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WolfgangIssel1-Visitor
1-Visitor
March 30, 2017
Solved

My question:

  • March 30, 2017
  • 3 replies
  • 3539 views

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


Best answer by MartinHanak

It seems to me that WOLFGANG ISSEL is asking how to find intersection point of three spheres.

MH

3 replies

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
March 30, 2017

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.

M
MartinHanak24-Ruby IIIAnswer
24-Ruby III
March 30, 2017

It seems to me that WOLFGANG ISSEL is asking how to find intersection point of three spheres.

MH

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
March 30, 2017

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 ??

L
LucMeekes23-Emerald IV
23-Emerald IV
March 30, 2017

...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

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-MFra-21-Topaz II
21-Topaz II
March 30, 2017

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: :

Coordinate del punto P intersezione delle rette per P1, P2 e P3.jpg

in other words:

solution 00.jpg

of course you have to avoid the imaginary solutions.

W
WolfgangIssel1-VisitorAuthor
1-Visitor
March 31, 2017

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

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