Intersection of 3 Cylinders

[markraz]

Hi So I found this graphic on how to find the intersection if 2 cylinders.


It looks pretty straight forward on how to solve with basic algebra.
My question is can I do something similar for finding the intersection of 3 cylinders? should I use a matrix and solve a non-linear system?or how do math folks solve this type of problem?? Thanks in advance

 

[Steven G]

I would find the intersection with two cylinders and then find the intersection of the 3rd cylinder and the intersecting points of the 1st two cylinders.

Usually, but not always, you do not use matrices for non-linear equations.

 

[markraz]

I would find the intersection with two cylinders and then find the intersection of the 3rd cylinder and the intersecting points of the 1st two cylinders.

Usually, but not always, you do not use matrices for non-linear equations.

Thanks appreciate it, makes sense. Just out of curiosity why wouldn't the matrix be the way to go??
thanks

 

[Cubist]

I made an animation of the shape revolving in orthographic projection. The original 3 cylinders had different colors, and the yellow lines went parallel to the axis of the original cylinder.

It looks quite cube-like from some angles (at a similar angle to OP's black and white image).



The lines of intersection are formed from different PAIRS of cylinders intersecting. @markraz , does this tell you anything about the equations of these lines? All THREE cylinders only intersect together at 8 single points (on the "corners") at a 3 line "Y" join. All 3 colors are seen coming together at these points. Can you see why it might be useful to calculate the coordinates of these, if you want fully-valid intersection line equations?

Between the intersections, in all areas of a single color, then the surface shape is obviously exactly the same as the surface of the original cylinder.

BTW: I don't believe I know anything about matrices within non-linear systems myself, so I can't help with that specific question. But that's probably good since I've probably said too much already. Is that the sound of people falling asleep