5 ms·

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. The first derivativ

by tobtoh 4y ago

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. The first derivative of postion (with respect to time) is velocity. The second derivative is acceleration (ie rate of change of velocity). And the third derivative is jerk (rate of change of acceleration). And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable.

keithnz 4y ago
I have a t-shirt which has "don't be a" and the equation for the third derivative
- WalterBright 4y ago
  Better than my schwarzchild radius nerd shirt!
  - taneq 4y ago
    I saw a shirt the other day that said there’s no place like G28 0 0 0. I think for now that wins my nerdshirt championship (I still like my “velociraptor = distraptor / timeraptor” short though, even if it fails dimensional analysis. =)
- ben_w 4y ago
  Reminds me of someone I knew at university whose T-shirt was the definite integral from 10 to 13 of 2x dx followed by a question mark.
  - deleted 4y ago
    [deleted]
  - rhn_mk1 4y ago
    ...9?
    - saagarjha 4y ago
      The answer is a nice, round number.
      - rhn_mk1 4y ago
        duh. it does contain 9 tho.
      - 8bitsrule 4y ago
        https://www.integral-calculator.com/ https://www.integral-calculator.com/
  - jwilk 4y ago
    ∫ 2x dx = x² + C 13² − 10² = 69
mgdlbp 4y ago
Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware.
- Gordonjcp 4y ago
  > This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware. Is this why it seems to be mostly Americans that are into the idea of self-driving cars, because the standard of driving is so low?
- WalterBright 4y ago
  > but few drivers or rapid transit systems seem to be aware I find that amazing. What the heck are drivers ed instructors doing? It's not just hard on the passengers, it's hard on the machinery. It's the same with the clutch. I've driven with enough people who fancy themselves as great shifters, but they jerk the hell out of the clutch every time, never attempting to match the shaft speed with the engine speed. If I comment on it, they always deny doing that :-/ If I'm on my game, I can shift smoother than an automatic. The bonus is the clutch will last a very long time.
  - 2143 4y ago
    "They way somebody treats their car is the way they treats themselves" — Frank Martin (paraphrased for gender neutrality). And you can tell how somebody treats their car by examining how long the clutch lasts, if they drive a manual.
    - InCityDreams 4y ago
salty_biscuits 4y ago
Jounce, crackle and pop for the 4th, 5th and sixth derivatives
- cperciva 4y ago
  Jounce, also known as snap. Which to people of a certain cultural background explains where the names for the 5th and 6th derivatives come from.
- kristiandupont 4y ago
  It feels wrong to me that pop comes after crackle. Crackle seems like the ultimate high-frequency effect. In fact, "pop" seems like it should come before "snap". But I guess it is somewhat arbitrary.
  - wetmore 4y ago
    https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop
cperciva 4y ago
And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable. It's not strictly a matter of threshold -- people might tolerate a higher jerk if it's for a much shorter duration, for example. In practice it doesn't much matter which metric you minimize; you'll end up with similar results. The simplest option is to minimize the mean absolute jerk, which has the side benefit of utterly confusing any non-physics-literate people listening in. (You want to do what to whom?)
- yccs27 4y ago
  Note that 'mean absolute jerk' can also be described as 'total variation of acceleration over time'. That implies it does not depend on how fast the acceleration changes, only about the difference between minimum and maximum (as long as the acceleration increases/decreases monotonically to/from the maximum). This may or may not be what you want.
  - rkagerer 4y ago
    I see what you did there
kimburgess 4y ago
This video has an excellent visual demo of that concept: https://youtu.be/aVwxzDHniEw?t=451 https://youtu.be/aVwxzDHniEw?t=451.
atoav 4y ago
A very similar thing is done in the creation of reflective surfaces on car bodies (typically in CAD software). They call these constraints by G and a number. G1 would be a positional constraint: the two surfaces meet each other at the same point G2 tangential: same as G1, but the surfaces are tangential G3: same as G2, but the curvature (radius^-1) of the surfaces is the same at the point where the two meet. This essentially means the curvature combs of the surfaces shall meet at the same position (G1) G4: same as G3, only now the meeting curvature combs have to be tangential as well G5: same as G4, only now the curvature combs of the curvature combs have to meet at the same position And so on. The goal is to create smooth transitions between two separate mathematical surfaces that cannot be seen in the reflections in the sheet metal. E.g. if you think about the connection of straight sheet of metal (curvature: 0) and a cylindrical surface (curvature: 1/radius) the curvature will go from zero to some different value immidiately on the transation you will definitly see this as a hard corner on the reflection or when light falls onto the surface.
- johnwalkr 4y ago
  A simple example of this is the squircle. This page [1] has a couple of nice images that are easy to understand. https://99percentinvisible.org/article/circling-square-designing-squircles-instead-rounded-rectangles/ https://99percentinvisible.org/article/circling-square-desig...
- thaumasiotes 4y ago
  > G2 tangential: same as G1, but the surfaces are tangential This makes me think "tangential to what?". Do you mean that, along the seam between G1 and G2, the tangent plane to G1 at a given point is equal to the tangent plane to G2 at the same point?
  - avianlyric 4y ago
    Yep, exactly that. Removes the appearance of a “fold” or “crease” at the surface transition, and makes the surface smooth and continuous.
  - swimfar 4y ago
dijerido 4y ago
Skateboarders in 2008 don't get this. https://www.youtube.com/watch?v=TkeCZfG_KaI https://www.youtube.com/watch?v=TkeCZfG_KaI

by tobtoh 4y ago

keithnz 4y ago

I have a t-shirt which has "don't be a" and the equation for the third derivative

