The article presents the results of research on developing a mathematical model allowing to identify the planes in a measured object, based on a cloud of points located on its walls.

A basic mathematical description of surfaces is presented. An algorithm for determining the general equation of the plane on the basis of three points described in the Cartesian coordinate system has been developed. The algorithm has then been used to determine all possible planes in a given set of measured points, which were then subjected to the process of elimination and normalization. Filtered equations of the planes were grouped in order to finally determine the set of the sought-after equations.

The designed algorithms have been implemented in a C++ computer program and their effect has been verified on a sample object with 3 methods of measurement: a contact measurement, a structured-light scanner method and with photogrammetry. The calculated equations have been compared with equations developed by a referenced commercial software. The results of the comparison have proved the correctness of the tested algorithms.

The mathematical model will be used for rapid assessment of the geometrical parameters of castings and of the size of the machining allowances, as well as in the automatic settings of the casting in the machining space.

The research was supported by the National Centre for Research and Development, Poland within the ongoing project No. LIDER / 07/76 / L-3/11 / NCBR / 2012.

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