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I am looking for a free application in order to calculate optimal coordinates of points, given a fixed set of points and the mutual distance between them. The system is over-constrained hence spatial adjustment by means of the least-square-method is required.

Background:

I need to draw a CAD plan with QCad of a non-rectangular, existing building. I already took all measurement manually by dividing the building into imaginary triangles. For a better understanding see this plan (black lines are actual walls, green lines are distances are took additionally).

Of course, the measurements are affected by noise. In order to mitigate noisy measurements and to enhance precision I took more distances than are necessary to define a unique solution.

First option would be to start drawing in QCad and then optimize the points by visual inspection, i.e. by looking at them such that most distances "feel" correct.

Second option would be to do the math and solve the resulting equation. (I know how to do it, but I would prefer not to write down the system by hand).

Third option, and this is what I hope for, is an existing program that just takes a set of points (A, B, C, ...), I define the mutual distances between the points and the program calculates the best positions. Is there any such program?

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