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Imagine a plain (x,y) with 3 points (x1,y1), (x2,y2), (x3,y3) at it, not positioned in a line.
At each of the 3 points is fixed a straight wire with given length L1, L2, L3, protruding to z-space.
Find the spatial coordinates of the point (x,y,z), where the 3 ends of the wires can find together.
From Wolfgang Issel using MC14 on Windows 7
Solved! Go to Solution.
It seems to me that WOLFGANG ISSEL is asking how to find intersection point of three spheres.
MH
This problem is not sufficiently defined.
Given any point not on the plane you can connect a straight line to the three points, (Two points define a straight line.) If the lines are normal to the plane (protruding into z-space) then they will never intersect.
It seems to me that WOLFGANG ISSEL is asking how to find intersection point of three spheres.
MH
If the lengths of the "wires" are specified then you are correct--this is the intersection point of three spheres.
Which then changes into problems for which there are n solutions, where n can be 0, 1 or ??
...2 solutions:
One example with (essentially) a single solution:
The red dots are the locations of the three points on the z=0 plane.
The blue cross is the projection of P on the z=0 plane.
Two solutions:
Note that two solutions for P are found, symmetrically w.r.t. the z=0 plane.
And of course there's the no (real) solution:
With the restriction that the three points on the z=0 plane are not on a single line, the case where you would infinite solutions (if the three points are the same, and the three lengths are the same) does not exist.
"Found a singularity".
and:
Ah, tricked by Maple providing only the Zero solution.
Luc
Hello Luc,
thank You for Your solution. Compared with the solution from F.M. and Fred K. the same results were obtained.
To be sure I verified these with a real model and also found accordance.
So my problem is solved in a very fast and elegant way.
Greetings from Wolfgang Issel
Hello Fred,
thank You for Your solution. I compared it with the solution from F.M. and got the same results. To be sure I verified these with a real model and also found accordance.
So my problem is solved in a fast and elegant way.
Greetings from Wolfgang Issel
It seems to me, insted, that hi is looking for the coordinates of the point P represented in the figure, knowing the coordinates of the three points P1, P2, P3 lying on the plane z = 0, and the lengths L1, L2 and L3: :
in other words:
of course you have to avoid the imaginary solutions.
Hello F.M.,
thank You for Your solution and Your MC-Sheet. I compared it with the solution of Fred Kohlhepp and got the same results. I also found accordance when I verified these with a real model (straight wires with given length starting at there respectively coordinates).
So my problem is solved in a fast and elegant way and I can continue my work.
Greetings from Wolfgang Issel