Development and application of α-hull and Voronoi diagrams in the assessment of roundness error

Abstract

Computational geometry has been used to select effective data points from the measured data points for evaluating the roundness error to improve the computational complexity. However, for precision parts most of the measured points are on the vertices of the convex hull; it cannot have any effect on improving the computational complexity with the Voronoi diagrams. In this paper the roundness error is evaluated with α-hull and the Voronoi diagram instead of convex hull. An approach for constructing α-hull with the minimum radius separation is presented to determine the vertices of the Voronoi diagram. The experimental results showed that the roundness error of the minimum zone circle could be solved efficiently with α-hull and the Voronoi diagram.