How to find co-ordinates of a point in 3D using Matlab functions?

I am trying to determine the (x,y,z) coordinates of a point p. What I have are the Euclidean distances to 3 different points m1, m2, m3 with known coordinates.

I am looking for Matlab functions that will help me solve this problem. My math is not so strong. Any help will be appreciated. Thank you

Answer 1

[Roger Stafford]

This problem is equivalent to finding the common points of intersection of three spheres. You should realize that if there are any solutions at all, there are almost always two of them. At the following Answers thread:

   http://www.mathworks.com/matlabcentral/answers/116045

you will find a method of solution for this problem which I gave back in February of this year.

Answer 2

[Zoltán Csáti]

Let the coordinates of the unknown point be x,y,z and m1(x1,y1,z1), m2(x2,y2,z2), m3(x3,y3,z3), moreover the known Euclidean distances d1, d2, d3 respectively. You can write 3 equations for the 3 unknowns: (x-x1)^2 + (y-y1)^2 + (z-z1)^2 = d1^2, ... Now, solve them for x, y and z.