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:

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

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:

 
SolveDistance(Func,Vars,Init)

The initial search domain for SolveDistance may be determined using the Bound_Distance procedure.