Increasing the Fitting Precision of Implicit Polynomial Curves in 2D Modeling Through Signomial Powers

Abstract

Today, common algorithms such as spline curves and triangulation methods are used in 2-and 3-dimensional modeling of objects. However, although these methods can express objects well in terms of visuality because they treat objects as a combination of many small parts, they cannot reveal the mathematical expression of the whole object. The most prominent method of expressing objects with a single equation is the implicit polynomial (IP) curves and the 3L method used to realize the more precise effects of these curves. In this study, the 3L method was accepted as the primary method, and signomial functions using real number powers were used to increase the fitting precision in 2D modeling. The artificial bee colony (ABC) algorithm was used to determine signomial terms. Based on the root mean square error, peak signal-to-noise ratio, coefficient of determination, and structural similarity values obtained in experimental studies, modeling success can be increased. Also, due to adding the initial power expression of IP as the population element for ABC, the sensitivity of the current IP model is increased rather than remodeled.

Keywords

• Signomial functions
• implicit polynomial curves
• 3L method
• artificial bee colony
• modeling