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Write a raytracer c

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Sebastian Raaphorst, Gemini Observatory. Little by little, a test here and a test there, you'll create an incredibly sophisticated ray tracing library. Because each change is so small, your ray tracer will sneak up on you. That's the devious part: By the end you'll have built an amazingly complex piece of software, but it will never feel difficult!
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Write a raytracer c
Write a raytracer c
Write a raytracer c
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As an aside, this ended up being a very long post. Aside from the obvious reflections, the program is notable for its depth-of-field blur and soft shadows. One immediate obstacle arose: the result of sweeping a 3D sphere along a 2D arc is a torus segment, and ray-torus intersection a bit hairy because it requires solving a quartic fourth-order polynomial. Sphere tracing works by computing or estimating the distance between the current point on the ray initially the ray origin and the nearest point in the scene, and advancing along the ray by that distance, as shown above. Although it may be slower than analytic raytracying, it is numerically robust and guaranteed to converge to an intersection as long as the ray starts in free space and the distance estimate is less than or equal to the true distance. So after playing a bit with distance functions and fonts, I whipped up version 0.
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Welcome to Part 2 of my series on writing a raytracer in Rust. Previously, we implemented a basic raytracer which can render only a single sphere with no lighting. Once we have multiple spheres, however, we need to know which one our ray hit. If they do, we can find the correct sphere by taking the nearest intersection to our camera.
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This post discusses a ray tracer in detail, talking you through the computation step-by-step. However, you should be able to adapt it to your needs once you understand the maths. Instead, I explain in words, maths, and pictures.
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