Ray Tracing Assignment Goal is to reproduce the following Whitted, - - PDF document

1

So You Want to Write a Ray Tracer

Checkpoint 6 – Refraction

Ray Tracing Assignment

 Goal is to reproduce the following Whitted, 1980

2

Ray Tracing Assignment



Seven checkpoints

  Setting the Scene  Camera Modeling  Basic Shading   Procedural Shading  Recursive Ray Tracing – Reflection  Recursive Ray Tracing – Transmission   Tone Reproduction

Ray Tracing Assignment



Seven checkpoints

  Setting the Scene  Camera Modeling  Basic Shading   Procedural Shading  Recursive Ray Tracing – Reflection  Recursive Ray Tracing – Transmission   Tone Reproduction

3

Refraction

 Perform recursive ray tracing by

considering reflection and refraction

 Parameters to add:

 For each object

 kr, kt – reflection and transmission constants  kt ≠ 0 for this checkpoint  Index of refraction (example 0.95)

Recursive Ray Tracing

color illuminate (ray, depth) find closest intersect if (!intersection) return background color else spawn shadow ray retcolor = local illumination if (depth < MAX_DEPTH)

if (kr > 0) spawn reflection ray retcolor += kr * illuminate (reflect ray, depth+1) if (kt > 0) spawn transmission ray retcolor += kt * illuminate (trans ray, depth +1)

return retcolor

4

Recursive Ray Tracing

For each pixel spawn ray from camera pos to pixel pixel_color = illuminate (ray, 1)

If negative – total internal reflection

Calculating Transmission Ray

t t i i

θ η θ η sin sin =

We can find the equation for t, the transmission ray:

2 2 2 i i

) ) n d ( 1 (

• 1

n ) n) n(d d ( t

t t

η η η η

• −

+

• −

=

Assume d and n are normalized. Starting with Snell’s law

i

• t

η

i

• t

θ

d t n d is the incoming ray, t is the transmission ray.

5

Total Internal Reflection

 an optical phenomenon that occurs

when light is refracted (bent) at a medium boundary enough to send it backwards, effectively reflecting all of the light.

 In these cases, the transmission ray will

be spawned in the reflection direction.

Total Internal Reflection

Wikipedia

6

Total Internal Reflection

Total internal reflection occurs around boundary of transparent sphere

Calculating transmission ray

 Snell’s law applet

 http://www.physics.northwestern.edu/ugrad/vpl/opt

ics/snell.html

 Index of refraction of air = 1.0  Optimization

 If indices of refractions are the same

 no bending  Transmission direction is the same as incoming direction

7

Things to think about

 Must keep track if you are inside or

• utside

η Index of refraction Normal vector

Things to think about

 2 ways to deal

 If n • d < 0 then

 Inside  Use –n as normal for calculations  Use inside η as

 Keep track as you are spawning rays

i

8

Things to think about

public Vector3f faceForward (Vector3f A Vector3f B)

{ // For acute angles, dot product will // be positive if (A.dot(B) >= 0) return A; // Obtuse angle, reverse the first vector Vector3f V = new Vector3f (A); V.scale (-1.0f); return V; }

Refraction

 For sake of checkpoint

 Make one sphere transparent (kt = 0.8)  Make other sphere non-transparent  May wish to test first with index of refraction = 1.0

9

Refraction

 Note:

 If done correctly, you should now have a faithful

reproduction of the target image.

 Sample parameters

Sphere1 – front Color (all) = white Ka = 0 .0 7 5 Kd = 0 .0 7 5 Ks = 0 .2 Ke = 2 0 .0 Kr = 0 .0 1 Kt = 0 .8 5 Sphere2 – rear Color (amb/diffuse)

(0.7, 0.7, 0.7)

Color (spec) = white Ka = 0 .1 5 Kd = 0 .2 5 Ks = 1 .0 Ke = 2 0 .0 Kr = 0 .7 5 Kt = 0 .0

Refraction

 Due date:

 Must be posted to Web site by Feb 6th  Recall:

 10% penalty per day

 Having trouble?

 Let me know EARLY.

 Questions?

10

Extra extra

 For 5 points:

 Adjust shadow ray based upon

transparency of objects.