Hyperbolic lines in Poincaré disk and Escher's works

Circle inversion of arcs
Hyperbolic line through two points inside the disk
Hyperbolic line through a point inside the disk and a point on the boundary
Hyperbolic line through two points on the boundary
Two parallels and infinite hyperparallels
angels&demons Pole construction (construction used by Escher)
angels&demons with new hyperbolic tools
Escher's fish
Eschers' lizards
– Daniela Ferrarello

Information: Hyperbolic lines in Poincaré disk and Escher's works