Many roguelikes have a choice of "class" for replay value. Could we have that in HyperRogue, with its focus on non-Euclidean geometry, and combat based on just positioning (no hitpoints etc.)?
Apparently yes! Here the Rogue switches his blade for a crossbow, and takes advantage of how the straight lines work in hyperbolic geometry in a different way!
As a consequence of hyperbolic geometry, the enemies naturally arrange themselves in a straight line, which this crossbow attack takes advantage of. This is work in progress that should be available soon (the classic HyperRogue combat is attack adjacent creature, which also takes advantage of this property, but in a different way). Of course there is more variety in HyperRogue from the choice of geometry, land structure, and change of genre from roguelike to action/FPS/racing/etc.
Two-point equidistant projection of the hyperbolic plane, but one point is in the center, and the other point is in the infinity, and changes its direction during this animation. The frame where horocycles are mapped to straight lines is insighftul. (Basically, a circle of radius 𝑟 around the center of ℍ² is mapped to a cirlce of radius 𝑟 around the center of 𝔼², and concentric horocycles are similarly mapped to straight lines; these two conditions determine where every point is mapped.) Based on an idea by bengineer8u.
By the way, our video "Portals to Non-Euclidean Geometries" https://youtu.be/yqUv2JO2BCs has just passed 1M views!