Subject: Re: [xsl] sorting by comparing two nodes From: David Carlisle <davidc@xxxxxxxxx> Date: Wed, 21 Dec 2005 23:58:18 GMT |
> angle the line segment P(0) - P(i) makes with the x-axis. So the angle is dependent > on the reference point, not the quadrant. sorry I meant "quadrant" after moving the reference point to the origin. if your points (after subtracting the reference point coordinates) are (a,b) and (c,d) are all positive (ie in the first quadrant) you don't need to compare points pairwise you can just work out the tangent y/x and sort on that. So that combined with some tests on the sign of the coordinates is all you need. > sorry, perhaps I missed your point. My english is not the best. > What do you mean by transitive? P>Q and Q>R implies P>R > Given a set of points the comparison > function of course determines just one possible sorting. as written I think not, if your points are (1,1) and (-1,-1) then your formula comes to 0 whichever way you compare the two points, so it is unspecified which order the points should be in. So you need to consider each quadrant separately, then as I say above you can just consider one point at a time, if you know all coordinates are positive the test p1x*p2y > p2x*p1y is equivalent to the test p1x/p1y > p2x/p2y so you can sort on x/y for each point separately. David ________________________________________________________________________ This e-mail has been scanned for all viruses by Star. The service is powered by MessageLabs. For more information on a proactive anti-virus service working around the clock, around the globe, visit: http://www.star.net.uk ________________________________________________________________________
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