MATLAB: Plotting an ellipsoild with an equation that is not set equal to one variable

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I thought this would be simple and straight forward but i really don't have a clue here. I need to plot an Ellipsoid with the eqution:

1 = (x^2)/4 + (y^2)/9 + (z^2)

Thanks, any help would be great. will "mupad" be helpful here?

Best Answer

Did you look up ellipsoid in the help? When or if you do, you'll find your answer with very very slight modifications to their demo:

[x, y, z] = ellipsoid(0,0,0, 2,3,1, 30);
surfl(x, y, z)
colormap copper
axis equal

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MATLAB: How can we plot this function as 3d with matlab

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:

You need to create 3 3-D arrays for x, y, and z, in the given range -- hint: linspace and meshgrid.
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.

MATLAB: Question about using Mapping Toolbox to project ETOPO1 data from structure array

Hi Nate,

Given how long ago you asked I expect you have already got your answer. I had a similar issue with irregular lat with the Smith and Sandwell bathymetry (satbath function).

I wanted to make a large scale plot which I think that you do as well, so to get around it I just defined a new lat axis - and then re-sampled data onto that grid. My argument being at large scale the problems caused by the interpolation won't even be visible. Once on a regular grid you can just define a reference matrix and plot it anyway you like.

So what I did for my plot was this.

%%First get bathymetry
[lat,lon,elevations] = satbath(3,[-66 -48],[-71 -24]);
lon = lon - 360;
% so re-sample onto a regular grid
num_X = 350.0;
num_Y = 470.0;
change_lat = lat(:,1);
dlat = (max(change_lat) - min(change_lat))/num_Y;
lat_grid_c1  = fliplr(min(change_lat):dlat:max(change_lat))';
lat_grid_new = repmat(lat_grid_c1, 1, num_X+1);
change_lon = lon(1,:);
dlon = (max(change_lon) - min(change_lon))/num_X;
lon_grid_r1  = min(change_lon):dlon:max(change_lon);
lon_grid_new = repmat(lon_grid_r1, num_Y+1, 1);
% ZI = interp2(X,Y,Z,XI,YI)
elevations_I = interp2(lon,lat,elevations,lon_grid_new, lat_grid_new);

Then I made my reference matrix with this code

% Define a reference vector
% makerefmat Construct affine spatial-referencing matrix  Syntax
% 
% R = makerefmat(x11, y11, dx, dy)
% R = makerefmat(lon11, lat11, dlon, dlat)
sat_refvec = makerefmat(lon_grid_new(1,1), lat_grid_new(1,1), (lon_grid_new(1,2) ...
    - lon_grid_new(1,1)), (lat_grid_new(2,1) - lat_grid_new(1,1)));
clear change_lat dlat elevations  lat num_X         
clear change_lon dlon lat_grid_c1 lon lon_grid_r1   num_Y

Then you can plot it as you will.

%%define bathy colourmap and plot it
bathycolourmap = [  0.02745098  0.478431373 1 ; ...
                    0.176470588 0.556862745 1  ; ...
                    0.301960784 0.576470588 0.956862745 ; ...
                    0.392156863 0.670588235 0.996078431 ; ...
                    0.529411765 0.807843137 0.992156863 ; ...
                    0.529411765 0.807843137 0.992156863 ; ...
                    0.701960784 0.898039216 0.988235294 ; ...
                    0.776470588 0.941176471 0.988235294 ; ...
                    0.968627451 0.984313725 1 ; ...
                    0.980392157 0.901960784 0.756862745 ];
figure
        axesm('MapProjection','mercator', 'MapLatLimit',[-64 -50],  ...
            'MapLonLimit',[-70 -25]);
        geoshow(elevations_I,sat_refvec, 'DisplayType','surface')
        colormap(bathycolourmap)
        getm(gca);
        setm(gca,'LabelUnits','degrees')
        setm(gca,'grid','on','MLineLocation',10,'PLineLocation',10);
        setm(gca,'MeridianLabel','on','ParallelLabel','on','MLabelParallel','south');
        setm(gca,'MLabelLocation',10.0,'PLabelLocation',10);
        set(gcf, 'Color', 'w');
        tightmap
        framem

And so you can see my area of interest! (I have to do something silly to plot the coastlines – which is why I am looking here).

It sounds like you may have to do a little bit with re-defining the x axis – but good luck.

Mark

Best Answer

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MATLAB: Question about using Mapping Toolbox to project ETOPO1 data from structure array

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