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Subject: Re: curvature and radius of curvature of a plane curve
Date: Mon, 10 Aug 2009 15:05:19 +0000 (UTC)
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> Hello Michael,
>   What is the difference between a clockwise and a counterclockwise arc?  If you move from one of its ends toward the other, that might be clockwise motion, but if you start from the opposite end, it would then be counterclockwise motion.  If you rotate an arc of a certain angle through 360 degrees you have gone through all possible such arcs.  At what point does it change from being clockwise to counterclockwise?  What I am saying is that there is nothing in a circular arc that makes it inherently clockwise or counterclockwise; it is only motion from one end toward the other end that would render it so.
>   Of course there is a difference between an arc that is convex toward the left from one convex toward the right, or between convex downwards and convex upwards, but that is a different matter.
> Roger Stafford

Hi Roger,

Good points.  I have worked with the images for so long that I had forgotten that there was an implicit reference point for cw and ccw.  I feel silly; an arc segment would have to have beginning point for it to have a cw or ccw direction.  

Assume there is a reference point directly in the center of the matrix and I want to evaluate each arc&#8217;s cw or ccw direction in regards to that center reference.  In other words, the closest endpoint of an arc segment to the center, is defined as the beginning point for a segment.

Think of the physics cloud chamber photographs of electron and positron paths.  It is easy just to look at the decaying spiral paths and know if it was an electron or positron. I had completely forgotten that an EM field was the implicit reference frame for such detectors.

I am not dealing with complete spirals, but with just some spiral arcs (less than 2pi of curvature) decaying into a center point.  My problem being that have both possible types, cw and ccw arcs crossing each other in the same image and I want write a program to separate them into two images.   

So I have to find the lines, and find out which end point of the line is closest to the center, and then characterize each line as cw or ccw, and then separate a complex image into two simpler ones.  No Problem.   <smile>

I think I can do most of that with a radial search, but not sure about the characterizing the cw or ccw directions.  On a side note, wonder if there is already code out there from particle physics, evaluating overlaying particle spirals would be a much harder task.