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. The 'Review' option will be developed in future versions of the worksheet to include comparison with a Least Squares determination of the fit to the target points.



Resource Type
affine  conformal  coordinates  frame  source  target  transformation 
Target Group (Age)
English (United Kingdom)
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