Using the implicit polynomial curves and 3L method for simple animation of the two dimensional shapes

Today, for two or three dimensional modelling of objects, common algorithms such as spline curves and triangulation methods are being used. However, while these methods are able to well express the objects visually, since they approach the objects as a composition of a large number of small pieces, they are not able to cognisably put forth the mathematical expression of the object as a whole. The most notable method in the literature, in order to express the objects with a single equation is implicit algebraic curves, and 3L method as a way to realize the more sensitive effects of these curves. In this study, coefficients of 2 dimensional images which are modelled using 3L method are changed in order to carry out a small animation in this process. Experimental study results show that the variation of the coefficients, change the final results of the model and demonstrated the feasibility of this process for animation.