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MGH_POLY_INSIDE

## Name

MGH_POLY_INSIDE

## Purpose

Determine whether a point or set of points is inside a polygon.

## Calling Sequence

Result = MGH_POLY_INSIDE(XP, YP, X, Y)

## Inputs

XP,YP: Vectors of X, Y positions defining the polygon.
X,Y: X, Y position(s) defining the point(s) to be tested. Can
be vectors.

## Input Keywords

EDGE: Set this keyword to accept edge (& vertex) points as
"inside". Default is to reject them.
NAN: Set this keyword to specify that all points for which
X or Y is not finite (eg Nan, Inf) are to return 0.
Default is to process non-finite points, which leads
to floating point errors and an undefined result for
that point.

## Outputs

The function returns an array of the same shape as X. Each element
is 0 if the point is outside the polygon, 1 if it is inside the polygon.

## Procedure

This routine calculates the displacement vectors from each point to
all the vertices of the polygon and then takes angles between each pair
of successive vectors. The sum of the angles is zero
for a point outside the polygon, and +/- 2*pi for a point
inside. A point on an edge will have one such angle
equal to +/- pi. Points on a vertex have a zero displacement vector.

## References

Note that the question of how to determine whether a point is
inside or outside a polygon was discussed on comp.lang.idl-pvwave
in October 1999. The following is quoted from a post by Randall Frank
<randall-frank@computer.org>:
I would suggest you read the Graphics FAQ on this issue and also
check Graphics Gem (I think volume 1) for a more detailed explanation
of this problem. The upshot is that there really are three core methods
and many variants. In general, you can sum angles, sum signed areas or
clip a line. There are good code examples of all these approaches on the
net which can be coded into IDL very quickly. It also depends on how
you intend to use the function. If, you are going to repeatedly test many
points, you are better off using one of the sorted variants of the line
clipping techniques. In general, the line clipping techniques are the
fastest on the average, but have poor worst case performance without
the sorting overhead. The angle sum is one of the slowest methods
unless you can get creative and avoid the transcendentals (and you
can). The area sum approach generally falls in between. In IDL code,
I believe you can vectorize the latter with some setup overhead, making
it the fastest for .pro code when testing multiple points with one
point per call.

## Further Resources

* "Misc Notes - WR Franklin", http://www.ecse.rpi.edu/Homepages/wrf/misc.html:
includes a reference (broken @ Jul 2001) to his point-in-polygon code.
* Comp.graphics.algorithms FAQ, http://www.faqs.org/faqs/graphics/algorithms-faq/:
See subject 2.03

MGH_PNPOLY, which implements a line-clipping technique.
###########################################################################
This software is provided subject to the following conditions:
1. NIWA makes no representations or warranties regarding the
accuracy of the software, the use to which the software may
be put or the results to be obtained from the use of the
software. Accordingly NIWA accepts no liability for any loss
or damage (whether direct of indirect) incurred by any person
through the use of or reliance on the software.
2. NIWA is to be acknowledged as the original author of the
software where the software is used or presented in any form.
###########################################################################

## Modification History

Mark Hadfield, June 1995:
Written based on ideas in MATLAB routine INSIDE.M in the WHOI
Oceanography Toolbox v1.4 (R. Pawlowicz, 14 Mar 94,
rich@boreas.whoi.edu).
Mark Hadfield, Dec 2000:
Updated.
Mark Hadfield, Jul 2001:
Changed argument order: polygon vertices are now before test
position(s).

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