Constructive solid geometry

Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex objects by combining a few primitive ones. In 3D computer graphics and CAD, CSG is often used in procedural modeling. CSG can also be performed on polygonal meshes, and may or may not be procedural and/or parametric. Contrast CSG with polygon mesh modeling and box modeling. The simplest solid objects used for the representation are called geometric primitives. Typically they are the objects of simple shape: cuboids, cylinders, prisms, pyramids, spheres, cones. The set of allowable primitives is limited by each software package. Some software packages allow CSG on curved objects while other packages do not. An object is constructed from primitives by means of allowable operations, which are typically Boolean operations on sets: union, intersection and difference, as well as geometric transformations of those sets. A primitive can typically be described by a procedure which accepts some number of parameters; for example, a sphere may be described by the coordinates of its center point, along with a radius value. These primitives can be combined into compound objects using operations like these: File:Boolean union.PNG|'''Union'''Merger of two objects into one File:Boolean difference.PNG|'''Difference'''Subtraction of one object from another File:Boolean intersect.PNG|'''Intersection'''Portion common to both objects Combining these elementary operations, it is possible to build up objects with high complexity starting from simple ones. Rendering of constructive solid geometry is particularly simple when ray tracing. Ray tracers intersect a ray with both primitives that are being operated on, apply the operator to the intersection intervals along the 1D ray, and then take the point closest to the camera along the ray as being the result.