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Ray casting is not a synonym for ray tracing, but can be thought of as an abridged, and significantly faster, version of the ray tracing algorithm.
Both are image order algorithms used in computer graphics to render three dimensional scenes to two dimensional screens by following rays of light from the eye of the observer to a light source.
Ray casting does not compute the new direction a ray of light might take after intersecting a surface on its way from the eye to the source of light.
This eliminates the possibility of accurately rendering reflections, refractions, or the natural falloff of shadows ; however all of these elements can be faked to a degree, by creative use of texture maps or other methods.
The high speed of calculation made ray casting a handy rendering method in early real-time 3D video games.

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