CSCE 441: Computer Graphics Ray Tracing

CSCE 441: Computer Graphics Ray Tracing

Jinxiang Chai

Ray Tracing

Is a global illumination technique

Provides rendering method with Refraction/Transparent surfaces Reflective surfaces Shadows

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

Ray Tracing

Is a global illumination technique

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

- Reflective surface- Realistic shadows

Ray Tracing Results

Click here

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

Overview

Ray Tracing Algorithm Shadows, Reflection, Refraction

Surface Intersection Infinite planes, spheres, polygons

OptimizationsReadings: HB 21-1

Essential Information for Ray Tracing

Eye pointScreen position/orientationObjects

Material properties Reflection/Refraction coefficients Index of refraction

Light sources

Direct and Indirect Light

Ray Tracing Assumption

The illumination of a point is determined by - illumination/shadow ray (direct lighting

from light sources)



from light sources)



from light sources) - reflection ray (light reflected by an object)



from light sources) - reflection ray (where the angle of reflection equals the angle

of incidence) - transparent ray (light passing through an

object)





object)





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

L1Object 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 removalReflection direction - mirror directionRefraction 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, intersecting the ray with plane

• Then, check if point is in triangle

Ray-Plane Intersection


Check if point is inside triangle algebraically

For each side of triangle evaluate if the intersection point P is above or below the

plane(P-P0)∙N1=0P on the

equation:P above the plane:

(P-P0)∙N1>0

P below the plane:

(P-P0)∙N1<0


Check if point is inside triangle algebraically

For each side of triangle

00

// P is outside triangle

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(

nn

cc

How to compute Transmission Ray?

V N1

Surface

2

N R

n1

n2

Given V and N, as well as n1 and n2, how to compute R?

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

ccV

||V

Snell’s Law

N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

||)sin())(cos( 22 VVNR

V V

||V

Snell’s Law

N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc


V V

||V

Snell’s Law

N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc


V V

||V

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

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

VNNVNR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

)sin()()sin())(cos(

122

VNNVNR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

))(())(cos(1

22 VNNV

ccNR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

))(()()sin(11

222 VNNV

ccNR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

))(()()sin(11

22

1

222

1 VNNVccN

ccR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

))(()(1)sin(1

2

1

21

22

21 VNNV

ccN

cccR

Snell’s Law

V N1

Surface

2

N R

)sin()sin(

2

1

2

1

cc

))(()(1))(1(1

2

1

222

21 VNNV

ccN

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

refractionDisadvantages 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.man.ac.uk/people/srp

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

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

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

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

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

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

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

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

http://www.povray.org/

http://www.povray.org/

Environment Mapping

An alternative way for modeling global reflections

How to create this effect?

Environment Mapping

An efficient technique for approximating the appearance of a reflective surface by means of a precomputed texture image.

Environment Mapping

Cheap attempt at modeling reflectionsMakes surfaces look metallic

The poor person’s ray tracing method (only consider reflection ray)

Use six textures to model faces of a cubeAssume cube faces infinitely far awayThe normal (or reflected eye vector) is used to

find which of the textures to use and what texture coordinate

Environment Mapping

Environment Mapping

Environment Mapping

Environment Mapping

reflective surface

viewer

environment texture image

v

n

r

Environment Mapping

Reflected ray: r=2(n·v)n-v

Texture is transferred in the direction of the reflected ray r from the environment map onto the objectWhat is in the map?

Incident ray reflected ray

How to represent the map

viewer


viewer


viewer


viewer

Store colors of every possible direction in texture maps


viewer


vc

cccc


viewer


Look up texture maps based on reflected vector

vc

cccc

Cubic Mapping

The map resides on the surfaces of a cube around the object Typically, align the faces of the cube with the coordinate axes

To generate the map: For each face of the cube, render the world from the center

of the object with the cube face as the image plane Rendering can be arbitrarily complex (it’s off-line)

To use the map: Index the R ray into the correct cube face Compute texture coordinates

Cubic Map Example


viewer


Sphere Mapping

Map lives on a sphereTo generate the map:

Render a spherical panorama from the designed center point

To use the map: Use the orientation of the R ray to index

directly into the sphere

Example

Environmental Mapping: Limitations

Assume distant environment

Only work for convex objects (i.e., no self-interreflections)

Documents

CSCE 441: Computer Graphics Ray Tracing