Fitting conic sections to measured data in 3-space

Abstract

We consider the problem of tting given data in 3-space by rotated plane conic sections in the least squares sense. For circles this was done in [4]. For ellipses we will use some details from [2]. Regarding hyperbolas there is a problem using the two branches. However we can follow [2]. Also for parabolas considered for plane data in [1] we can extend the solution method to spatial data. In all cases the use of three rotations (instead
of formerly two ones) is discussed and suitably done. All methods will be based on the necessary conditions for a least squares solution. These algorithms are also related to those ones for tting data in 3-space by paraboloids [5] and elliptic paraboloids [6] with only two out of three possible rotations used here.