Parts Localization Oriented Practical Method for Point Projection on Model Surfaces Based on Subdivision

ABSTRACT

In algorithm of part localization, the distances between the measured points and their projections on the model surface is evaluated as the machining allowance or machining error of the parts with free-form surfaces. Point projection of a measured point on the model surface is the key to process the localization of the measured data points to the CAD model. At present, iteration-type methods are the most popular solving strategy. However, it cannot provide full assurance that all roots have been found. This paper presents a subdivision-based method for computing point projection on the model surface. Different from the previous methods, our method is to use the position relationships of the graph of the first derivative of the squared distance function and the u-v parametric plane to eliminate the invalid surface segments. A simple formula is derived based on AMBP (arithmetic of multivariate Bernstein-form polynomial) to facilitate the use of this criterion. Compared with the iteration-type methods, one advantage of our method is that it can avoid providing any initial value for achieving the proper result and guarantee the roots for all conditions. Finally, some examples are given to demonstrate the effectiveness and robustness of the proposed method.

GRAPHICAL ABSTRACT

Keywords:

• parts localization
• point projection
• model surfaces
• subdivision

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (grant no. 51105058), China Postdoctoral Science Foundation (grant no. 2013M540221, 2014T70246) and the Fundamental Research Funds for the Central Universities (grant no. DUT14QY35).