Visualizing Results

To visualize and compare the results of the different bases, we take a corner of the house and show the images of the corner under the two similarity transformations together with the final result of both computations (Figure 3).

Figure 3. A zoomed-in picture of a corner of the new house, where you can see the effect of the different choices.

In Figure 3 the green corner is the image under the first transformation, the red corner is the image under the second transformation, and the black corner is the final result of both computations.

We can also perform a numerical check: the final results of the second computation should be numerically equal to those of the first computation.

We can make a picture of the warping by applying PlotVectorField from the package Graphics`PlotField`. The vector field has been combined with the map using Show. Figure 4 shows the result: the "vector field" is like a vortex with two "sinks" at the basis points pt30 and pt31 where the corrections should be zero.

Figure 4. A "vector field" showing the relative size and direction of the corrections to the transformed coordinates.