# Creating a set of equally spaced cylinders with common centre

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Minas Emiris on 16 Apr 2018
Edited: Jan on 20 Apr 2018
I was wondering how to create a set of equally spaced cylinders around the centre of a circle (like a set of radii) but on 3D plot. I know how to use cylinder function, but I am confused when trying to generate a lot of cylinders without having to change the direction of each manually. Ideally, I wish to have 20 cylinders of height 80, starting not actually form the same point, but from the circumference of a circle with radius 20 (yet I want all of them to point to the centre of the circle.
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Minas Emiris on 16 Apr 2018

Jan on 16 Apr 2018

You can use cylinder to get the coordinates of one cylinder and apply some arithmetic to translate and rotate them.

This might be easier:

```function H = DrawCylinder(P1, P2, R, nVertex, FaceColor, FaceLite)
[RX, RY, RZ] = CylinderCoor(P1, P2, R, nVertex);
H = surface(RX, RY, RZ, ...
'FaceColor',        FaceColor, ...
'FaceLighting',     FaceLite, ...
'EdgeColor',        'none', ...
'AmbientStrength',  0.5, ...
'DiffuseStrength',  0.4, ...
'BackFaceLighting', 'lit', ...
'Clipping',         'off');
end
```
```function [RX, RY, RZ] = CylinderCoor(P1, P2, R, nVertex)
smallVal = 1.49e-008;  % SQRT(EPS)
```
```% Vector in the center of the cylinder:
nL12 = P2 - P1;
nL12 = nL12 ./ sqrt(sum(nL12 .* nL12, 2));
```
```% Base vectors of a circle around the center with normal nL12:
cX    = [nL12(:, 2), -nL12(:, 1)];
LencX = sqrt(cX(:, 1) .* cX(:, 1) + cX(:, 2) .* cX(:, 2));
```
```badInd        = (not(isfinite(LencX)) | LencX <= smallVal);
```
```cX       = cX ./ [LencX, LencX];
cX(:, 3) = 0;
```
```% cY as normalized cross product of nL12 and cX:
cY = [-nL12(:, 3) .* cX(:, 2), ...
nL12(:, 3)  .* cX(:, 1), ...
nL12(:, 1)  .* cX(:, 2) - nL12(:, 2) .* cX(:, 1)];
cY = cY ./ sqrt(sum(cY .* cY, 2));
```
```% Circle with nVertex points:
% theta = (0:nVertex) * (2 * pi / nVertex);
theta    = 0:(6.283185307179586 / nVertex):6.283185307179586;
costheta = R * cos(theta);
sintheta = R * sin(theta);
sintheta(nVertex + 1) = 0;  % Delete rounding errors (?!)
```
```% Dyadic products: [M x 1] * [1 x N] = [M x N]
DX  = transpose(cX(:, 1) * costheta + cY(:, 1) * sintheta);
DY  = transpose(cX(:, 2) * costheta + cY(:, 2) * sintheta);
DZ  = transpose(cX(:, 3) * costheta + cY(:, 3) * sintheta);
```
```P1T = transpose(P1);
P2T = transpose(P2);
RX(2, :, :) = bsxfun(@plus, DX, P2T(1, :));
RY(2, :, :) = bsxfun(@plus, DY, P2T(2, :));
RZ(2, :, :) = bsxfun(@plus, DZ, P2T(3, :));
RX(1, :, :) = bsxfun(@plus, DX, P1T(1, :));
RY(1, :, :) = bsxfun(@plus, DY, P1T(2, :));
RZ(1, :, :) = bsxfun(@plus, DZ, P1T(3, :));
end
```

This draws a cylinder from point P1 to point p2 with radius R, nVertex vertices and the specified colors and face lighting. Now all you have to do is to calculate the wanted P1 and P2.

Jan on 20 Apr 2018
Edited: Jan on 20 Apr 2018

Copy&paste of function definitions to the command line are not working. You have to define functions inside M-files. I suggest to read the "Getting Started" chapters of the documentation or running the "Onramp" (ask an internet search engine for the link).

Save the function CylinderCoor to a file called "CylinderCoor.m" and store it in a folder of your Matlab path. Then create a new function or script, which contains:

```[RX, RY, RZ] = CylinderCoor(P1, P2, R, nVertex)
```

Now Rx, Ry and RZ contain the values needed for a surface plot. Because mesh replies a surface object also, the inputs should be valid for this command also.

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