File: inside.pro

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;+
; NAME:
;    INSIDE
;
; PURPOSE:
;
;    The purpose of this function is to indicate whether a specified
;    2D point is inside (returns a 1) a specified 2D polygon or outside
;    (returns a 0).
;
; AUTHOR:
;
;   FANNING SOFTWARE CONSULTING
;   David Fanning, Ph.D.
;   1645 Sheely Drive
;   Fort Collins, CO 80526 USA
;   Phone: 970-221-0438
;   E-mail: david@idlcoyote.com
;   Coyote's Guide to IDL Programming: http://www.idlcoyote.com/
;
; CATEGORY:
;
;    Utility.
;
; CALLING SEQUENCE:
;
;    result = INSIDE(x, y, xpts, ypts)
;
; INPUTS:
;
;    x:        A scalar or vector of the x coordinates of the 2D point(s) to check.
;    y:        A scalar or vector of the y coordinates of the 2D point(s) to check.
;    xpts:     The x coordinates of the 2D polygon.
;    ypts:     The y coordinates of the 2D polygon.
;
; OUTPUTS:
;
;    result:  A scalar or vector set to 1 if the point is inside the polygon and to
;             0 if the point is outside the polygon.
;
; KEYWORDS:
;
;    INDEX:   An output keyword. If set to a named variable, will return the indices
;             of the X and Y points that are inside the polygon.
;
; ALGORITHM:
;
;    Based on discussions on the IDL newsgroup (comp.lang.idl-pvwave) and
;    discussed here:
;
;      http://www.idlcoyote.com/tips/point_in_polygon.html
;
;    Primarily the work of B�rd Krane and William Connelly.
;
; MODIFICATION HISTORY:
;
;    Written by: David W. Fanning, 4 September 2003.
;    Vectorized the function in accord with William Connelly's suggestions 24 July 2005. DWF.
;-
;******************************************************************************************;
;  Copyright (c) 2008, by Fanning Software Consulting, Inc.                                ;
;  All rights reserved.                                                                    ;
;                                                                                          ;
;  Redistribution and use in source and binary forms, with or without                      ;
;  modification, are permitted provided that the following conditions are met:             ;
;                                                                                          ;
;      * Redistributions of source code must retain the above copyright                    ;
;        notice, this list of conditions and the following disclaimer.                     ;
;      * Redistributions in binary form must reproduce the above copyright                 ;
;        notice, this list of conditions and the following disclaimer in the               ;
;        documentation and/or other materials provided with the distribution.              ;
;      * Neither the name of Fanning Software Consulting, Inc. nor the names of its        ;
;        contributors may be used to endorse or promote products derived from this         ;
;        software without specific prior written permission.                               ;
;                                                                                          ;
;  THIS SOFTWARE IS PROVIDED BY FANNING SOFTWARE CONSULTING, INC. ''AS IS'' AND ANY        ;
;  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES    ;
;  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT     ;
;  SHALL FANNING SOFTWARE CONSULTING, INC. BE LIABLE FOR ANY DIRECT, INDIRECT,             ;
;  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED    ;
;  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;         ;
;  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND             ;
;  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT              ;
;  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS           ;
;  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.                            ;
;******************************************************************************************;
FUNCTION Inside, x, y, xpts, ypts, INDEX=index

    On_Error, 1

    sx = Size(xpts)
    sy = Size(ypts)
    IF (sx[0] EQ 1) THEN NX=sx[1] ELSE Message, 'X coordinates of polygon not a vector.'
    IF (sy[0] EQ 1) THEN NY=sy[1] ELSE Message, 'Y coordinates of polygon not a vector.'
    IF (NX EQ NY) THEN N = NX ELSE Message, 'Incompatable vector dimensions.'

    ; Close the polygon.
    tmp_xpts = [xpts, xpts[0]]
    tmp_ypts = [ypts, ypts[0]]

    ; Set up counters.
    i = indgen(N)
    ip = indgen(N)+1

    nn = N_Elements(x)
    X1 = tmp_xpts(i)  # Replicate(1,nn) - Replicate(1,n) # Reform([x],nn)
    Y1 = tmp_ypts(i)  # Replicate(1,nn) - Replicate(1,n) # Reform([y],nn)
    X2 = tmp_xpts(ip) # Replicate(1,nn) - Replicate(1,n) # Reform([x],nn)
    Y2 = tmp_ypts(ip) # Replicate(1,nn) - Replicate(1,n) # Reform([y],nn)

    ; Calculate the dot and cross products of the point to neighboring points in the polygon.
    ; Calculate the tangent of the angle between the two nearest adjacent points. If the point
    ; is outside the polygon, then summing over all possible angles will give a small number,
    ; in this case less than an arbitrary 0.1.
    dp = X1*X2 + Y1*Y2 ; Dot-product
    cp = X1*Y2 - Y1*X2 ; Cross-product
    theta = Atan(cp,dp)

    ret = Replicate(0L, N_Elements(x))
    i = Where(Abs(Total(theta,1)) GT 0.01, count)
    IF (count GT 0) THEN ret(i)=1

    ; Make this a scalar value if there is only one value.
    IF (N_Elements(ret) EQ 1) THEN ret=ret[0]

    ; If the index keyword is set, then return indices.
    IF (Arg_Present(index)) THEN ret=(Indgen(/Long, N_Elements(x)))(Where(ret eq 1))

    RETURN, ret

END