how can we plot this function as 3d with matlab?

how can we plot this fucntion as 3d with matlab? I tried surf and ezplot to plot function. but they didnt work. thanks for help.

Answer 1

[Matt Tearle]

Aww, cute.

The reason you can't use surf or ezplot is that these are not designed for this kind of equation. To use surf you need to have a surface defined as z = f(x,y). You have g(x,y,z) = 0. If you could rearrange that into z = f(x,y), you could use surf, but the equation you have doesn't really allow that.

So... instead, go back to the definition of the surface as g(x,y,z) = 0. Think of this as a particular isosurface of the function g(x,y,z) (with isosurface value of 0).

To make a surface in MATLAB from that kind of setup, you need (surprise, surprise) isosurface. Look in the documentation at the examples for isosurface. They will guide you through the visualization.

The one thing you need that isn't in the isosurface doc is to create the data to plot. (The examples do [x,y,z,v] = flow; which creates the data from a canned routine for a specific example.) So:

1. You need to create 3 3-D arrays for x, y, and z, in the given range -- hint: linspace and meshgrid.
2. Then you need to evaluate the function g(x,y,z) at each of those x, y, z locations: V = (X.^2+9*Y.^2/4+Z.^2-1).^3 - X.^2.*Z.^3 (etc)

Now you have the data, you can plot, using the examples in the isosurface documentation.

You'll "love" the result. Haha. I'm so funny.

[murat can]

i did something but i didnt make it 3d array. it gave an error V must be a 3D array.

[Sean de Wolski]

Here is some help with (1)

[X,Y,Z] = meshgrid(linspace(-3,3,25));

[Azzi Abdelmalek]

the question asked was to plot X.^2+9*Y.^2/4+Z.^2-1).^3 - X.^2.*Z.^3=0 which don't correspond to the answer. you must solve the equation before ploting

[murat can]

OH MY GOODNESS =) its really cool thing. friend of mine said me solve it ^^ its pretty cool =) its an heart

http://s12.postimage.org/v5ypu04sd/HEARTH.jpg

[Sean de Wolski]

@Azzi - no you don't!

isosurface is essentially a three dimensional contour plot. When you set the threshold value to zero, it will draw the isosurface at that interface thus automagically solving the equation for you :)

[Azzi Abdelmalek]

Ok Sean, I widhdraw

Answer 2

[Azzi Abdelmalek]

sol=[];
for k=-3:0.1:3
  for m=-3:0.1:3
      x=[k m];
      a=x(1)^2+x(2)^2*9/4-1;
      v=[1 0  3*a 0 + 3*a^2 0 a^3 ]; 
      z=roots(v);
      z=z(imag(z)==0);
      n=length(z);
      if n>0
          xyz=[repmat(x(1:2),n,1) z];
          sol=[sol;xyz];
      end
  end
end
plot3(sol(:,1),sol(:,2),sol(:,3))

[murat can]

it works wrong i think.

Answer 3

[murat can]

i did something again but it didnt work again... =)

clear all
close all
syms X Y Z V
[X,Y,Z] = meshgrid(linspace(-3,3,25));
V = (X.^2+9*Y.^2/4+Z.^2-1).^3 - X.^2.*Z.^3
fv=isosurface(X,Y,Z,V,0)
fv = isosurface(V,0)
fvc = isosurface(V,'red')
p = patch(isosurface(X,Y,Z,V,-0))
isonormals(X,Y,Z,V,p)
set(p,'FaceColor','red','EdgeColor','none');
view(3); 
axis tight
camlight

[murat can]

i think axis is wrong. but i dont know much think about 3d axises.

[Sean de Wolski]

You don't need to define X,Y,Z,V as syms since they won't be syms but rather double arrays....

Removing that line, it works for me.

[murat can]

its excess. i will delete it. i tought i was need it for equation.

i tried another way. i forgot to delete it. thx for remember.

Answer 4

[murat can]

for axises i used daspect([1 1 1]) and it worked fbetter i think ^^ thank you all for help.

clear all
close all
syms X Y Z V
[X,Y,Z] = meshgrid(linspace(-3,3,25));
V = (X.^2+9*Y.^2/4+Z.^2-1).^3 - X.^2.*Z.^3
fv=isosurface(X,Y,Z,V,0)
fv = isosurface(V,0)
fvc = isosurface(V,'red')
p = patch(isosurface(X,Y,Z,V,-0))
isonormals(X,Y,Z,V,p)
set(p,'FaceColor','red','EdgeColor','none');
daspect([1 1 1])
view(3); 
axis tight
camlight

and the result is good. to see results: http://postimage.org/image/6altq3zqf/