Ray tracing secondary rays: refraction, reflection and ... · Refraction recursion: inescapable I Where we just have re ections, we can avoid recursion: I Do the rest of the illumination

Ray tracing secondary rays:refraction, reflection and supersampling

COSC342

Lecture 1526 Apr 2016

Whitted’s ray tracer clearly supported refraction

COSC342 Ray tracing secondary rays: refraction, reflection and supersampling 2

i

r

n

What is refraction?

sin i = n sin r

COSC342 Ray tracing secondary rays: refraction, reflection and supersampling 3

Effect of refraction

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Refractive index n

I The refractive index n is actually a ratio.

I Velocity of light in a medium = cn

I n depends on the medium

I n1 sin i = n2 sin r

I n for air is almost 1.0

I (Also, note that this is the third unrelated type of ‘n’ that we havediscussed recently, alongside normal vectors (n) and the Phongspecular exponent.)

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n

iv

Using vectors

I Ray is u + tv

I n, v are unit vectors

I sin i = ‖v − (v · n)n‖

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Refracted ray

The refracted ray v′ will have:

I a ‘parallel’ part v′par in the direction of v − (v · n)n, i.e., the directionthat’s perpendicular to n . . .

I . . . but whose magnitude is affected by the refractive index, i.e., thechange of speed of the light: ‖v′par‖ = ‖v − (v · n)n‖n1

n2

I Ray v′ also has a ‘normal’ part v′nor , that is the right size for v′ to bea unit vector. So v′nor = k(v · n)n for some scalar k .

I We know that that ‖v′‖ = 1, and v′ = v′par + v′nor

I From Pythagoras’ Theorem,(v′par

)2+ (k(v · n)n)2 = 12

I So, we have:

k =

√1− (v′par )2

((v · n)n)2

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n

r

i

Total internal reflection

I n1 sin i = n2 sin r

I sin r = n1n2

sin i

I if n1 > n2, then we forsome i angles we needsin r > 1 (impossible!)

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The truth is more complicated

I As the incident ray approaches the critical angle the proportion oflight reflected goes up to 100%.

I The amount of reflected and transmitted light is given by Fresnel’sequations. . .

I . . . but those are not part of COSC342 (phew!)

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Ray propagation—from the eye . . .

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. . . to the reflected/refracted rays . . .

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. . . and considering shadow rays from each hit point

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Refraction recursion: inescapable

I Where we just have reflections, we can avoid recursion:I Do the rest of the illumination before sending the reflective rayI i.e., use an accumulator to collect the colour so far, and pass it forward

to the code that handles the reflected ray.

I But when we have refraction, we can spawn two, new, recursive raysat each and every intersection point.

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How deep should we go in terms of recursion?

I Real reflection and refraction is never perfect. We will always lose alittle light energy at each surface interaction.

I So our coefficients kd , ks , kr , kt , for diffuse, specular, reflection andrefraction are all less than 1.0

I For an object with kr = 0.8, after 30 reflections the contribution willbe 0.830 < 1

1000

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Do it in the right order...

void ray(fraction, depth, u, v ...)

{

if (depth > LIMIT) return;

if (fraction < TINY) return;

get hit... do local lighting...

shadows...

ray(fraction*kr, depth+1,

hit, r(v) ...)

ray(fraction*kt, depth+1,

hit, t(v) ...)

}

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Our progress compared to Whitted’s ray tracer

We can now achieve:

I Ambient,

I Lambert,

I Phong,

I shadows,

I reflection,

I refraction,

I point light sources.

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Actually, in some ways this is just the beginning . . .

Problems that we have yet to discuss in detail:

I Aliasing artefactsI No surface/surface illumination

I If you want to read up on this, you might enjoyhttp://escience.anu.edu.au/lecture/cg/

GlobalIllumination/printNotes.en.html

I No caustics

I Shadows are hard (i.e., have hard edges)

I Colour problems

I Very slow

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We would like to avoid aliasing effects

I The jaggies,

I versus antialiased output:

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Aliases

I A given set of samples can represent more than one picture.

I The alternatives are called aliases.

I Antialiasing is mostly about getting the samples to look like thepicture we want.

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Supersampling

I Fire multiple rays per pixel

I How expensive will this be?

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There are many potential patterns for supersampling rays

I What are the pros and cons of the different patterns shown here?

I Is there an answer that will suit all potential scenes?

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Adaptive Sampling

I Another approach is to determine what rays to fire depending on theresults of rays you have alread fired, i.e., adaptive sampling.

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Jittering

I Even when just using one sample per pixel this is an improvement onuniform sampling.

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