Abstract: Data can’t be rationally segmented and even wrong geometric elements are used in traditional data fitting. Therefore recognizing data fitting is proposed, based on the robustness theorem of generalized cross product, which states that an orthogonal matrix brings a robust product vector. To identify the geometric element of a fitted data point cloud, firstly feature parameters are extracted with its local data points, then an orthogonal matrix is constructed and the extracted feature vectors are mapped to product vectors. The mappings of feature vectors can overcome the measurement noises and magnify the variation of the feature parameters of wrong geometric elements in fitted data. Right geometric element is easily identified if the product vectors are constant in a certain data segment and the corresponding boundaries are accurately positioned. This method is feasible and efficient in experiments, and it can be widely used in the surface reconstruction of reverse engineering or used as a universal method in pattern classification.

Key words: Data fitting, Generalized cross product, Pattern recognition, Point cloud, Robustness