Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller

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    CSG - Constructive Solid Geometry -

Boolean Algebra with Solids

    Here I want to explain some of the fundamental principals of constructing new and more complex solids by combining primitive shapes. For this we use the technique called 'csg', which allows roughtly speaking the same operations with solids which are custom in boolean algebra - and a little bit more than that. In this case a solid is considered as a special set of points in the three dimensional space. On this set of points we can work with boolean set operations.
    csg objects: Such operations may be used with all solids and all shapes which have a clear defined "inside" and "outside". The most important of these are: "box", "sphere", "cylinder", "cone", "torus", "prism". A "plane" must be considered specially: the normal vector points to the "outside" of the plane while any points on the other side of this "plane" are defined as "inside". Also mesh objects (mesh, mesh2) can be used with csg if they have an "inside_vector".
All csg operations may be combined freely.
The csg operations are in detail:

union of sets	difference	intersection	complement	opening by cuting off
union{...} or merge{...}	difference{...}	intersection{...}	inverse	clipped_by{...}