2D Linear Transformations

2D (Plane) coordinate transformations are applied extensively in the spatial information sciences. This worksheet explores the characteristics of the four-parameter (conformal) and six-parameter (affine) transformations.
The 'Fit to Target Points' option allows students to use sets of target points to determine best-fit transformation parameters. In practise, source points have uncertainty as they will usually have been determined by a measurement process. The 'Distortions' option allows random and systematic errors to be introduced to the source points (the sliders control the maximum values - actual values are randomly generated within the maximum). Students can experiment with the determination of those parameters of either transformation type that can provide the best-fit on the target points. The 'Review' option reveals the ideal result of the transformation on the full figure - this can be used to check the goodness of fit.