Solving Changing Cross Sectional Area of Curved Cylinder

Hello all,

I have vertex and face matrices of a curved cylinder of uneven cross-sectional area (essentially an arch where the orange point is the centroid).

I am looking for a way to calculate the diameter of the cylinder as a function of angle around the arch.

I am considering either converting the matrices into a volume and then using the slice function with planes iterating around the centroid, however, I'm worried that because the curve is not exactly circular this method will give skewed measurements.

I also thought about iterating through the vertices, solving for cross sectional area likely using points along the centerline to predict the next plane in which the area should be measured? But I honestly have no idea where to start with that.

I am very open to any other solutions to this or development on my current ideas! Thank you

Answer 1

[Ben Drebing]

If you are making a function of angle, what point is that angle in relation to? Could you use your angle to rotate a plane about a point projected directly below the centroid like:

The results will probably still be a little skewed for the reasons you said above, but maybe less so? Then you could use the process described in this link to make cross sections.

https://www.mathworks.com/matlabcentral/answers/347789-cross-section-of-pointcloud#answer_273276

[Ben Drebing]

If you wanted to try that center line approach, you could find a line of best fit for your data projected onto the xy plane. Then do this again for your data projected onto the zy plane.

This would give you two equations that, when used together, could help you define some points on the centerline of the arch.