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Representing a Path Through Space
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wswartzendruber
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PostPosted: Fri Feb 09, 2018 2:06 am    Post subject: Representing a Path Through Space Reply with quote

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.
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notageek
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PostPosted: Fri Feb 09, 2018 2:18 am    Post subject: Reply with quote

What kind of path? Is it a curve? Is it a straight line?

If it is a curve, what kind of curve is it?
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richk449
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PostPosted: Fri Feb 09, 2018 2:25 am    Post subject: Reply with quote

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
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wswartzendruber
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PostPosted: Fri Feb 09, 2018 3:25 am    Post subject: Reply with quote

I assume that t can represent time? Such an obvious solution, I'm embarrassed that I didn't intuitively figure it out.
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PostPosted: Fri Feb 09, 2018 3:39 am    Post subject: Reply with quote

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


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richk449
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PostPosted: Fri Feb 09, 2018 5:07 am    Post subject: Reply with quote

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.
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juniper
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PostPosted: Fri Feb 09, 2018 2:04 pm    Post subject: Reply with quote

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

surfaces have a two variable dependence etc.
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