The homogeneous model is well suited to applications in which incidences of offset flat subspaces are central, but less so when metric properties are also important. In this, it plays a role similar to Grassmann-Cayley algebra. This chapter gives details on its direct use in applications.

In the first part, we discuss the coordinate representations of the homogeneous elements. This naturally embeds the powerful Plücker coordinates for line computations, which are seen to be are a natural extension of homogeneous point coordinates (using the outer product). We show how you can master them and derive new application formulas simply. Those coordinates for lines, as well as points and planes, permit compact ...

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