Reply by the author to M. Ivan

I thank M. Ivan for the suggestion to substitute an arctangent term and another term for the arccosine term in equation (3). Without verifying the mathematics, I assume that this substitution would permit faster arctangent addition for clusters of four terms, a mathematical operation that I discussed in the section entitled “Supplementary Notes.” Okabe (1979, p. 739) and M. Ivan have questioned my use of the theorem from analytic geometry, which calculates the angle between intersecting lines with given slopes.