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README.md

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Ray Tracing In One Weekend Book Series
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====================================================================================================
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| ![Ray Tracing in One Weekend][cover1] | ![Ray Tracing: The Next Week][cover2] | ![Ray Tracing: The Rest Of Your Life][cover3]
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|:------------------:|:-----------------:|:-------------------------:|
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| [In One Weekend][] | [The Next Week][] | [The Rest Of Your Life][] |
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| ![RT in One Weekend][cover1] | ![RT The Next Week][cover2] | ![RT The Rest Of Your Life][cover3] |
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|:----------------------------:|:---------------------------:|:-----------------------------------:|
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| [In One Weekend][] | [The Next Week][] | [The Rest Of Your Life][] |
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Getting the Books
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[cover1]: images/RTOneWeekend-small.jpg
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[cover2]: images/RTNextWeek-small.jpg
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[cover3]: images/RTRestOfYourLife-small.jpg
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[In One Weekend]: InOneWeekend
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[In One Weekend]: books/RayTracingInOneWeekend.html
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[releases]: https://github.com/RayTracing/raytracing.github.io/releases/
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[Hack the Hood]: https://hackthehood.org/
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[Real-Time Rendering]: https://realtimerendering.com/#books-small-table
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[submit issues via GitHub]: https://github.com/raytracing/raytracing.github.io/issues/
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[The Next Week]: TheNextWeek
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[The Rest Of Your Life]: TheRestOfYourLife
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[The Next Week]: books/RayTracingTheNextWeek.html
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[The Rest Of Your Life]: books/RayTracingTheRestOfYourLife.html

books/RayTracingInOneWeekend.html

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<meta charset="utf-8">
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<!-- Markdeep: https://casual-effects.com/markdeep/ -->
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**Ray Tracing in One Weekend**
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Peter Shirley

books/RayTracingTheNextWeek.html

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<meta charset="utf-8">
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<!-- Markdeep: https://casual-effects.com/markdeep/ -->
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**Ray Tracing: The Next Week**
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Peter Shirley
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50% of all payments donated to programming education related not-for-profits
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Overview
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====================================================================================================
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====================================================================================================
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This part is by far the most difficult and involved part of the ray tracer we are working on. I am
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sticking it in Chapter 2 so the code can run faster, and because it refactors `hitable` a little,
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sticking it in this chapter so the code can run faster, and because it refactors `hitable` a little,
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and when I add rectangles and boxes we won't have to go back and refactor them.
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The ray-object intersection is the main time-bottleneck in a ray tracer, and the time is linear with

books/RayTracingTheRestOfYourLife.html

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<meta charset="utf-8">
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<!-- Markdeep: https://casual-effects.com/markdeep/ -->
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**Ray tracing: The Rest of Your Life**
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Peter Shirley
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One Dimensional MC Integration
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====================================================================================================
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Integration is all about computing areas and volumes, so we could have framed Chapter 1 in an
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Integration is all about computing areas and volumes, so we could have framed Chapter 2 in an
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integral form if we wanted to make it maximally confusing. But sometimes integration is the most
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natural and clean way to formulate things. Rendering is often such a problem. Let’s look at a
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classic integral:
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====================================================================================================
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In this chapter we won't actually implement anything. We will set up for a big lighting change in
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our program in Chapter 5.
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our program in the next chapter.
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Our program from the last books already scatters rays from a surface or volume. This is the commonly
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used model for light interacting with a surface. One natural way to model this is with probability.
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(uniform)
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$$ b(\theta) = 2*\pi*f(\theta)\sin(\theta) $$
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For uniform random numbers $r_1$ and $r_2$, the material presented in Chapter 2 leads to:
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For uniform random numbers $r_1$ and $r_2$, the material presented in Chapter 3 leads to:
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$$ r_1 = \int_{0}^{\phi} \frac{1}{2\pi} = \frac{\phi}{2\pi} $$
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easier. When we sample a sphere’s solid angle uniformly from a point outside the sphere, we are
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really just sampling a cone uniformly (the cone is tangent to the sphere). Let’s say the code has
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`theta_max`. Recall from Chapter 6, that to sample $\theta$ we have:
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`theta_max`. Recall from Chapter 9, that to sample $\theta$ we have:
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$$ r2 = \int_{0}^{\theta} 2 \pi \cdot f(t) \cdot sin(t) dt $$
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