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November 14th, 2016, 07:49 AM   #1
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Finding arc length

I want to find the length of an arc with the following data:

XYZ coordinates of start point

XYZ coordinates of center point of the arc

XYZ coordinates of end point

arc direction

Radius

I can find the chord but there is 2 possible arcs with these values

The arc is on a plane (XY,XZ,YZ) but I dont know which one

Last edited by VincentP; November 14th, 2016 at 08:46 AM.
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November 14th, 2016, 01:21 PM   #2
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well as you've said there are two arcs that meet those conditions.

fortunately if you know the arc length of one, $\ell_1$, the arc length of the other is just

$\ell_2 = 2\pi r - \ell_1$
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November 14th, 2016, 02:44 PM   #3
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If you know the coordinates of the center point of the arc, this will tell you which of the 2 possible arcs defined by the chord. This can be done by examining the chord from the end point to the midpoint of the arc. Compare it to $\displaystyle \frac{r\sqrt{2}}{2}$. Less is the shorter angle, more is the longer angle.

Last edited by mathman; November 14th, 2016 at 02:46 PM.
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