[SrTobi]

Hi, I was the one nerdsniped :) In the end I don't think blub space is the best way to do the whole zoom thing, but I was intrigued by the idea and had already spend too much time on it and the result turned out quite good.

The problem is twofold: which path should we take through the zoom levels,x,y and how fast should we move at any given point (and here "moving" includes zooming in/out as well). That's what the blub space would have been cool for, because it combines speed and path into one. So when you move linearly with constant speed through the blub space you move at different speeds at different zoom levels in normal space and also the path and speed changes are smooth.

Unfortunately that turned out not to work quite as well... even though the flight path was alright (although not perfect), the movement speeds were not what we wanted...

I think that comes from the fact that blub space is linear combination of speed and z component. So if you move with speed s at ground level (let's say z=1) you move with speed z at zoom level z (higher z means more zoomed out). But as you pointed out normal zoom behaviour is quadratic so at zoom level z you move with speed z². But I think there is no way to map this behaviour to a euclidean 2d/3d space (or at least I didn't find any. I can't really prove it right now that it's not possible xD)

So to fix the movement speed we basically sample the flight path and just move along it according to the zoom level at different points on the curve... Basically, even though there are durations in the flight path calculation, they get overwritten by TimeInterpolatingTrajectory, which is doing all the heavy work for the speed.

For the path... maybe a quadratic form with something like x^4 with some tweaking would have been better, but the behaviour we had was good enough :) Maybe the question we should ask is not about the interesting properties of non-euclidean spaces, but what makes a flightpath+speed look good

[pfedak]

The nice thing about deciding on a distance metric is that it gives you both a path (geodesics) and the speed, and if you trust your distance metric it should be perceptually constant velocity. I agree it's non-euclidean, I think the hyperbolic geometry description works pretty well (and has the advantage of well-studied geodesics).

I did finally find the duration logic when I was trying to recreate the path, I made this shader to try to compare: https://www.shadertoy.com/view/l3KBRd

[phiresky]

Wow, amazing how you managed to convert that into a compact shader, including a representation of the visualization!