5 ms·
This is also what's happening in an elevator. You not only want the speed to increase slowly, you also want the acceleration to increase slowly, cause that's wh
by d--b 11mo ago
This is also what's happening in an elevator. You not only want the speed to increase slowly, you also want the acceleration to increase slowly, cause that's what actually makes your guts go down. And the best way to do this is to have the acceleration of the acceleration continuous.
In the end the position of the elevator is 3-continuous (why is it called G3? in France we call this C3). And the apple corner is just a graph of the position of an elevator wrt time. Mind blowing
- LiamPowell 11mo agoG and C continuity have slightly different meanings. You can have curves that are G^n but not C^n and vice-versa. I'll leave it to you to find a maths textbook that gives a better explanation than I would if I attempted to here.
- andrewingram 11mo agoI'm always reminded of snap, crackle and pop (https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...) for this topic. Essentially it's not enough to just have continuous acceleration, you have to ease into it (low snap), you can probably go into further derivatives for ultra smoothness but maybe not worth it?
- quietbritishjim 11mo agoAs your link says, acceleration is 2nd derivative of position, so rate of change of acceleration is 3rd derivative, often called jolt. As you say, you want acceleration to vary slowly, so it's low jolt that you want. Snap (or jounce), crackle and pop are 4th/5th/6th derivative. They're probably less of a problem.
- nkrisc 11mo agoI’ve also heard it called “jerk”.
- quietbritishjim 11mo agoOops, that's what I meant to say! So much for my correction. I actually heard, many years ago, the higher derivatives referred to as "jerk" (3rd, as you said), "jolt" (4th) and "jounce" (5th). But that contradicts the Wikipedia article that says "jounce" is 4th derivative.
- andrewingram 11mo agoOops, yeah you’re right!
- rcxdude 11mo agoIt can help because the higher derivatives also tend to promote vibrations in the system, but I doubt it'd be perceptible by people. I have heard of 5th-order smooth curves being used for very sensitive structures, like the movement of big observatory telescopes.
- oasisaimlessly 11mo agoG^n curvature solely depends on the geometry of the curve, while C^n continuity also depends on how you parameterize the curve. So, G^n is what you want if you're talking about a purely geometric shape rather than an (x(t), y(t)) trajectory. * reference: section 2.1 of https://graphics.stanford.edu/courses/cs348a-21-winter/ReaderNotes/handout27.pdf https://graphics.stanford.edu/courses/cs348a-21-winter/Reade...