What additional capability does the affine transformation provide compared to the similarity transformation?

The affine transformation extends the capabilities of the similarity transformation primarily through the introduction of skewing as an additional geometric manipulation. While a similarity transformation can only alter the position and scale of a shape while preserving angles and proportions (resulting in transformations like rotation and uniform scaling), an affine transformation goes further by allowing for transformations that include scaling, translation, rotation, and skewing.

Skewing involves slanting the shape in a particular direction, which alters the original angles between points without preserving the overall shape's proportions. This manipulation enables the representation of complex systems and geometries in GIS and mapping, where such distortions might be necessary to fit certain datasets or map projections onto a surface.

The other transformations—such as changing area and distorting angles—are not the additional capabilities provided by affine transformations. For example, while affine transformations can lead to changes in area and may alter angles indirectly, these are not their defining or unique characteristics compared to similarity transformations. The specific attribute that highlights the versatility of affine transformations over similarity transformations is their ability to skew geometries.