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Constructive Solid Geometry (CSG):

The methods of constructive solid geometry (CSG) gives us a way to describe complicated solid shapes as combinations of simpler solid shapes. This makes it an important tool for computer graphics and geometric modelling. CSG uses Boolean operators to construct a procedural model of a complex solid. This model, or rather the data describing the model, is stored in the mathematical form of a binary tree, where the leaf nodes are simple shapes, or primitives, sized and positioned in space, and each branch node is a Boolean operatör: union, difference, or intersection.

(Mortenson, M., E., Mathematics for Computer Graphics Applications, 2nd ed.)

Geometrical Tolerances:

Geometric tolerances apply variably constraints to a particular feature having a geometrical form.

A GT can be applied to any feature that can be defined by a theoretically exact shape, e. g. A plane, cylinder, cone, square, circle, sphere or a hexagon.

GTs are needed because in the real world, it is impossible to produce an exact theoretical form.

GTs define the geometric deviation permitted such that the part can meet the requirements of correct functioning and fit.

Note it is always assumed that if GT sor indeed tolerances in general are not given on a drawing, it is with the assumption that, regardless of the actual situation, a part will normally fit and functional satisfactorily.

(Griffiths, B., Engineering Drawing for Manufacture, 2003)

Sweep Representation:

A set of points moving in space may sweep a one-, two-, or three- dimensional object, which can be

represented by the moving set plus the trajectory. Sweep representations for modeling solids are easy to

understand and execute yet offer a fertile field for development. Basically there are two kinds of sweep

representation: translational sweeping and rotational sweeping.

(Xue, Q., World Scientific Series in Robotic and Automated Systems - Vol. 3, Intelligent Robotic Planning Systems, p. 13)