Determining the coordinates of a node between two known nodes and knowing the distances between the known nodes
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Hi! This may seem like a rather trivial question. Do you know how to determine the coordinates of a node C knowing node A, node B, distance AC and distance CB?
At the moment I can use these two equations:
C = [x, y, z]; %unknown
A = [x_A, y_A, z_A];
d1 = (x-x_A)^2;
d2 = (y-y_A)^2;
d3 = (z-z_a)^2;
d_AC = sqrt(d1 + d2 + d3);
B = [x_B, y_B, z_B];
d4 = (x_B-x)^2;
d5 = (y_B-y)^2;
d6 = (z_B-z)^2;
d_CB = sqrt(d4 + d5 + d6);
A third equation is missing. At the moment I have no idea, and I don't know if it is possible to determine the coordinates directly on matlab.
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Torsten
2024-1-13
There is only a unique solution for this problem if AC + CB = AB. In all other cases, you either get no solution (AC + CB < AB) or infinitly many solutions (AC + CB > AB).
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Hassaan
2024-1-13
function C = findPointC(A, B, d_AC, d_CB)
% Define the system of equations
function F = distanceEquations(C)
F(1) = (C(1) - A(1))^2 + (C(2) - A(2))^2 + (C(3) - A(3))^2 - d_AC^2;
F(2) = (C(1) - B(1))^2 + (C(2) - B(2))^2 + (C(3) - B(3))^2 - d_CB^2;
end
% Initial guess (can be changed based on the problem context)
initialGuess = (A + B) / 2;
% Solve the equations
C = fsolve(@distanceEquations, initialGuess, optimoptions('fsolve', 'Display', 'off'));
end
You can use this function by passing the coordinates of points A and B, and the distances dAC and dCB. Keep in mind that this approach might find one of the possible solutions or may fail if the distances provided are not physically consistent with the positions of A and B.
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