Curve and surface fitting by implicit polynomials: Optimum degree finding and heuristic refinement

Finding an implicit polynomial that fits a set of observations X is the goal of many researches in recent years. However, most existing algorithms assume the knowledge of the degree of the implicit polynomial that best represents the points. This paper presents two main contributions. First, a new distance measure between X and the implicit polynomial is defined. Second, this distance is used to define an algorithm able to find the degree of the polynomial needed for the representation of the data set. The proposed algorithm is based on the idea of gradually increase the degree, while there is an improvement in the smoothness of the solutions. The experiments confirm the validity of the approach for the selected 2D and 3D datasets. © 2017 Elsevier Ltd. All rights reserved.