WalterBright 4y ago
Better than my schwarzchild radius nerd shirt!
- taneq 4y ago
  I saw a shirt the other day that said there’s no place like G28 0 0 0. I think for now that wins my nerdshirt championship (I still like my “velociraptor = distraptor / timeraptor” short though, even if it fails dimensional analysis. =)
ben_w 4y ago
Reminds me of someone I knew at university whose T-shirt was the definite integral from 10 to 13 of 2x dx followed by a question mark.
- deleted 4y ago
  [deleted]
- rhn_mk1 4y ago
  ...9?
  - saagarjha 4y ago
    The answer is a nice, round number.
    - rhn_mk1 4y ago
      duh. it does contain 9 tho.
    - 8bitsrule 4y ago
      https://www.integral-calculator.com/ https://www.integral-calculator.com/
- jwilk 4y ago
  ∫ 2x dx = x² + C 13² − 10² = 69

mgdlbp 4y ago

Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware.

Gordonjcp 4y ago
> This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware. Is this why it seems to be mostly Americans that are into the idea of self-driving cars, because the standard of driving is so low?
WalterBright 4y ago
> but few drivers or rapid transit systems seem to be aware I find that amazing. What the heck are drivers ed instructors doing? It's not just hard on the passengers, it's hard on the machinery. It's the same with the clutch. I've driven with enough people who fancy themselves as great shifters, but they jerk the hell out of the clutch every time, never attempting to match the shaft speed with the engine speed. If I comment on it, they always deny doing that :-/ If I'm on my game, I can shift smoother than an automatic. The bonus is the clutch will last a very long time.
- 2143 4y ago
  "They way somebody treats their car is the way they treats themselves" — Frank Martin (paraphrased for gender neutrality). And you can tell how somebody treats their car by examining how long the clutch lasts, if they drive a manual.
  - InCityDreams 4y ago

salty_biscuits 4y ago

Jounce, crackle and pop for the 4th, 5th and sixth derivatives

cperciva 4y ago
Jounce, also known as snap. Which to people of a certain cultural background explains where the names for the 5th and 6th derivatives come from.
kristiandupont 4y ago
It feels wrong to me that pop comes after crackle. Crackle seems like the ultimate high-frequency effect. In fact, "pop" seems like it should come before "snap". But I guess it is somewhat arbitrary.
- wetmore 4y ago
  https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop

cperciva 4y ago

And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable. It's not strictly a matter of threshold -- people might tolerate a higher jerk if it's for a much shorter duration, for example. In practice it doesn't much matter which metric you minimize; you'll end up with similar results. The simplest option is to minimize the mean absolute jerk, which has the side benefit of utterly confusing any non-physics-literate people listening in. (You want to do what to whom?)

yccs27 4y ago
Note that 'mean absolute jerk' can also be described as 'total variation of acceleration over time'. That implies it does not depend on how fast the acceleration changes, only about the difference between minimum and maximum (as long as the acceleration increases/decreases monotonically to/from the maximum). This may or may not be what you want.
- rkagerer 4y ago
  I see what you did there

kimburgess 4y ago

This video has an excellent visual demo of that concept: https://youtu.be/aVwxzDHniEw?t=451 https://youtu.be/aVwxzDHniEw?t=451.

atoav 4y ago

A very similar thing is done in the creation of reflective surfaces on car bodies (typically in CAD software). They call these constraints by G and a number. G1 would be a positional constraint: the two surfaces meet each other at the same point G2 tangential: same as G1, but the surfaces are tangential G3: same as G2, but the curvature (radius^-1) of the surfaces is the same at the point where the two meet. This essentially means the curvature combs of the surfaces shall meet at the same position (G1) G4: same as G3, only now the meeting curvature combs have to be tangential as well G5: same as G4, only now the curvature combs of the curvature combs have to meet at the same position And so on. The goal is to create smooth transitions between two separate mathematical surfaces that cannot be seen in the reflections in the sheet metal. E.g. if you think about the connection of straight sheet of metal (curvature: 0) and a cylindrical surface (curvature: 1/radius) the curvature will go from zero to some different value immidiately on the transation you will definitly see this as a hard corner on the reflection or when light falls onto the surface.

johnwalkr 4y ago
A simple example of this is the squircle. This page [1] has a couple of nice images that are easy to understand. https://99percentinvisible.org/article/circling-square-designing-squircles-instead-rounded-rectangles/ https://99percentinvisible.org/article/circling-square-desig...
thaumasiotes 4y ago
> G2 tangential: same as G1, but the surfaces are tangential This makes me think "tangential to what?". Do you mean that, along the seam between G1 and G2, the tangent plane to G1 at a given point is equal to the tangent plane to G2 at the same point?
- avianlyric 4y ago
  Yep, exactly that. Removes the appearance of a “fold” or “crease” at the surface transition, and makes the surface smooth and continuous.
- swimfar 4y ago

dijerido 4y ago

Skateboarders in 2008 don't get this. https://www.youtube.com/watch?v=TkeCZfG_KaI https://www.youtube.com/watch?v=TkeCZfG_KaI