Also, Wordpress does not seem to like *’s in URLs. Huh.

Not sure if that’d feel more natural or not.

I kinda doubt your last time formula. On perfect timing, that’d make time be close to zero throughout. Maybe a ‘+’ instead of a ‘-’?

Good catch. This is an average so it should be a +.

I suspect the speed bump could come from checkerboard vs not. I.e., your t_now is start_paint, but the user sees end_paint time. If the regular page drawing takes more time than the checkerboard drawing, you’d get a speed up, going from the delayed page-rendering parabola to the less-delayed checkerboard-rendering parabola.

I was always testing with a completely rendered page, without any checkerboards. I think you’re right about the delay being different later in the pan though.

I wonder if you can already assume that the time-location data that you use to calculate initial position and velocity are page-rendering delayed. If so, you’d get into the parabula fine. If not, you’d end up with a skewed initial path, too.

I had toyed with this idea, shifting time a little more in the beginning than in the end. Ultimately I found something that worked but felt the time average was more elegant and improved the smoothness of the animation at the same time.

That said, have you tried other friction algorithms? Like an eddy current brake? Not sure that’s even terminating in time, but you could add a tad of mechanical friction to it for that.

I based my parabola on classical friction that you learn in mechanical physics. Classical friction force is a function of the normal force and the textures of the two surfaces but not position or velocity or time, so if F=ma then a=F/m, so the acceleration factor is a constant for us, creating a parabola. I don’t really know anything about eddy current brakes and I didn’t find any useful formulas with a quick Google search.

I have been curious about other higher-order formulas. I’ve tried a few different polynomials several months ago, and I believe Fennec has used sqrt in earlier iterations. At the end it comes down to “how does it feel,” and so far parabolas have felt the best to me.

I suspect the speed bump could come from checkerboard vs not. I.e., your t_now is start_paint, but the user sees end_paint time. If the regular page drawing takes more time than the checkerboard drawing, you’d get a speed up, going from the delayed page-rendering parabola to the less-delayed checkerboard-rendering parabola.

Taking a mean between real time and equidistant timing probably eases that effect, as you’re late in the page-rendering part, and you claim you’re not by taking some fraction of the equidistant timing, and thus making your start_paint be a tad early. Kind-of averages out the being-late of the last step with the being late of the next step.

I wonder if you can already assume that the time-location data that you use to calculate initial position and velocity are page-rendering delayed. If so, you’d get into the parabula fine. If not, you’d end up with a skewed initial path, too.

That said, have you tried other friction algorithms? Like an eddy current brake? Not sure that’s even terminating in time, but you could add a tad of mechanical friction to it for that.

Ben — you are a mathematician masquerading as a programmer. Someone will find you out. You can’t hide forever.