CSCE 641: Computer Graphics Ray Tracing Jinxiang Chai.

CSCE 641: Computer Graphics Ray Tracing

Jinxiang Chai

Ray Tracing

Provides rendering method with

Refraction/Transparent surfaces

Reflective surfaces

Shadows

Image taken from http://www.tjhsst.edu/~dhyatt/superap/samplex.jpg

Ray Tracing

Provides rendering method with

Refraction/Transparent surfaces

Reflective surfaces

Shadows

Image taken from http://www.tjhsst.edu/~dhyatt/superap/samplex.jpg

Any difference for rendering three pixels?

Local Illumination vs. Ray Tracing

Ray Tracing Results

Click here

http://www.irtc.org/irtc/

Overview

Ray Tracing Algorithm

Shadows, Reflection, Refraction

Surface Intersection

Infinite planes, spheres, polygons

Optimizations

Essential Information for Ray Tracing

Eye point

Screen position/orientation

Objects

Material properties

Reflection/Refraction coefficients

Index of refraction

Light sources

Ray Tracing Assumption

The illumination of a point is determined by

- illumination/shadow ray (direct lighting from light sources)







- reflection ray (light reflected by an object)





- transparent ray (light passing through an object)











Illumination / Shadow Rays

A ray is cast from an object’s surface towards a light.

If the light is not occluded, then the light contributes to the object’s surface color.

If the light is occluded, then the light does not contribute to the object’s surface color.

If ray hits a semi-transparent object, scale the contribution of that light and continue to look for intersections

Occluder

Pixels

Reflected Rays

A ray is cast from the surface of an object based on its material properties.

The contribution results in the specular reflection.

Transparency/transmission/refracted Rays

Some objects are transparent or translucent.

The transmitted light also contributes to the surface color, called specular transmission.

The ray can be refracted based on the object’s composition.

Recursive Ray Tracing

1

2

3

4

L1

L2


1

2

3

4

L1

L2


1

2

3

4

L1

L2


refractedareflectededirect IIII 1

2

3

4

L1

L2



2

3

4

L1

L2



2

3

4

L1

L2

speculardiffuseambientdirect IIII



2

3

4

L1

L2


1

2

3

4

L1

L2


1

2

3

4

L1

L2


1

2

3

4

L1

L2

What are real light paths?

Recursive Ray Tracing and Light path

1

2

3

4

L1

L2

Ray tracing paths just reverses real light paths!


1

2

3

4

L1

L2



1

2

3

4

L1

L2



1

2

3

4

L1

L2



1

2

3

4

L1

L2



1

2

3

4

L1

L2


Ray Tree

Object 1 L2

Shadow of Obj 4

Object 3

Reflection

ReflectionL2

L1

Object 2

Transmission

ReflectionL2

L1

Eye


For each pixel

Intersect ray from eye through pixel with all objects in scene

Find closest (positive) intersection to eye

Compute lighting at intersection point

Recur for reflected and refracted rays (if necessary)


refractedareflectededirect IIII

speculardiffuseambientdirect IIII

directI

reflectedI refractedI

refractedIrefractedIreflectedI reflectedI

e

e e

a

aa

Termination Criterion

1. The ray intersects no surfaces

2. The ray intersects a light source that is not a reflecting surface

3. The tree has been generated to its maximum allowable depth.

Three Issues

Ray-object intersection

- hidden surface removal

Reflection direction

- mirror direction

Refraction direction

- Snell’s law

Ray-object Intersection

eye

screen

Similar to ray casting!

Ray-object Intersection

eye

screen

Similar to ray casting!

But how to determine the intersection point between a ray and an object such as sphere or triangle?

Ray Casting

Implementation

- Parameterize each ray as

- Each object Ok returns tk>0 such that first intersection with ok occurs at r(tk)

- Q: given the set {tk}, what is the first intersection point?

)()( cptctr ij

Ray-Sphere Intersection

Ray-Triangle Intersection

• First, intersection ray with plane

• Then, check if point is in triangle

Ray-Plane Intersection

Ray-Triangle Intersection

Check if point is inside triangle algebraically

For each side of triangle

0

0

Reflection

Mirror-like/Shiny objects

V

N

Surface

R

VNNVR )(2

Refraction

Bending of light caused by different speeds of light in different medium

Each (semi-)transparent

object has an index of

refraction ni

Use Snell’s law to find

refracted vector

Image taken from http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr2.html

Snell’s Law

V N1

Surface

2

N R

1

2

2

1

2

1

)sin(

)sin(

n

n

c

c

How to compute Transmission Ray?

V N1

Surface

2

N R

n1

n2

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

cV

||V

Snell’s Law

N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

||)sin())(cos( 22 V

VNR

VV

||V

Snell’s Law

N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

||)sin())(cos( 22 V

VNR

VV

||V

Snell’s Law

N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

||)sin())(cos( 22 V

VNR

VV

||V

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

||

)()sin())(cos( 22 V

VNNVNR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

)sin(

)()sin())(cos(

122

VNNVNR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

))(())(cos(1

22 VNNV

c

cNR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

))(()()sin(11

222 VNNV

c

cNR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

))(()()sin(11

22

1

222

1 VNNVc

cN

c

cR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

))(()(1

)sin(1

2

1

21

22

21 VNNV

c

cN

cccR

Snell’s Law

V N1

Surface

2

N R

)sin(

)sin(

2

1

2

1

c

c

))(()(1

))(1(1

2

1

222

21 VNNV

c

cN

cNVccR


Recur for reflective/transparent objects


Recur for reflective/transparent objects

Optimizations

Lots of rays to cast!

Ray-Surface intersections are expensive

Associate with each object

Bounding box in 3-space

If ray doesn’t intersect box, then ray doesn’t intersect object

Parallel Processing

Ray tracing is a trivially parallel algorithm!

Cast rays in parallel

Cast reflection, refraction, shadow rays in parallel

Calculate ray/surface intersections independently in parallel

Ray Tracing Results: Special Effects

Copyright Newline Cinema

Ray Tracing Results: Video Games

Ray Tracing Results: Massive Models

Pros and Cons of Ray Tracing

Advantages of ray tracing

All the advantages of the local illumination model

Also handles shadows, reflection, and refraction

Disadvantages of ray tracing

Computational expense

No diffuse inter-reflection between surfaces (i.e., color bleeding)

Not physically accurate

Other techniques exist to handle these shortcomings, at even greater expense!

Ray Tracing References

Peter Shirley, “Realistic Ray Tracing”, ISBN 1-56881-110-1

Andrew Glassner, “An Introduction to Ray Tracing”, ISBN 0-12-286160-4

Steve Pettifer (http://www.cs.man.ac.uk/people/srp)

Anselmo Lastra (http://www.cs.unc.edu/~lastra)

Paul Rademacher (http://www.cs.unc.edu/~rademach)

Mark Harris (http://www.cs.unc.edu/~harrism)

Kenny Hoff (http://www.cs.unc.edu/~hoff)

POV-Ray (http://www.povray.org)

http://www.cs.man.ac.uk/people/srp

http://www.cs.unc.edu/~lastra

http://www.cs.unc.edu/~rademach

http://www.cs.unc.edu/~harrism

http://www.cs.unc.edu/~hoff

http://www.povray.org/

CSCE 641: Computer Graphics Ray Tracing Jinxiang Chai.

Documents

ray tracing slide

recursive ray tracing

ray tracing assumption

ray tracing results

object transparent ray

l1 l2 slide

herehere slide

transmitted light