Real-time tensor polynomial approximation of crosshatch measured geometric surface data

This paper addresses the issue of methods for the approximation of crosshatch measured data by a tensor polynomial model. Such measurements are found in modern manufacturing processes such as RTM for hybrid composite materials. A new algebraic approach to the approximation yields a Sylvester equation which must be solved to obtain the coefficients for the tensor. All derivations for the method are provided. The solution has a computational complexity of O (n³), as opposed to O(n⁶) for past solutions of the same problem. The method has been applied to measurement data from a dedicated device used to measure prototype samples in a production process. The fit surface models are then contoured and analysed using Elliptical Fourier Descriptors to yield qualitative evaluation of deformation.