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 Representing a Path Through Space
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wswartzendruber
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 Posted: Fri Feb 09, 2018 2:06 am    Post subject: Representing a Path Through Space I'm having trouble finding resources on this. How do I mathematically represent a path through space? Assume the presence of X, Y and Z dimensions._________________Gun: Glock 19 Gen 4 Sights: XS DXT Big Dot Holster: StealthGear VentCore IWB Ammunition: Federal Premium HST 124gr Light: Inforce APLc
notageek
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 Posted: Fri Feb 09, 2018 2:18 am    Post subject: What kind of path? Is it a curve? Is it a straight line? If it is a curve, what kind of curve is it?_________________"Defeat is a state of mind. No one is ever defeated, until defeat has been accepted as a reality." -- Bruce Lee
richk449
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Joined: 24 Oct 2003
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 Posted: Fri Feb 09, 2018 2:25 am    Post subject: Not sure what you are looking for, but one easy way is to parameterize the path as the function of a fourth variable. Typically, this would be something like: X = sin(t) Y = t^2 Z = 3t The over some range of t, all your coordinates are defined. https://en.m.wikipedia.org/wiki/Parametric_equation
wswartzendruber
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 Posted: Fri Feb 09, 2018 3:25 am    Post subject: I assume that t can represent time? Such an obvious solution, I'm embarrassed that I didn't intuitively figure it out._________________Gun: Glock 19 Gen 4 Sights: XS DXT Big Dot Holster: StealthGear VentCore IWB Ammunition: Federal Premium HST 124gr Light: Inforce APLc
Muso
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Posted: Fri Feb 09, 2018 3:39 am    Post subject:

 wswartzendruber wrote: I assume that t can represent time? Such an obvious solution, I'm embarrassed that I didn't intuitively figure it out.

I'll stop calling you "Sir Isaac".
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richk449
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Joined: 24 Oct 2003
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Posted: Fri Feb 09, 2018 5:07 am    Post subject:

 wswartzendruber wrote: I assume that t can represent time? Such an obvious solution, I'm embarrassed that I didn't intuitively figure it out.

Sure, t can be time, or something else (including having no real meaning) if you want.

Everything is obvious once you have seen it.
juniper
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Joined: 22 Oct 2004
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Location: EU

Posted: Fri Feb 09, 2018 2:04 pm    Post subject:

as rich said, paths have a single variable dependence in 3-space.

surfaces have a two variable dependence etc.
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