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Spherical Coordinates

A quadruple of real numbers (*x*:*y*:*z*:*t*), with *t*0, is a set of
**homogeneous coordinates** for the point *P* with cartesian
coordinates (*x*/*t*, *y*/*t*, *z*/*t*). Thus the same point has many sets of
homogeneous coordinates: (*x*:*y*:*z*:*t*) and (*x'*:*y'*:*z'*:*t'*) represent the
same point if and only if there is some real number
such that
*x'*=*x*, *y'*=*y*, *z'*=*z*, *t'*=*t*. If *P*
has cartesian coordinates (*x*,*y*,*z*), one set of homogeneous
coordinates for *P* is (*x*,*y*,*z*,1).

See Section 1.4 for more information on the relationship between cartesian and homogeneous coordinates. See Section 10.2 for formulas of space transformations in homogeneous coordinates.

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.