An approach to the application of shift-and-add algorithms on engineering and industrial processes

Different kinds of algorithms can be chosen so as to compute elementary functions. Among all of them, it is worthwhile mentioning the shift-and-add algorithms due to the fact that they have been specifically designed to be very simple and to save computer resources. In fact, almost the only operations usually involved with these methods are additions and shifts, which can be easily and efficiently performed by a digital processor. Shift-and-add algorithms allow fairly good precision with low cost iterations. The most famous algorithm belonging to this type is CORDIC. CORDIC has the capability of approximating a wide variety of functions with only the help of a slight change in their iterations. In this paper, we will analyze the requirements of some engineering and industrial problems in terms of type of operands and functions to approximate. Then, we will propose the application of shift-and-add algorithms based on CORDIC to these problems. We will make a comparison between the different methods applied in terms of the precision of the results and the number of iterations required.

Footwear bio-modelling: An industrial approach

There is a growing need within the footwear sector to customise the design of the last from which a specific footwear style is to be produced. This customisation is necessary for user comfort and health reasons, as the user needs to wear a suitable shoe. For this purpose, a relationship must be established between the user foot and the last with which the style will be made; up until now, no model has existed that integrates both elements. On the one hand, traditional customised footwear manufacturing techniques are based on purely artisanal procedures which make the process arduous and complex; on the other hand, geometric models proposed by different authors present the impossibility of implementing them in an industrial environment with limited resources for the acquisition of morphometric and structural data for the foot, apart from the fact that they do not prove to be sufficiently accurate given the non-similarity of the foot and last. In this paper, two interrelated geometric models are defined, the first, a bio-deformable foot model and the second, a deformable last model. The experiments completed show the goodness of the model, with it obtaining satisfactory results in terms of comfort, efficiency and precision, which make it viable for use in the sector.