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The SolveDistance procedure

The SolveDistance procedure allows to solve systems of distance equations. A distance equation describes that the distance between m points in a n-dimensional space is given. The unknowns are the n coordinates $x_1^k,\ldots, x_n^k$ of the points. Hence a distance equation may be written as:

&& \sum_{j=1}^{j=n}(x_j^k-a_j)^2 =l_k^2\\
&& \sum_{j=1}^{j=n}(x_j^k-x_j^l)^2 =l_{kl}^2\\

where $a_j$ are numerical values. Furthermore the algorithm allows for the use of virtual points. The coordinates of a virtual point M are linear combination of the coordinates of $k$ real points:

x_j^M = \sum_{l=1}^{l=k} b_l x_j^l

Hence a distance equation may also be written as:

\sum_{j=1}^{j=n}(x_j^M-x_j^l)^2 =l_{kl}^2

The syntax of SolveDistance is:
The initial search domain for SolveDistance may be determined using the Bound_Distance procedure.

Jean-Pierre Merlet 2012-12-20