy surface– Fuzzy glass– Soft shadow– Depth of field– Motion blur

• Conclusion

Conclusion

Basic ray tracing algorithm generates images with direct illumination + Mirror reflection + Glass transmission.

Sampling rays in space and time to obtain various ray tracing effects.

Monte Carlo integration is easy to implement, but needs sufficient samples for better approximation.