**mwg@mouton.UUCP** (06/25/84)

++ Since three points determine a parabola, just plug them into y = Ax^2 + Bx + C and solve the system. If you are in more than two dimensions, you can probably do a transformation somehow into the plane determined by the three points and solve; then translate back. -Mark

**piety@hplabs.UUCP (Bob Piety)** (06/26/84)

3 points can lie on a parabola, circle, cubic, or other shape. There is not enough information in just 3 points unless you know the nature of the curve. Bob

**gwyn@brl-vgr.ARPA** (06/28/84)

Usually the correct approach is to take the parameterized curve that is expected by theory to pass through the data and do a weighted (by inverse error squared) least squares fit (i.e. determine the values of the parameters that minimizes the weighted sum of the squares of the deviations of the known data points from the curve). One method that works well is the Marquardt gradient-expansion technique described in Bevington's "Data Reduction and Error Analysis for the Physical Sciences". Of course this assumes that you HAVE a theory...