Example

Here is the example of Figure 2. Table 1 gives the measured coordinates and the coordinates of the database. First we choose pt3 and pt504 as a basis for the similarity transformation. Then we show that another basis, for example pt30 and pt31, will give the same result for the final coordinates of a measurement.

Table 1. Measured coordinates and database coordinates.

We choose and as a basis. The other control points are the points , , and . We transform the local coordinates of the control points and the free points (, , , and ) with respect to the chosen basis. Here we only work out .

We transform the local coordinates of the control points and the free points (, , , and ) with respect to the chosen basis. Here we only work out .

Next we compute the database coordinates of the new house with the following formula.

Here are the final coordinates of , , , and .

Table 2 summarizes the result.

Table 2. The transformed coordinates with respect to pt3 and pt504.