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From: "Dale" <hazelREMOVETHISnusse@gmail.com>
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Subject: Deciding which side a numerically generated line you are on
Date: Fri, 16 Jan 2009 23:41:02 +0000 (UTC)
Organization: University of California Davis
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I am looking at a number of functions of two variables (say x and y), and I am restricting my attention to x \in [-pi/2, pi/2] and y \in [-pi, pi].  Call this set S \subset R^2.  The problem is such that I really only want to look at some of the data in this subset of the plane.  I numerically generate some boundary curves that separate feasible (x,y) coordinates from infeasible ones (by solving a system of two equations in two unknowns), and I need to be able to decide if an arbitrary point in S is on one side or the other side of the numerically generated curve.  I have the points on the curve as a 2xn array, each column of which is a point (x,y) on the curve.  

Here is a link to what the boundary curves look like:
http://www.dlpeterson.com/feasible_lean_steer.pdf

The reason for why I need to do this is because on one side of my curve I can't compute a number of the quantities and if I try, I run into a slew of other numerical non-convergence issues due to the inherent infeasibility of points on that side of the line.

Any ideas?

Thanks,
Luke