Ray Tracing Chapter 10.11 CAP4730: Computational Structures in Computer Graphics.

Ray TracingRay Tracing

Chapter 10.11Chapter 10.11

CAP4730: Computational Structures in Computer Graphics

OutlineOutline

What is raytracing?What is raytracing? How is raytracing different than How is raytracing different than

what we’ve done before?what we’ve done before? Math behind raytracingMath behind raytracing Uses of raytracingUses of raytracing

Forward MappingForward Mapping

Forward mapping is what we are Forward mapping is what we are used to.used to.

Forward MappingForward Mapping

Take each primitiveTake each primitive Figure out where on the screen it Figure out where on the screen it

should appearshould appear Also known is feed-forwardAlso known is feed-forward

Ray TracingRay Tracing

Ray tracing is the “inverse” of the Ray tracing is the “inverse” of the “forward” mapping we are used to.“forward” mapping we are used to.

Ray TracingRay Tracing

Also known as inverse mapping or feed-Also known as inverse mapping or feed-backwardbackward

Feed-Forward vs.Feed-Forward vs. Feed-Backward Feed-Backward

Pros and Cons of eachPros and Cons of each

Ray-TracingRay-Tracing Attempts to trace the paths of Attempts to trace the paths of

light that contribute to each light that contribute to each pixel that make up a scenepixel that make up a scene

Instead of computing visible Instead of computing visible surfaces, determine surfaces, determine intensity intensity contributionscontributions

Compute Compute global illuminationglobal illumination Allows for:Allows for:

– ReflectionReflection– RefractionRefraction– Atmospheric effectsAtmospheric effects– ShadowsShadows

Results in very realistic scenesResults in very realistic scenes– Used in movies, animations, Used in movies, animations,

cut-scenescut-scenes

Center of Center of ProjectionProjection– Infinite RaysInfinite Rays– Care about ones Care about ones

that pass through that pass through the virtual screenthe virtual screen

– For each pixelFor each pixel Compute ray to a Compute ray to a

pixelpixel For each object in For each object in

the scenethe scene– Compute the Compute the

intersection intersection between ray between ray and objectand object

Find closest Find closest intersectionintersection

Calculate Calculate illuminationillumination

Similar to a Similar to a pinhole camerapinhole camera

for (j=0;j<IMAGE_HEIGHT;j++)for (j=0;j<IMAGE_HEIGHT;j++)

for (i=0;i<IMAGE_WIDTH;i++)for (i=0;i<IMAGE_WIDTH;i++)

result=CheckForIntersection(i,j)result=CheckForIntersection(i,j)

SetPixel(i,j,result);SetPixel(i,j,result);

CheckForIntersection(i,j)CheckForIntersection(i,j)

ray = vector from eye through pixel on ray = vector from eye through pixel on display planedisplay plane

if (DetermineIntersection(ray, color))if (DetermineIntersection(ray, color))

return color;return color;

Computational Cost of Ray Computational Cost of Ray TracingTracing

Let’s compute a formula for how much Let’s compute a formula for how much work we have to do:work we have to do:

O(i*j*intersection tests)O(i*j*intersection tests) What is an intersection test?What is an intersection test? What is the cost of an intersection test?What is the cost of an intersection test? We test the ray going from the eye We test the ray going from the eye

through each pixel for an intersection through each pixel for an intersection with with anyany object. object.

How are objects specified?How are objects specified?

Ray Triangle IntersectionRay Triangle Intersection

Ray is specified as a vector and a starting Ray is specified as a vector and a starting position (camera)position (camera)

There are many different methods (search the There are many different methods (search the web) to do ray - triangle intersectionweb) to do ray - triangle intersection

One solution: Intersect with the plane of the One solution: Intersect with the plane of the triangle. Determine if the intersection point is triangle. Determine if the intersection point is within the trianglewithin the triangle

Defining objectsDefining objects

We don’t have to use triangles We don’t have to use triangles exclusively.exclusively.

Let’s think about other objects and the Let’s think about other objects and the different intersections. How would we different intersections. How would we specify:specify:– SpheresSpheres– CylindersCylinders– CubesCubes– Other base geometric objectsOther base geometric objects

Ray IntersectionsRay Intersections

http://www.swin.edu.au/astronomy/pbourke/geometry/sphereline/

Since performance is so closely tied to ray-object intersections, we’d like to speed it up. How can we speed things up?

Break down things into two steps, detecting intersections, and determining location of intersection.

Ray IntersectionsRay Intersections

We are emulating “reality” where light We are emulating “reality” where light reaches our eye.reaches our eye.

We are asking “what is the path of the We are asking “what is the path of the light that reached our eye for that light that reached our eye for that pixel?”pixel?”

Ray Tracing (in the way we know it), Ray Tracing (in the way we know it), was started by Turner Whitted (1980).was started by Turner Whitted (1980).

With ray tracing, we can solve for With ray tracing, we can solve for global illuminationglobal illumination..

