The Implicit Equation in 2D

An implicit equation of a curve is an equation in two variables x and y. Here we give some examples:

The implicit equation can be entered as in these examples. Below, one finds the graph of x*cos(y)+y*cos(x)=0:

Graph of x*cos(y)+y*cos(x)=0

In order to draw these types of graphs, the window area is divided into small triangles. It is then checked in every triangle if it contains a part of the graph. If the resulting graph is too coarse, it can be refined by increasing the accuracy. This increases the number of triangles but at the cost of computation time.

VisuMath only checks for singularities in a primitive way. Consequently, it could happen that artifacts that do not belong to the actual graph are produced when passing such a singularity. So care should be taken when using implicit functions in combination with singularities. Sometimes, it might be good to rewrite the equation in order to improve the visualization.