Clifford algebra of points, lines and planes

The Clifford algebra for the group of rigid body motions is described, that is points, lines and planes are identified as homogeneous elements of the algebra. In each case the action of the group of rigid motions an the linear elements is found. The relationships between these linear elements are found in terms of operations in the algebra. That is, incidence relations, conditions for a point to lie on a line for example are found. Distance relations, like the distance between a point and a plane are found. Also the meet and join of linear elements, for example, the line determined by two plane and the plane defined by a line an a point, are found. Finally three examples of the use of the algebra are given: a computer graphics problem on the visibility of the apparent crossing of a pair of lines, an assembly problem concerning a double peg-in-hole assembly, and a problem from computer vision on finding the epipolar line in a stereo vision system.