[mathcad] Re: MathCad 3D-plot lines

Author: Chris Whitford Posted: Mon, 26 Jun 2006 11:54:24 +0100

An alternative is an algebraic solution. A line in space is the solution to
a set of 2 simultaneous equations in 3 unknowns: x,y,and z. The
intersection of 2 lines (if it exists) is the solution of the set of 4
simultaneous equations formed by combining those for the 2 lines. Write
this in matrix form as AX = B (X is the vector of the 3 coordinates x,y,z).
In general this does not have an exact solution, but the least squares
solution is given by X = LB where L is the left pseudo-inverse of A. The
closeness of this solution (i.e. how close the 2 lines are to intersecting)
can be found from the residual AX - B. I'm afraid I haven't the time to
follow this through and give you a detailed solution.

Chris

At 14:47 13/06/2006 +0200, you wrote:
>I have a problem with 3D-plots.
>I want to plot several of straight lines in 3D.
>The information I´ve got is the start coordinates and the end coordinates
>for each line, given in x,y,z.
>But how will I plot them in the same plotview?
>The thing is that I want to see if any of the lines collide with eachother.

+ Chris Whitford
+ Research Fellow, University of Leicester, Space Research Centre,
+ Physics and Astronomy Department, University Road, LEICESTER LE1 7RH, UK
+ Tel: +44 (0)116 252 3496, Fax: +44 (0)116 252 2464
+ email: "chw" http://www.star.le.ac.uk/

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