Feature request: horocycles and hypercycles in drawing tool

[josephcsible]

Can the drawing tool be updated to allow drawing horocycles and hypercycles too? The way I imagine it working:

• For horocycles, you get a horocycle that passes through both the point where you pressed the mouse and the point where you released it. (Since there are two such horocycles for any given pair of points, you could get the other one by swapping the order of those points.)
• For hypercycles, call point A the point where you pressed the mouse, and point B the point where you released the mouse. Let the guiding line be the line perpendicular to AB that passes through A, and then draw the hypercycle that passes through B. For example, the attached picture shows a choice of A and B that would draw the boundary of the Haunted Woods.

[zenorogue]

There is actually a fun way of drawing horocyclic arcs: in creative mode -> animations, you enable "parabolic" movement, and in the drawing tool, you just hold the mouse in place. (And similar ways for drawing other arcs.)

(Although that did not actually work due to a bug. And also inconvenient due to not being to enable to easily access the animation menu from the map editor -- I have added some parser constant such as holdmouse so one can enter holdmouse*10 as "cells to go" so that the animation runs only when the mouse is held and drawing, although these are still undocumented).

For drawing horocycles directly, I would probably prefer the interface of first selecting the center and then marking start and end points (in case if not on the same level, the start would be moved to the level of the end) -- this would draw a horocyclic arc, but probably that is enough? (drawing an infinite horocycle would be harder)

[josephcsible]

I just gave the animation trick a try with your latest changes, and it works well if you just want some horocycle, but if you want a specific one that lines up with something else, it can be really tricky to get the right one.

And I like that interface idea. It would let you draw horocycles and hypercycles the exact same way, the only difference being whether the center you choose is a point in the hyperbolic plane or an ideal point.