Bending the plane into a closed surface / cylinder
I am doing a math experiment in Matlab and the result should be a circle in the x, y plane. But sometimes the circle starts to spin. I am currently trying to bend the x, y plane into a cylinder (like in the following figure). At the moment I only have the x and y coordinates of the points.
I tried to convert them to polar coordinates and then use some "surf" commandos, but now nothing works
(source: wtcoeselgem.be )
Edit: I used the plot3 command as suggested by Ander Biguri, resulting in the following figure.
(source: wtcoeselgem.be )
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The following seems to do more or less of what you want
%// Data xmin = -3; xmax = 3; %// this piece will get folded into a cylinder Rc = 5; %// cylinder radius zmaxc = 5; %// cylinder max z zminc = -5; %// cylinder min z %// Spiral t = linspace(0,1,1000); r = 1+2*t; theta = 2*pi*3*t; x1 = r.*cos(theta); y1 = r.*sin(theta); %// example spiral. Defined by x1, y1 %// Do the bending z2 = y1; phi = (x1-xmin)/(xmax-xmin)*2*pi; x2 = Rc*cos(phi); y2 = Rc*sin(phi); %// Plot cylinder [xc yc zc] = cylinder(Rc*ones(1,100),100); zc = zminc + (zmaxc-zminc)*zc; surf(xc,yc,zc) shading flat hold on %// Plot bent spiral plot3(x2,y2,z2, 'k.-');
Original spiral:
Two kinds of result:
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I will assume that you have a curve defined by coordinates x
and y
that you want to reset around the cylinder.
%% // Generate sample data x = linspace(0,10*pi) ; y2 = cos(x) ; y1 = 10*cos(x/10) ; y = y1+y2 ; y = y-min(y) ; figure, plot(x,y,'-o') ;
This produces: 
Next, I define the base cylinder, nothing original:
%% // Basic cylinder (just for background)
[Xc,Yc,Zc] = cylinder(1,100);
Zc = Zc * max(y) ;
hs = surf(Xc,Yc,Zc) ;
set(hs,'FaceColor',[.8 .8 .8],'FaceAlpha',0.5,'EdgeColor','none') ;
hold on
And here's the interesting bit:
%% // Fold the points around the cylinder Number_of_turn = 2 ; xrange = [min(x),max(x)] ; xspan = xrange(2)-xrange(1) ; xc = x / xspan * 2*pi * Number_of_turn ; Xp = cos(xc) ; Zp = y ; Yp = sin(xc) ; hp = plot3(Xp,Yp,Zp,'-ok') ;
What render: 
In this example, I assumed you wanted to wrap your curve around the "2 turns" of the cylinder. This can be easily changed with a variable Number_of_turn
.
Note that you can also change the radius of the cylinder by multiplying the coordinates Xp
and Yp
by your radius.
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