Coordinate Transformations
In the case of a Least Squares transformation between a source and a target coordinate frame, using
i. 2D four-parameter (Conformal),
ii. six-parameter (Affine) and
iii. eight-parameter (Perspective) transformations, answer the following three questions:
1. What is the minimum number of common points required to determine the transformation parameters in the case of the three transformations?
a) 2D four-parameter (Conformal) – 2 points
b) Six-parameter (Affine)- 3 points
c) Eight-parameter (Perspective) transformations- 4 points
2. What affect does the transformation type have on the goodness-of-fit of both coordinate frames?
Transformation establishes a relationship between the source frame and the target frame. Different transformation types conserve different aspects of the source frame and this in return has a ripple effect on the goodness of fit of both coordinate frames. If the transformation type distorts some properties of the source frame during the process of transformation, the target frame will lose the distorted properties. Different properties of the source frame including the shape, direction, area and scale may be affected by the type of transformation. Each transformation type conserve different properties while at the same time distorting some other properties. In some transformations such as the conformal method, the area may be exaggerated in some sections while the direction remains intact. It can therefore be stated that the type of transformation causes a ripple effect such that the characteristics of the transformation method determines the nature of the target frame. When this occurs, the accuracy and appearance of the resulting target frame is affected as compared to the source frame. It is due to this reason that the choice of the type of transformation that is meant to be used is normally dependent on the aspects to be transformed, the location of the source frame and the purpose of the transformation.
3. What distortions in a source frame may be removed by each of the three transformations?
a. 2D four-parameter (Conformal) – distortions in the shape
b. Six-parameter (Affine)- distortions in the area
c. Eight-parameter (Perspective) transformations- distortions in the direction and scale of the source frame 1 of 1
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