Using A-patches to Tessellate Algebraic Curves and Surfaces

An implicit function is defined to be the zero set of a scalar function F over space. Further, for points not on the implicit function, the sign of this scalar function tells us whether the point lies inside or outside the implicit function. The choice of whether positive values are inside or outside is arbitrary, since we may multiply an implicit function by −1 and change the notion of inside and outside. An algebraic function is an implicit function that is a polynomial. The following example illustrates these ideas. Consider F (P ) = x + y − 1.