Matching Minimum Strain Energy Curves to B-Spline Curves for Thick Layer Manufacturing

One of the key issues of thick layer manufacturing is matching the shape of the flexible cutting blade to the local surface curvature of the model to be created. In this paper we explore a method to find the best matching minimum strain energy (MSE) curve for a given B-spline curve. For this purpose we developed software to a) generate a dataset containing MSE curves for a range of settings of the cutting tool and b) find the best matching curve from this MSE dataset to the given target curve. Both the MSE and the target curves are represented as point sets, the target curves having a considerable higher point density than the curves in the MSE dataset. The best matching MSE curve is defined as the curve with the minimum directed Hausdorff distance to the target curve. It is found that despite the relative low density of the dataset, for several practical domains of target curve shape, a satisfying match can be found. Numerical results concerning the matching accuracy are presented.