Graphing implicit functions f(x,y)=0

摘要

A simple algorithm for producing rough sketches of implicit equations of the form f(x,y)=0 in two variables in a given region is suggested. The region is represented as a square window of pixel points centered on a screen. The method is based on the criterion that the function f(x,y) undergoes a change in sign as the graph of the equation is crossed in course of scanning the window in the horizontal or in the vertical direction. A color dot is marked at each point of the region where such a change in sign is encountered, thus exhibiting the graph in the region. This procedure does not involve the implicit function theorem and computation of the partial derivatives of f(x,y) and therefore is useful in generating shapes and structures of graphs of varieties of complex implicit functions in two variables. A corresponding program in Vax C in combination with a Digital VT340 terminal for graphic emulation is given.