Interpolating affine transformations

This is in response to a question asked on the Mathematics StackExchange. It demonstrates the use of fractional exponents to perform interpolation of an affine transformation matrix. The demonstration was created using Cinderella.

Linear matrix plus translation

The first approach does a power interpolation of the linear part of the affine transformation, and a linear interpolation of the translation part. The resulting interpolation depends on where the point triples lie with respect to the (invisible) coordinate system.

Please enable Java for an interactive construction (with Cinderella).

Single transformation matrix

The second approach does the interpolation using a single 3×3 matrix which describes all aspects of the transformation. It is independent of the position of the point triples.

Please enable Java for an interactive construction (with Cinderella).