I think that I shall never see a model lovely as geometry

 [with apologies to Joyce Kilmer and a tip of the hat to Edna St. Vincent Millay]

Many of the computer software tools for building geometric models of real objects use Boolean operations on simple shapes to build more complex shapes.  Union (addition or sum) and intersection (common region or product) are used, but negation is usually replaced by (asymmetric) difference (x and not y) to avoid generating 'every point except those in y'.

'Symmetric difference' (exclusive or', x or y and not (x and y) )is rarely used and usually not implemented, but can be obtained as (x - y) v (y - x).

These Boolean operations are usually supplemented by 2D to 3D operations such as rotation around an axis or extrusion of a (2D) curve along a line or path.

Curves are usually represented as a sequence of straight lines, which does not appear smooth when viewed close up, or a sequence of cubic splines or Bezier curves, which appears smooth at the vertices between segments.