Axioms and Hulls - Donald E. Knuth

One way to advance the science of computational geometry isto make a
comprehensive study of fundamental operations thatare used in many
different algorithms. This monographattempts such an investigation in the
case of two basicpredicates: the counterclockwise relation pqr, which
statesthat the circle through points (p, q, r) is
traversedcounterclockwise when we encounter the points in cyclicorder p, q, r, p,...; and the incircle relation pqrs, whichstates that s lies
inside that circle if pqr is true, oroutside that circle if pqr is false.
The author, DonaldKnuth, is one of the greatest computer scientists of
ourtime. A few years ago, he and some of his students werelooking at amap that pinpointed the locations of about 100cities. They asked, "Which ofthese cities are neighbors ofeach other?" They knew intuitively that some
pairs of citieswere neighbors and some were not; they wanted to find
aformal mathematical characterization that would match theirintuition.This monograph is the result.