31. A direct isometry is an affine transformation with an orthogonal matrix that has a determinant of 1. 32. Equivalently, it is a manifold that is ( if connected ) monodromy acting by affine transformations . 33. Notice that this is an affine invariant construction since parallelism and midpoints are invariant under affine transformations . 34. It is not classified as a linear transformation, but is instead known as an affine transformation . 35. Since an affine transformation preserves straight lines and ratios of areas, it sends equidissections to equidissections. 36. Other methods can handle problems such as translation, scale, image rotation and even all affine transformations . 37. In particular two Siegel domains are isomorphic if and only if they are isomorphic by an affine transformation . 38. An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of " 1. 39. The goal of the affine invariant detector is to identify regions in images that are related through affine transformations . 40. Camellia uses four 8 ?8-bit S-boxes with input and output affine transformations and logical operations.
