Conformal hiperbolic cat

There are numerous mappings for non-Euclidean planes. Unfortunately, if we map a plane of non-zero curvature, we must decide what to distort: the distances or the angles among objects. We call conformal the mappings that preserve angles.

According to the Riemann mapping theorem, there exists a biholomorphic mapping from any non-empty simply connected open subset of C to open unit disk in C; by composing such a mapping with the Poincaré disk model we can get a projection of the hyperbolic plane of any (simply connected) shape.

Even if the mentioned theorem is fundamental, there used to be a strange fashion among people related to the applications of mathematics in art. They tended to call every mapping "model". We got bored of subsequent papers entiled, e.g., "conformal square model of hyperbolic plane", therefore we decided to suggest a (nearly) ultimate algorithm for mapping arbirtary shapes. See this article for details.