November 14th, 2016, 07:49 AM  #1 
Newbie Joined: Nov 2016 From: Canada Posts: 1 Thanks: 0  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. 
November 14th, 2016, 01:21 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 600 Thanks: 320 
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 $\ell_2 = 2\pi r  \ell_1$ 
November 14th, 2016, 02:44 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,136 Thanks: 468 
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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