Section 13.2 Plotting Implicit Functions
The
implicitplot() command can be used to plot implicit functions and requires that the plots package is loaded first. Packages are loaded using the with() command and it is typically a good idea to load any necessary packages at the top of your worksheet. Loading a package only needs to be done once per Maple worksheet, but needs to be run each time you open a new or previously closed document.
Unlike the normal
plot() command, each curve that is being plotted must be in the form of an equation of two variables, including the \(=\) sign. Additionally, you must specify an interval for both variables.
Below are the graphs of the two implicit curves defined in Implicit Functions.
> with(plots):
> E := y^2 = x^3 - 2*x + 1;
\begin{equation*}
\displaystyle E\, := \,{y}^{2}={x}^{3}-2\,x+1
\end{equation*}
> implicitplot(E, x=-5..5, y=-5..5);
Most of the implicit functions used in this lab manual will produce smooth curves when plotted. However, if your plot appears to have jagged edges as shown in Figure 13.1, then you may wish to set the optional parameter
numpoints=30000. This increases the number of points plotted to make a smoother graph. The higher that numpoints is set to, the smoother the graph may be. Be careful not to set too high of a number to avoid Maple freezing.
implicitplot() output where numpoints is set too low.> L := x^2 + (y - surd(x^2,3))^2 = 1;
\begin{equation*}
\displaystyle L\, := \,{x}^{2}+ \left( y-\sqrt [3]{{x}^{2}} \right) ^{2}=1
\end{equation*}
> implicitplot(L, x=-1.2..1.2, y=-1.2..1.8,
coloring = ["red","blue"], filledregions=true);
