Advanced computer graphics lecture 2 ray tracing
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Advanced Computer Graphics Lecture 2: Ray Tracing. David Luebke [email protected] http://www.cs.virginia.edu/~cs551dl. Recursive Ray Tracing. Idea dates back to Descartes (1637) In graphics: Turner Whitted (1980) Used recursive ray tracing as general framework for:

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Advanced Computer Graphics Lecture 2: Ray Tracing

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Advanced computer graphics lecture 2 ray tracing

Advanced Computer GraphicsLecture 2: Ray Tracing

David Luebke

[email protected]

http://www.cs.virginia.edu/~cs551dl

David Luebke6/10/2014


Recursive ray tracing

Recursive Ray Tracing

  • Idea dates back to Descartes (1637)

  • In graphics: Turner Whitted (1980)

    • Used recursive ray tracing as general framework for:

      • Hidden surface problem

      • Shadow computation

      • Reflection/refraction

    • Much work in the 80’s, then fell into academic disfavor (Turner’s old joke)

David Luebke6/10/2014


Recursive ray tracing1

Recursive Ray Tracing

David Luebke6/10/2014


Recursive ray tracing2

Recursive Ray Tracing

Pixel

ImagePlane

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Recursive ray tracing3

Recursive Ray Tracing

“Direct” Ray To Eye

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Recursive ray tracing4

Recursive Ray Tracing

“Indirect” Ray To Eye

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Recursive ray tracing5

Recursive Ray Tracing

  • Physically, we’re interested in path of light rays from light source to eye.

  • In practice, we trace rays backwards from eye to source (Why?)

David Luebke6/10/2014


Recursive ray tracing6

Recursive Ray Tracing

  • Physically, we’re interested in path of light rays from light source to eye.

  • In practice, we trace rays backwards from eye to source (Why?)

    • Computational efficiency: we want the finite subset of rays that leave source, bounce around, and pass through eye

    • Can’t predict where a ray will go, so start with rays we know reach eye

David Luebke6/10/2014


Basic algorithm

Basic Algorithm

  • Function TraceRay() Recursively trace ray Rand return resulting color C

    • IfRintersects any objects then

      • Find nearest object O

      • Find local color contribution

      • Spawn reflected and transmitted rays, using TraceRay() to find resulting colors

      • Combine colors; return result

    • else

      • return background color

David Luebke6/10/2014


Basic algorithm code

Basic Algorithm: Code

Object allObs[];

Color image[];

RayTraceScene()

allObs = initObjects();

for (Yall rows in image)

for (X all pixels in row)

Ray R = calcPrimaryRay(X,Y);

image[X,Y] = TraceRay(R);display(image);

David Luebke6/10/2014


Basic algorithm code1

Basic Algorithm: Code

Color TraceRay(Ray R)

ifrayHitsObjects(R) then

Color localC, reflectC, refractC;

Object O = findNearestObject(R);

localC = shade(O,R);

Ray reflectedRay = calcReflect(O,R)

Ray refractedRay = calcRefract(O,R)

reflectC = TraceRay(reflectedRay);

refractC = TraceRay(refractedRay);

return localC  reflectC refractC

else returnbackgroundColor

David Luebke6/10/2014


Refining the basic algorithm

Refining theBasic Algorithm

Color TraceRay(Ray R)

ifrayHitsObjects(R) then

Color localC, reflectC, refractC;

Object O = findNearestObject(R);

localC = shade(O,R);

Ray reflectedRay = calcReflect(O,R)

Ray refractedRay = calcRefract(O,R)

reflectC = TraceRay(reflectedRay);

refractC = TraceRay(refractedRay);

return localC  reflectC refractC

else returnbackgroundColor

David Luebke6/10/2014


Ray object intersection

Ray-Object Intersection

  • Given a ray and a list of objects, what (if any) objects does the ray intersect?

  • Query: Does ray R intersect object O?

    • How to represent ray?

    • What kind of object?

      • Sphere

      • Polygon

      • Box

      • General quadric

David Luebke6/10/2014


Representing rays

R = O+ tD

O

t < 0

t = 1

t > 1

D

Representing Rays

  • How might we represent rays?

  • We represent a ray parametrically:

    • A starting point O

    • A direction vector D

    • A scalar t

  • Why?

David Luebke6/10/2014


Ray sphere intersection

Ray-Sphere Intersection

  • Ray R = O + tD

    x = Ox + t * Dx

    y = Oy + t * Dy

    z = Oz + t * Dz

  • Sphere at (l, m, n) of radius r is:

    (x - l)2 + (y - m)2 + (z - n)2 = r 2

  • Substitute for x,y,z and solve for t…

David Luebke6/10/2014


Ray sphere intersection1

Ray-Sphere Intersection

  • Works out as a quadratic equation:

    at2 + bt + c = 0

    where

    a = Dx2 + Dy2 + Dz2

    b =2Dx(Ox - l) + 2Dy(Oy - m) + 2Dz(Oz - n)

    c = l2 + m2 + n2 + Ox2 + Oy2 + Oz2 - 2(l Ox + m Oy + n Oz + r2)

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Ray sphere intersection2

Ray-Sphere Intersection

  • If solving for t gives no real roots: ray does not intersect sphere

  • If solving gives 1 real root r, ray grazes sphere where t = r

  • If solving gives 2 real roots (r1, r2), ray intersects sphere at t = r1& t = r2

    • Ignore negative values

    • Smallest value is first intersection

David Luebke6/10/2014


Ray sphere intersection3

Ray-Sphere Intersection

  • Find intersection point Pi = (xi, yi, zi) by plugging t back into ray equation

  • Find normal at intersection point by subtracting sphere center from Pi and normalizing:

    (When might we need the normal? When not?)

David Luebke6/10/2014


Ray polygon intersection

Ray-Polygon Intersection

  • Polygons are the most common model representation (Why?)

  • Basic approach:

    • Find plane equation of polygon

    • Find intersection of ray and plane

    • Does polygon contain intersection point?

David Luebke6/10/2014


Ray polygon intersection1

y

N

P2

P1

d

x

Ray-Polygon Intersection

  • Find plane equation of polygon:ax + by + cz + d = 0

  • How?

    N = [a, b, c]

    d = N  P1

    (How to find N ?)

David Luebke6/10/2014


Ray polygon intersection2

Ray-Polygon Intersection

  • Find intersection of ray and plane:

    t = -(aOx + bOy + cOz + d) / (aDx + bDy + cDz)

  • Does poly contain intersection point Pi ?

    • Book’s algorithm:

      • Draw line from Pi to each polygon vertex

      • Measure angles between lines (how?)

      • If sum of angles between lines is 360°, polygon contains Pi

    • Slow — better algorithms available

David Luebke6/10/2014


Ray box intersection

Ray-Box Intersection

  • Often want to find whether a ray hits an axis-aligned box (Why?)

  • One way:

    • Intersect ray with pairs of parallel planes that form box

    • If intervals of intersection overlap, the ray intersects the volume.

David Luebke6/10/2014


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