Plotting 3D by rotate 2D plot around y-axis

Illustration
Tuan - 2023-03-30T11:16:53+00:00
Question: Plotting 3D by rotate 2D plot around y-axis

I have a question to draw a 3D cup of coffe (no need to draw a handle). I think to be easy we need to draw 2 parabol ( inner and outter ) , the upper bound and bottom bound, then rotate that 2D plot around y-axis, but I dont have any idea and knowledge to do that, is there another way ? Can anyone help me with this, many thanks    

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    • Expert Answer

    Profile picture of Prashant Kumar Prashant Kumar answered . 2025-11-20

    Probably the easiest way is to define a cylinder and a shape vector —

     

    yv = [linspace(0.3, 1, 50)];
ys1 = yv.*exp(-1.75*yv)*5;
ys2 = (1-exp(-25*(yv-0.3)))*0.7;

figure
plot(ys1, yv)
hold on
plot(ys2, yv)
hold off
grid
% xlim([0 1.5])
axis ('equal')

[X1,Y1,Z1] = cylinder(ys1,50);
[X2,Y2,Z2] = cylinder(ys2,50);

figure
surf(X1,Y1,Z1, 'EdgeColor','interp', 'FaceAlpha',0.5)                                               % Outer Surface
hold on
surf(X2,Y2,Z2, 'EdgeColor','interp')                                                                % Inner Survface
patch([X1(end,:) X2(end,:)], [Y1(end,:) Y2(end,:)], [Z1(end,:) Z2(end,:)], 'r', 'EdgeColor','r')    % Top Rim
patch([X1(1,:) X2(1,:)], [Y1(1,:) Y2(1,:)], [Z1(1,:) Z2(1,:)], 'b', 'EdgeColor','b')                % Lower Surface

hold off
colormap(turbo)

    plotting-3d-by-rotate-2d-plot

     

    [X1,Y1,Z1] = cylinder(ys1,50);
[X2,Y2,Z2] = cylinder(ys2,50);
figure
surf(X1,Y1,Z1, 'EdgeColor','interp', 'FaceAlpha',0.5)                                               % Outer Surface
hold on
surf(X2,Y2,Z2, 'EdgeColor','interp')                                                                % Inner Survface
patch([X1(end,:) X2(end,:)], [Y1(end,:) Y2(end,:)], [Z1(end,:) Z2(end,:)], 'r', 'EdgeColor','r')    % Top Rim
patch([X1(1,:) X2(1,:)], [Y1(1,:) Y2(1,:)], [Z1(1,:) Z2(1,:)], 'b', 'EdgeColor','b')                % Lower Surface
hold off
colormap(turbo)
    plotting-3d-by-rotate-2d-plot
     
     
     
     
    This demonstrates the construction approach, and setting the outer ‘FaceAlphs’ value to plotting-3d-by-rotate-2d-plot shows the internal structure as well.
     
    Experiment with the ‘ys1’ and ‘ys2’ shape vectors to get the result you want. To get the inner and outer thicknesses, it will likely be necessary to use two cyllinder objects with different shapes, and the hold function to plot both of them on the same axes. The patch call creating the top rim will autoomatically adapt to whatever the inner and outer contour functions are. Another patch call can provide a solid lower surface as well, if that is necessary. (I use the turbo colormap her because I like it. Choose the appropriate colormap for your plot.)


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