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Re: Point/Polygon Routine [message #5596 is a reply to message #5401]

Wed, 03 January 1996 00:00

jlaw
Messages: 11
Registered: November 1995

Junior Member

In article 760@ncar.ucar.edu, cavanaug@uars1.acd.ucar.edu (Charles Cavanaugh) writes:
>
> Does anyone have a routine that determines if a given 2-D point is inside a
> given 2-D polygon?

I did have, but I left it behind when I changed jobs.

Are you any good at finite elements??( This is where I looked this up)

Consider a triangle of points I,J,K with coordinates
( Xi,Yi) , (Xj,Yj ) , (Xk,Yk).

the Area of the triangle is then

( 1 Xi Yi )
0.5 * det ( 1 Xj Yj )
( 1 Xk Yk )

Now take the point P at ( Xp, Yp ).

( Strictly, if P is inside the triangle) we can define "Area coordinates"
as follows:

Li = area(pjk) / area(ijk)

Lj = area(pki) / area(ijk)

Lk = area(pij) / area(ijk)

If P is indeed inside the triangle, all the area coordinates are positive.
But if P is outside the triangle, one or more is negative.

For a polygon, split it into a set of triangles. If the point is inside one
of the triangles, it must be inside the polygon.

I think this all depends on the points being placed in the correct sense
around the triangle ( ie clockwise or anticlockwise.)You had better experiment
a little, but that is the basic principle.

It is not actually many lines of code.

all the best

f.

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[Message index]

		Point/Polygon Routine By: cavanaug on Tue, 02 January 1996 00:00
		Re: Point/Polygon Routine By: tildes on Tue, 09 January 1996 00:00
		Re: Point/Polygon Routine By: jlaw on Wed, 03 January 1996 00:00

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