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

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So You Want to Write a Ray Tracer

Checkpoint 6 – Refraction

Ray Tracing Assignment

• Goal is to reproduce the following

Whitted, 1980

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Ray Tracing Assignment

• Seven checkpoints
• 1. Setting the Scene
• 2. Camera Modeling
• 3. Basic Shading
• 4. Procedural Shading
• 5. Recursive Ray Tracing – Reflection
• 6. Recursive Ray Tracing – Transmission
• 7. Tone Reproduction

Ray Tracing Assignment

• Seven checkpoints
• 1. Setting the Scene
• 2. Camera Modeling
• 3. Basic Shading
• 4. Procedural Shading
• 5. Recursive Ray Tracing – Reflection
• 6. Recursive Ray Tracing – Transmission
• 7. Tone Reproduction

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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

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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

η

t

η

i

θ

t

θ

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

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Calculating transmission ray

• Snell’s law applet

– http://www.physics.nwu.edu/ugrad/vpl/optics/snell.htm l

• 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

Things to think about

• Must keep track if you are inside or outside

η Index of refraction Normal vector

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Things to think about

• 2 ways to deal

– If n • d < 0 then

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

– Use faceForward

i

η

Things to think about

• FaceForward (RenderMan)

– The result is A, if A and B form an acute angle when placed head to tail, otherwise the result is -A. A (input): This is the first input vector. B (input): This is the second input vector. OUT (output): The result is A, if A and B form an acute angle when placed head to tail, otherwise the result is -A.

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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

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Refraction

• Note:

– If done correctly, you should now have a faithful reproduction of the target image. – Sample parameters

Sphere1 – front Color (all) = white Ka = 0.075 Kd = 0.075 Ks = 0.2 Ke = 20.0 Kr = 0.01 Kt = 0.85 Sphere2 – rear Color (amb/diffuse)

(0.7, 0.7, 0.7)

Color (spec) = white Ka = 0.15 Kd = 0.25 Ks = 1.0 Ke = 20.0 Kr = 0.75 Kt = 0.0

Refraction

• Due date:

– Must be posted to Web site by Midnight Feb 7th – Recall:

• 10% penalty per day

– Having trouble?

• Let me know EARLY.
• Questions?

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Extra extra

• For 5 points:

– Like reflection…spawn multiple rays.