A planar algebraic curve is the solution set of a polynomial equation
F(x,y) = 0
where x and y are the unknowns. Planar examples are straight lines and cone sections.
The degree of the polynomial F is called the order of the algebraic curve. The order of a planar algebraic curve is the maximal number of intersection points with a straight line. If F is reducible into two factors F = GH then the algebraic curve F = 0 is the union of the two curves G = 0 and H = 0 and is called reducible.
As a guide, polygons should be connected, no degenerate edges, no duplicate vertices.