Sweeping a cylinder along a line

Hello everyone,

I am trying to create an algorithm that automatically builds support structure for Selective Laser Melting produced parts. I am able to extract the points that need supports by a thermal-mechanical analysis which gives me results about the deformations of the part.

Anyway, I am able to define the supported points and define a tree-shaped support structure. Attached is a very simplified version of the script that you can run so to understand the situation I am in.

startPoint =  10*rand(1,3);
normalVector = [0.5, 0.5, -0.5].*rand(1,3); 
normalizedVector = normalVector / norm(normalVector);
middlePoint = [startPoint(1), startPoint(2), startPoint(3)] + (startPoint(3)*0.3)* normalizedVector;
plot3([startPoint(1), middlePoint(1)], [startPoint(2), middlePoint(2)], [startPoint(3), middlePoint(3)], 'b'); 
hold on;
plot3([middlePoint(1), middlePoint(1)], [middlePoint(2), middlePoint(2)], [middlePoint(3), 0], 'r');

Now, I would like to sweep a cylinder of 1 mm diameter along this line, and if possible, connect the two lines with a spline to reduce to avoi the sharp edge. Is there a way to perform what I need?

I have been looking around but couldn't find anything unfortunately.

Thanks in advance for your kind availability and for the time,

LP

Answer 1

[Vinayak]

Hi Lorenzo,

To address your query on plotting a cylinder tilted along a reference line defined by two points, here's a function that takes in the start and end points to plot a tilted cylinder:

function plotTiltedCylinder(startPt, endPt, radius, color)
height = norm(endPt - startPt);
[x, y, z] = cylinder([radius, radius], 100);
z = z * height;

dir = endPt - startPt;
dir = dir / norm(dir);

% Create Rotation Matrix
Z = dir / norm(dir);
X = [1, 0, 0];
if abs(dot(Z, X)) > 0.99
    X = [0, 1, 0];
end
X = X - dot(X, Z) * Z;
X = X / norm(X);
Y = cross(Z, X);
R = [X; Y; Z]';

cylinderCoords = R * [x(:)'; y(:)'; z(:)'];
x = reshape(cylinderCoords(1, :), size(x)) + startPt(1);
y = reshape(cylinderCoords(2, :), size(y)) + startPt(2);
z = reshape(cylinderCoords(3, :), size(z)) + startPt(3);

surf(x, y, z, 'FaceColor', color, 'EdgeColor', 'none');
end

For further understanding, refer to the following documentation:

https://www.mathworks.com/help/matlab/ref/cylinder.html

https://www.mathworks.com/help/matlab/ref/reshape.html

To create the spline, you can use the Curve Fitting Toolbox and plot the resulting function. Here's an example using a cubic spline:

splinePoints = [startPoint; middlePoint; [middlePoint(1), middlePoint(2), 0]];
splineCurve = cscvn(splinePoints');
fnplt(splineCurve, 'g', 2);

For more on spline constructions, check out:

https://www.mathworks.com/help/curvefit/construction.html

This results in something similar to the below image:

[Lorenzo Pollicini]

Thank you very much!