  Consider the straightening phi of a Beltrami form that is constant on a
square, with the corresponding ellipses having a vertical major axis, and null
outside. A generalized Schwarz-Christoffel formula is used to express the
inverse of phi. The formula is found by introducing an affine Riemann surface.
This formula is used to draw on a computer the image of the square by phi, and
practical aspects are discussed. The resulting shapes are shown for different
values of the constant dilatation ratio of the ellipses (=major axis/minor
axis). The limit when this ratio tends to infinity is surprising. A model of
this limit is proposed, produced by an affine surface uniformization.
