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Subject: Re: Coping with asymptotes in tan function
Date: Tue, 7 Dec 2010 20:35:29 +0000 (UTC)
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"Jane " <j.l.terry@hotmail.co.uk> wrote in message <idlsbt$9ip$1@fred.mathworks.com>...
> Hi, I have written a function (probably not very efficiently) to measure the distance along a line, defined by the angle from the negative y-axis and passing through a known point.
> 
> The problem I am having is coping with instance where the user selects the angle phi = [0, 90, 180, 270,...] the problem becoems ill-conditioned.  I'm sure there must be an easy work around for this, but I've become so bogged down in the details I can't see it!
> 
> I would appreciate any help.
>.......
- - - - - - - -
  You are making a hard job out of a very easy problem, Jane.  In effect, you are rotating to a new coordinate system with a changed origin.  The equations for that are:

 v = (y-ey)*cos(phi) - (x-ex)*sin(phi)
 u = (y-ey)*sin(phi) + (x-ex)*cos(phi)

where (x,y) are the coordinates of the grid point in question, phi is the angle measured counterclockwise from the positive y-axis to the "centre plume line", (ex,ey) are the coordinates of the "emission source", and u and v are the requested orthogonal distance and distance along the plume line, respectively.

  Note that u and v are signed quantities which can be either positive or negative depending on the coordinates x and y.  If you wish phi to measured clockwise, just change the signs of the sin(phi) in the above equations.  If you wish to switch the directions u or v are to be measured in, just switch their signs in the equations accordingly.  You were not specific on this point.

Roger Stafford