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

In case you want to plot an implicit surface, for example a Horned cube, you can do something like the following.

The idea is to calculate all values of the function (even if they don't equal to zero) and then create an isosurface that will define your equality. In this example the implicit function equals to zero.

fun=@(x,y,z)(1-x.^8-3.*y.^8-2.*z.^8+5.*x.^4.*z.^2.*y.^2+3.*y.^4.*x.^2.*z.^2) ;

[X,Y,Z]=meshgrid(-2:0.1:2,-2:0.1:2,-2:0.1:2);

val=fun(X,Y,Z);

fv=isosurface(X,Y,Z,val,0);

p = patch(fv);
isonormals(X,Y,Z,val,p)
set(p,'FaceColor' , 'red');
set(p,'EdgeColor' , 'none');
daspect([1,1,1])
view(3); axis tight
camlight 
lighting phong
axis off

Additionally there is a Matlab File Exchange submission called ezimplot3D that seems to do the job also, as @knedlsepp suggests.