How to create a 3-D Cardioid shape in MatLab? (a cylinder with a cardioid base)
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Currently, I am able to plot a 2-D cardioid in MatLab using this code:
% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
plot(r.*cos(theta) *1.25, (r.*sin(theta) *1.25))
axis equal
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-3.5 3.5])
ylim([-3.5 3.5])
zlim([-3.5 3.5])
However, I would like to plot a 3-D cardioid, such that there is the z-dimension included.
(At the moment, the cardioid is only in 2-D, as it solely includes the x-dimension and y-dimension)
Here is the idea I want to visualize in MatLab please:
(The idea is a 3D cylinder with a cardioid-shaped base)
Is anyone able to provide some advice or insight into how to create this please? Thank you for your help.
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Accepted Answer
DGM
on 26 Jun 2023
Edited: DGM
on 26 Jun 2023
Here's one way.
% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
x = r.*cos(theta)*1.25;
y = r.*sin(theta)*1.25;
% expand everything
zlevels = 10;
zrange = [-1 1];
X = repmat(x,[zlevels 1]);
Y = repmat(y,[zlevels 1]);
Z = linspace(zrange(1),zrange(2),zlevels);
Z = repmat(Z.',[1 numel(x)]);
% plot using surf()
hs = surf(X,Y,Z);
hs.FaceColor = [0.65 0.6 1];
hl = lightangle(gca,45,45);
material(hs,[0.5 1 1])
set(gca,'projection','perspective')
view([-46 38])
axis equal
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-2 2])
ylim([-2.5 1.5])
zlim([-2 2])
You'll probably want to play with the colormapping and lighting as you see fit.
4 Comments
DGM
on 26 Jun 2023
I was just trying to approximate the figure setup that would have been used to create the sample image. All of the additional fluff (lighting, color, projection) can simply be omitted.
% 2-Dimensional Cardioid
theta = linspace(0, 2*pi);
r = 1-(0.7*sin(theta));
x = r.*cos(theta)*1.25;
y = r.*sin(theta)*1.25;
% expand everything
zlevels = 10;
zrange = [-1 1];
X = repmat(x,[zlevels 1]);
Y = repmat(y,[zlevels 1]);
Z = linspace(zrange(1),zrange(2),zlevels);
Z = repmat(Z.',[1 numel(x)]);
% plot using surf()
surf(X,Y,Z);
axis equal
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
xlim([-2 2])
ylim([-2.5 1.5])
zlim([-2 2])
More Answers (1)
Dyuman Joshi
on 26 Jun 2023
Edited: Dyuman Joshi
on 26 Jun 2023
% 2-Dimensional Cardioid
a = 1.25;
%Equation referenced from Wikipedia, not the same as used above
eqn = @(x,y,z) (x.^2+y.^2).^2 + 4.*a.*x.*(x.^2+y.^2) - 4.*a^2.*y.^2;
%The intervals defined are [xmin xmax ymin ymax zmin zmax]
fimplicit3(eqn, [-2*pi 2*pi -5 5 -2 2])
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
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