Challenge(?): Intersection curve between two cylinders in a specific position  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: Challenge(?): Intersection curve between two cylinders in a specific position (/thread250479.html) 
Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09162013
How do you solve this with you calculator (2) (? (eventually, are you able to plot the solution and/or the 3d scenario with the curve highlighted?)
Some restrictions to avoid tricks:
(1) For axis I mean: the line that is normal to the base of the cylinder and that cross the center of that base.
Edited: 16 Sept 2013, 6:07 a.m.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  JeanMichel  09162013 Hello Pier Re: Challenge(?): Intersection curve between two cylinders in a specific position  peacecalc  09162013 Hello Pier, that is a funny story. The hobby card modeling has to solve such questions with a lot of intersecting shapes. I wrote for the hp 50g such a program for finding the point whichs belonges to the shapes both. Some of the card modeling collegues thinks that I'm a crazy guy doing this task with on a calculator and not with an 3D program like rhino or blender. The main idea of my program is that one surface is build with plane triangles. The other surface is builded with a bunch of lines. The lines are used to be straight lines which are intersected with the triangles of the other shape. The hp 50g can handle in excellent way vectors and in connection with the dotproduct it is easy to find out where the lines and the plane triangles have common points or not. The program is written in RPL (of course) and a bit long. The documentation is a bit spartan. So I don't know if it make sence to show you here the program text.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Thomas Klemm  09162013 Black cylinderAssume r = 1: x^{2} + y^{2} = 1
Blue cylinder
Assume r = 1:  x   0 
So we end up with the following possible parametrisation: x = cos(t) We could have expected this. For symmetric reasons the intersection curve must be in a plane. Cut that with a cylinder and you get an ellipsis. Furthermore tan(67.5) = 1 + sqrt(2) and tan(22.5) = 1  sqrt(2).
Quote:
Cheers Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09162013 yes, you can do a plane projection (specifing the plane). Or: Is the curve given by the intersection on a plane (1)? (i don't know actually, even if i guess not)
(1) That is: are all the intersection points on the same plane ? Edited: 16 Sept 2013, 5:42 p.m.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09162013 Why not? Is just another contribution! Don't feel ashamed.
I'm ashamed here, there are really good people both in using calculators and math! But, imo, it's better to contribute (as best as you can) anyway.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09162013 Nice! Quick and elegant! (moreover i'll analyze it more asap)
About "where in this do you need a calculator?", it's not mandatory but if someone want to use it, why not?
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Thomas Klemm  09162013 Oops, just noted that e should rather be (0, 1, 1). But it doesn't change much: just switch the sign of z.
Cheers Re: Challenge(?): Intersection curve between two cylinders in a specific position  Csaba Tizedes (Hungary)  09172013
Maybe it is required some thinking to calculate intersection curves, but the manufacturing is VERY simple, because the equal diameter pipes intersection curve is always two line in side view. This is a simple straight cut on pipes.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09172013 Why do you get a sort of triangle on the blue cylinder?
Remember that one "side" of the blue cylinder is untouched (the green one in the picture), while the other can be "cut" by the intersection line.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Csaba Tizedes (Hungary)  09172013 Those triangles are not visible, only I don't erase them. Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09172013 A cylinder has no sides :P, what I meant is the green (dotted) line/side of the blue cylinder in the first picture.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Kimberly Thompson  09172013 Pier
This is not an answer to your challenge, but rather an edification resource;
SlideRule
Re: Challenge(?): Intersection curve between two cylinders in a specific position  peacecalc  09172013 Okay Pier,
%%HP: T(3)A(R)F(,); So you get what you want (YGWYW ;)) The input are four lists with 3D vectors, the first two list discribe f. example the blue cylinder (there are only the coordinates needed in form of the bottom and top circle (the frames or formers of the cylinder)), the next two lists describe f. example the black cylinder (in the same form). The user decides how fine (how many intersections points should be find), by the size of the lists. The lists of the different shapes can have a different size, but the pair itself must have the same size. The user gets after some time two lists back "U1" and "U2", these two lists contain the intersections points in 3D vectors. It is not a analytical solution, it's numerical, but it works for all different shapes, which could be generated by two frames (two 3D polygons). It is a very clumsy piece of program, but you have to imagine, the calculator has to find out, if there are common points and where they are.
Greetings Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09172013 Whoa, it's huge! Thanks for your contribution.
Re: Challenge(?): Intersection curve between two cylinders in a specific position  Pier Aiello  09172013 Thanks a lot :)
