Why would it be desirable to compute a unique transformation on a given data set rather than a least squares transformation?
Many surveyors look for a transformation which will hold their field tied points. There are good reasons for wanting this, since a least squares solution will yield transformed coordinates which will be close to their field tied points in a good transformation, but not exactly the same, resulting in duplicate coordinate pairs for the same point, which is anathema to good surveying practitioners. All of the transformations included in 2-D Coordinate Transformations are numerical transformations, mathematically defined as interpolating parametric equations yielding approximate transformed coordinate pairs. If the Systems 1 and 2 control coordinates selected are the exact number of points required for each of the transformations included in this program; matrices can be written which will describe a set of linear independent normal equations, with the unknowns in these equations the parameters which define the transformation. This program solves for these parameters using Gaussian elimina
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