The sweep S_w of a solid

Solid geometry

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. It was developed following the development of plane geometry...

 S is defined as the solid created when a motion M is applied to a given solid. The solid S should be considered to be a set of points in the Euclid

Euclid

Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

ean space R3. Then the solid S_w which is generated by sweeping S over M will contain all the points over which the points of S have moved during the motion M.