Ray Tracing ObservationsRay Tracing Observations

Each pixel must be evaluatedEach pixel must be evaluated Hard for non solid objectsHard for non solid objects No screen space coherenceNo screen space coherence Difficult to do in parallelDifficult to do in parallel Difficult to accelerateDifficult to accelerate

Recursive Ray-TracingRecursive Ray-Tracing How would we compute lighting? How would we compute lighting?

Let’s Let’s reversereverse the light ray that got the light ray that got to our eyeto our eye

Upon intersection, fire ‘secondary Upon intersection, fire ‘secondary rays’rays’

Vector to the light

Refraction RayReflected Ray

Upon IntersectionUpon Intersection

How do we compute each?How do we compute each? Why follow each ray?Why follow each ray?

– Each contributes intensity to the intersection Each contributes intensity to the intersection position!position!

u

N

L, shadow ray

T

Θi

Θr

R

indices of refractionindices of refraction

u

N

L, shadow ray

T

Θi

Θr

NuT ir

ir

r

i

coscosi

r

ir

2

2

cos11cos

NNuuR 2

R

Ray-Surface IntersectionRay-Surface Intersection

RayRay– P=PP=P00 + s*u + s*u

– PP00 - initial point of ray - initial point of ray

– u – unit vectoru – unit vector– u = (pixel – COP)/|(pixel-COP)u = (pixel – COP)/|(pixel-COP)– s – distance along vectors – distance along vector

Recursive Ray-TracingRecursive Ray-Tracing

ShadowsShadows

Vector to the light

Refraction RayReflected Ray

Recursive Ray-TracingRecursive Ray-Tracing

For each ray, we repeat the For each ray, we repeat the processprocess

How many “levels of recursion” How many “levels of recursion” should we do?should we do?

Refraction Ray

Reflected Ray

Vector to the light

RercursionRercursion

How do we compute the refraction vector? How do we compute the refraction vector? What properties would you want to include What properties would you want to include

with an object?with an object?

Refraction Ray

Reflected Ray

Vector to the light

Depth of recursionDepth of recursion Time vs. AccuracyTime vs. Accuracy Tree Data Tree Data

StructureStructure– ray-tracing treeray-tracing tree– pg. 599 in bookpg. 599 in book– How deep is the How deep is the

tree?tree? What are some end What are some end

conditions?conditions? What are some What are some

acceptable end-acceptable end-limits?limits?

LightingLighting

So how do we compute the final color?So how do we compute the final color? We can employ many lighting modelsWe can employ many lighting models

– Phong LightingPhong Lighting– Torrence-SparrowTorrence-Sparrow– BRDF modelsBRDF models

What lighting can it not do?What lighting can it not do?– Caustics (focused light like in water)Caustics (focused light like in water)– specular to specular or diffusespecular to specular or diffuse– diffuse to diffuse or speculardiffuse to diffuse or specular

LightingLighting

We’ll cover lighting much more in depth We’ll cover lighting much more in depth laterlater

For now:For now:– Three termsThree terms

Ambient – global light that exists (hack)Ambient – global light that exists (hack) Diffuse –contribution of a light. Dependent on Diffuse –contribution of a light. Dependent on

light locationlight location Specular – contribution of a light that is wrst Specular – contribution of a light that is wrst

user’s eyeuser’s eye

– L = kL = kaaIIaa + k + kdd(n*L) +k(n*L) +kss(h*N)(h*N)nsns

Ray Tracing Pros and ConsRay Tracing Pros and Cons

ProsPros– TransparencyTransparency– ReflectionsReflections– ShadowsShadows– Complex Complex

Primitives (math Primitives (math equations)equations)

– Easy to writeEasy to write

ConsCons– Hard to accelerateHard to accelerate– Isn’t the complete Isn’t the complete

global illuminationglobal illumination– Very slow per Very slow per

pixel calculation.pixel calculation.

What is slow about Ray What is slow about Ray Tracing?Tracing?

Ray Triangle intersectionsRay Triangle intersections Let’s talk about bounding volumesLet’s talk about bounding volumes Heirarchies?Heirarchies? What are some properties of the What are some properties of the

volumes that determines how “good” a volumes that determines how “good” a bounding volume is?bounding volume is?

Spatial SubdivisionSpatial Subdivision

Divide space into regions

Place objects into different regions

Compute which regions you can “see” from your current position

Only test those objects

Developing a hierarchy of tests

Other TricksOther Tricks

How would we doHow would we do– antialiasingantialiasing– texturingtexturing– transparencytransparency– different material propertiesdifferent material properties

Refraction Ray

Reflected Ray

Vector to the light

Ray TracingRay Tracing

http://graphics.lcs.mit.edu/http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture20/classes/6.837/F98/Lecture20/RayTrace.javaRayTrace.java

POV-Ray (www.povray.org)POV-Ray (www.povray.org)