Calculation of the Unit Normal Vector Using the Cross-Curve Moving Mask for Measurement Data Obtained from a Coordinate Measuring Machine

This study presents a cross-curve moving mask method to calculate the unit normal vector based on 5 or 9 data points of a freeform surface measurement. The middle point and 4 or 8 neighboring points can be constructed as two crossed curves - longitude and latitude. The unit normal vector at the middle point can be determined by calculating the cross product of two tangent vectors along these 2 crossed curves. Different curve fitting methods passing 5 or 9 data points, such as Lagrange, parametric polynomial, Bezier and B-spline methodologies, are investigated. Two kinds of surfaces, namely, a sphere surface and a shoe-shaped geometric surface are selected for evaluating the accuracy of the calculated unit normal vectors