Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression

Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to recognise the actual surface shape from a set of measured data points. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. A new method is introduced to fit quadric surfaces by implicit functions in the sense of orthogonal distance regression. The fitting accuracy and stability can be greatly improved. This method has no requirement on the surface type or initial position of the data. Finally some numerical examples are given to compare the proposed algorithm with the linear least squares method and the specific geometric modelling and to demonstrate its superiority on accuracy, stability and wide applicability.