A 3D Voronoi diagram based form error estimation method for fast and accurate inspection of free-form surfaces

Abstract

Coordinate Measuring Machines (CMM) are widely used in form inspection of free-form surfaces. Generally, the form error at each measured point is estimated using the widely known and accurate point-inversion method. This method has relatively high time complexity and cannot be preferred for fast inspection. Hence in this work, an alternative two-stage methodology based on the concept of the Voronoi diagram is proposed. In the first stage, the poles data is extracted from the Voronoi diagram of the discretized surface. In the second stage, the form-error-estimate algorithm executing in O(m log n) time estimates the errors using the poles data and the discretized surface. Numerical and experimental implementations are executed using NURBS surfaces. The proposed method’s accuracy is on par with the point-inversion method and is 94.97% faster than the latter. Hence this method can be used for fast and accurate CMM and CNC based (in-situ) free-form surface inspection.