plot - Plotting Implicit Algebraic equations in MATLAB

Question

I wish to plot implicit functions in MATLAB. Like x^3 + xy + y^2 = 36 , equations which cannot be made into simple parametric form. Is there any simple method ?

Answer 1

Here are a couple of options...

Using ezplot (or fplot recommended in newer versions):

The easiest solution is to use the function ezplot:

ezplot('x.^3 + x.*y + y.^2 - 36', [-10 10 -10 10]);

Which gives you the following plot:

Using contour:

Another option is to generate a set of points where you will evaluate the function f(x,y) = x^3 + x*y + y^2 and then use the function contour to plot contour lines where f(x,y) is equal to 36:

[x, y] = meshgrid(-10:0.1:10);   % Create a mesh of x and y points
f = x.^3+x.*y+y.^2;              % Evaluate f at those points
contour(x, y, f, [36 36], 'b');  % Generate the contour plot
xlabel('x');                     % Add an x label
ylabel('y');                     % Add a y label
title('x^3 + x y + y^2 = 36');   % Add a title

The above will give you a plot nearly identical to the one generated by ezplot: