John K Masters
|| at Aug 13, 2007 at 8:54 pm
On 10:58 Mon 13 Aug , Erik Max Francis wrote:
Steve Holden wrote:
About the best interpretation I can think of is to add 180 degrees to
the angle and reverse the sign of the magnitude, but this would be a
hack. Where are those coordinates coming from?
Well, sometimes in polar coordinates (r, theta), r is allowed to be
negative. The usual translation from polar to Cartesian coordinates
makes this meaningful, albeit weird, so in effect the resulting
positions are just reflections around the origin.
Which I suppose is what the original poster was asking about, but it's
still not clear.
Many years ago when I started programming machine tools (on punched
paper tape) if you wished to specify a cutter path around a radius as
being more than 180 degrees you programmed it as a negative r value.
There are 2 possible paths from x1y1 to x2y2 along a radius r and going
in the same direction; that less than 180 deg and that more than 180
deg, unless the radius is exactly 180. But this was rarely used, the
other method of specifying the end point as an incremental value in
relation to the radius centre is less error prone when the arcs are
close to 180.
Sorry about the slight diversion but I'm getting nostalgic.
War is God's way of teaching Americans geography
Ambrose Bierce (1842 - 1914)