[R] points with-in boundaries of a map

[(Ted Harding)]

Apologies (red-faced)!! In my reply below I wrote "pi" and "-pi" where
it should have been "2*pi" and "-2*pi". See at [***] below.
Sorry for the noise,
Ted.

On 23-Mar-2014 22:50:50 Jim Lemon wrote:
> On 03/23/2014 10:29 PM, eliza botto wrote:
>> Thankyou very much jim. it worked! but regarding second part of my
>> question, isn't there a way to read the coordinates of intersecting
>> lines with the premises of the map?
> 
> Hi Eliza,
> I think you want the "locator" function, which will return the 
> coordinates to the accuracy that you can click on a point in the plot.
> 
> Jim

There is a possible analytical approach to this. If the boundary of
a simple closed region is given as a series of straight lines which
join successive points as one proceeds continuously round the boundary
of theregion, and one has the data of the (x,y) coordinates of the points
in that order (with the last point the same as the first), then one
can proceed as follows:

Let the points be P1=(x1,y1), P2=(x2,y2), ... , PN=(xN,yN)=P1
in the order specified above.

Since the grid lines have been drawn at specified intervals, you
can work through every point (x0,y0) which is an intersection.

Let (x0,y0) be a point of intersection of the grid of lines. Now you
know the coordinates of (x0,y0) already, so the question is whether
this point is inside or outside the region.

Consider a line jpoining (x0,y0) to (x1,y1). Now work out the angle
through which the line rotates when it is moved so that it joins
(x0,y0) to (x2,y2); say this is phi2 (clockwise positive, anticlockise
negative). Similarly work out phi3, the angle through which the line
next rotates when it is further moved so that it joins (x0,y0) to (x2,y2);
and so on.

Now add up phi2 + phi3 + ... + phiN

If the point (x0,y0) is inside the region, and you have proceeded
consecutively along the boundary, then this sum of angles will be
[***]pi or -pi. [***Should be] 2*pi or -2*pi.
If (x0,y0) is outside the region, then this sum will be zero.

So you can work through all the intersections of the grid lines,
and for each intersection you can determine whether it is inside
or outside; and, if it is inside, you already know its coordinates.

It can get more complicated if the region is not simply-connected.
E.g. if you do not want to count points (x0,y0) which are within
the boundary coastline but also are within the boundary of an
inland lake; or, further, you do want to count points which are
on an island in the lake; and so on.

The essential for following a procedure of this kind is that you
can extract from the data from which the map is drawn the coordinates
of a series of points which are in consecutive order as one proceeds
along the boundar of a region. Not all geographic data have the
coordinates in such an order -- one can find datasets such that the
boundary is drawn as a set of separate partial boundaries which
are in no particular order as a whole; and in some datasets the
different separate parts of the boundary do not exactly match up
at the points where they should exactly join.

Hoping this helps,
Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 23-Mar-2014  Time: 23:47:15
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E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 24-Mar-2014  Time: 08:06:23
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