How do I plot a toroid in MATLAB?

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MathWorks Support Team
MathWorks Support Team am 27 Jun. 2009
Beantwortet: DGM am 8 Jan. 2022
I would like to plot a toroid in MATLAB but MATLAB does not have a built in function to do this.

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MathWorks Support Team
MathWorks Support Team am 27 Jun. 2009
You will need to formulate the x, y, and z-coordinate matrices manually and then plot them using the SURF function.
The SURF and MESH functions accept only one set of x, y, and z-coordinates, but in a toroid, (x,y) ordered pairs can have two corresponding z-coordinates. Therefore, to plot a toroid in MATLAB, you will need to plot the top and bottom halves as two separate surfaces on the same plot. For example:
%%Create R and THETA data
theta = 0:pi/10:2*pi;
r = 2*pi:pi/20:3*pi;
[R,T] = meshgrid(r,theta);
%%Create top and bottom halves
Z_top = 2*sin(R);
Z_bottom = -2*sin(R);
%%Convert to Cartesian coordinates and plot
[X,Y,Z] = pol2cart(T,R,Z_top);
hold on;
[X,Y,Z] = pol2cart(T,R,Z_bottom);
axis equal
shading interp
  3 Kommentare
Alex Pedcenko
Alex Pedcenko am 27 Sep. 2019
you're right

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Alex Pedcenko
Alex Pedcenko am 5 Nov. 2017
Bearbeitet: Alex Pedcenko am 27 Sep. 2019
R=5; % outer radius of torus
r=2; % inner tube radius
th=linspace(0,2*pi,36); % e.g. 36 partitions along perimeter of the tube
phi=linspace(0,2*pi,18); % e.g. 18 partitions along azimuth of torus
% we convert our vectors phi and th to [n x n] matrices with meshgrid command:
% now we generate n x n matrices for x,y,z according to eqn of torus
surf(x,y,z); % plot surface
daspect([1 1 1]) % preserves the shape of torus
colormap('jet') % change color appearance
  6 Kommentare
Stephen23 am 5 Jul. 2020

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DGM am 8 Jan. 2022
MATLAB may not have a built-in function, but that doesn't mean there aren't any functions out there that can conveniently do the work.
I'm sure this isn't the only thing on the File Exchange, but it's the one I use. Syntax is similar to sphere() or ellipsoid(), returning three matrices which can be fed to surf() or mesh(). The input arguments are the center location, radii, order, and number of points.
center = [0 0 0];
radius = [1 1 1 3];
order = 2;
npoints = 100;
[x y z] = supertoroid(center,radius,order,npoints);
shading flat
axis equal
As axis orders are independent and user-defined, the profile and sections do not have to be circular, but can be any superellipse:
radius = [1 1 2 3];
order = [5 3];
radius = [1 1 1 3];
order = [0.8 4];
Also included is a generalized superellipsoid tool.


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