Applications of surface normal measurements to coordinate metrology

Methods for applying the measurement of surface normals to coordinate metrology are developed. The addition of surface normal measuring capabilities to probing Coordinate Measuring Machines (CMMs) can reduce invalid measurements, increase measurement throughput and, reduce the overall uncertainty of the measurement process. A model for cubic spline interpolation between data points is used as the basis for an adaptive sampling algorithm for measurement of 2D profiles. The uncertainty of the interpolant contributed by variation in the measured data and form errors on the workpiece is characterized. Adaptive sampling for complete surfaces is demonstrated with a triangular Bezier surface patch as the interpolant. An implementation of 2D adaptive sampling is demonstrated on a CMM using smooth and rough reference surfaces. A method for least squares fitting of basic geometric shapes with measured surface normal and position data is shown. Criteria for using surface normal measurements to eliminate invalid measurement points are developed for both dense and sparse sample densities.