Polygonal Equations

Have you ever wondered how to encode a polygon as a single equation? Clearly, such an equation should be nonlinear, but it should not contain terms which are products of variables (x and y). Once we introduce terms involving products, we get curvature. It turns out that we can use an approach closely linked with systems of linear inequalities. I used Desmos to produce all the plots below. If you have ever played around with plotting inequalities, you know that it is easy to plot a polygonal shape by satisfying multiple inequalities simultaneously. To see how this works, note that if we plot a single linear inequality, we divide the plane in two parts. The solution set of the inequality will be all points to one side of this line. Such a region is referred to as a half-plane. For example, in Figure 1 we plot the linear inequality <a href="https://medium.com/@brunsondougm/polygonal-equations-51a7c3fab1ec">Read More</a>