Most of the information can be applied to any 3d package, but is primarily for 3ds max's default scanline renderer.
How Raytracing works:
Raytracing is used to create shiny reflective surfaces, like a mirror or a metal ball, or see-through objects that refract light. Essentially, it simulates how a light particle would move.
However, there is one important piece of information you should know about this - rays are traced backwards.
The diagram below shows how a reflective sphere would be simulated:
For every pixel on the screen that shows a raytraced object, the renderer will shoot one ray (unless you use anti-aliasing or defocusing).
Refraction is also another important part of raytracing. It simulates how light would bend through glass or some other clear material.
Refraction is controlled through a material's IOR (index of refraction). A value of 1 means there's no bending (vacuum). Glass has a value of 1.55. Air has a value of about 1.05 (very little bending, almost unnoticeable).
The renderer draws reflections and refractions by first rendering a Reflect/Refract map and then overlaying it on the object's diffuse color. Reflections are mixed with the diffuse color by addition for each pixel: diffuse+percentage(reflection)=finalcolor, because reflections only increase the object's diffuse color.
Anti-Aliasing and Defocusing
Normally, the renderer only shoots one ray for every reflective/refractive pixel on the screen. This may be okay, but for high-detail images, it'll make everything jaggy. To anti-alias reflections, the renderer must shoot more rays. This can also be used for defocusing. For some surfaces, closer objects will be sharper than faraway objects, which can be blurred beyond recognition. As the rays leave the object, they spread out.
So, the closer it is, the less the rays have spread out. Therefore, less blurring. The further away, the more spreading and more blurring. As you can guess, doing blurry reflections/refractions takes a lot more rendering time.
If you're not doing blurry reflections/refractions and just want to make the raytracing smoother, then you can just use SuperSampling, available in the Rendertab of the Render dialog window.
Hopefully, after reading through this, you have a better idea of how raytracing works, and how to use it in newer and better ways.
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