Message-ID: <44353210.2020704@lancaster.ac.uk>
Date: 2006-04-06T15:21:52Z
From: Barry Rowlingson
Subject: Truncating polygons in R
In-Reply-To: <07E228A5BE53C24CAD490193A7381BBB30E920@LP-EXCHVS07.CO.IHC.COM>
Gregory Snow wrote:
> I have one suggested extension to Barry's idea.
>
> With Barry's idea the polygons will all be inside the square, but there
> will be some area in the square that is not inside any of the polygons.
> If you want the entire square to be included within the polygons then
> take Barrys Idea of projecting the points perpendicular to the sides,
> but instead of projecting them onto the sides, project them beyond that
> side so that they are the same distance from the side of the square.
> Then the set of points that are equal distance from the projected point
> and the original point will fall along the border of the square.
Nice.
I implemented my method this afternoon and one thing I hadn't expected
was that it can generate disconnected polygons! If you have a point over
in a corner with not much near it the guard points round the edges can
cut it off from the rest of the data points. Obviously the tessalation
as a whole is connected, but when you drop the guard points' polygons
you get an island. I suspect Greg's technique can't do that since the
whole square is filled with polygons from your data points.
Fun.
Barry