Neural-network-based curve fitting using totally positive rational bases

This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation

Global-Support Rational Curve Method for Data Approximation with Bat Algorithm

Part 3: Data Representation and AnalysisInternational audienceThe problem of obtaining an approximating curve from a given set of data points appears recurrently in several applied and industrial domains, such as CAD/CAM, computer graphics and animation, medicine, and many others. Although polynomial blending functions are usually applied to tackle this issue, some shapes cannot yet be adequately approximated by using the polynomial scheme. In this paper we address this limitation by applying rational global-support blending functions, particularly rational Bézier curves. Our method is based on a nature-inspired meta-heuristic called bat algorithm, which has been recently introduced to solve difficult optimization problems. To check the performance of our approach, it has been applied to some illustrative examples of 2D and 3D curves. Our results show that the method performs very well, being able to yield a satisfactory approximating curve with a high degree of accuracy