On Bezier Curves and analemmae

[Anselmo P�rez Serrada]

We all know that we need just two points to draw a stright line (like the solar time ones), five points to draw an hyperbola (like the datelines) but...       Which is the minimum number of points (ie., of dates) we need to draw an analemma (in a flat dial) within a worst-case precision of, say, 1 minute of time?   I am trying to solve this question using Bezier curves to approximate the analemmae and brute-force to find the best solution, but it is not so easy to find a general one (for any position of the dial)...   Any suggestion?  Or maybe my question is useless because the classical twelve zodiacal dates make a good balance 'generality vs. precision'?   [ 41.63 N   4.73 W]