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arcsample.pro
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arcsample.pro
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;+
; NAME:
; ARCSAMPLE
;
; PURPOSE:
;
; Given X and Y points that describe a closed curve in 2D space,
; this function returns an output curve that is sampled a specified
; number of times at approximately equal arc distances.
;
; 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:
; Utilities
;
; CALLING SEQUENCE:
;
; ArcSample, x_in, y_in, x_out, y_out
;
; INPUT_PARAMETERS:
;
; x_in: The input X vector of points.
; y_in: The input Y vector of points.
;
; OUTPUT_PARAMETERS:
;
; x_out: The output X vector of points.
; y_out: The output Y vector of points.
;
; KEYWORDS:
;
; POINTS: The number of points in the output vectors. Default: 50.
;
; PHASE: A scalar between 0.0 and 1.0, for fine control of where interpolates
; are sampled. Default: 0.0.
;
; MODIFICATION HISTORY:
;
; Written by David W. Fanning, 1 December 2003, based on code supplied
; to me by Craig Markwardt.
;-
;******************************************************************************************;
; 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. ;
;******************************************************************************************;
PRO ArcSample, x_in, y_in, x_out, y_out, POINTS=points, PHASE=phase
; Check parameters.
IF N_Elements(points) EQ 0 THEN points = 50
IF N_Elements(phase) EQ 0 THEN phase = 0.0 ELSE phase = 0.0 > phase < 1.0
; Make sure the curve is closed (first point same as last point).
npts = N_Elements(x_in)
IF (x_in[0] NE x_in[npts-1]) OR (y_in[0] NE y_in[npts-1]) THEN BEGIN
x_in = [x_in, x_in[0]]
y_in = [y_in, y_in[0]]
npts = npts + 1
ENDIF
; Interpolate very finely.
nc = (npts -1) * 100
t = DIndgen(npts)
t1 = DIndgen(nc + 1) / 100
x1 = Spl_Interp(t, x_in, Spl_Init(t, x_in), t1)
y1 = Spl_Interp(t, y_in, Spl_Init(t, y_in), t1)
avgslopex = (x1(1)-x1(0) + x1(nc)-x1(nc-1)) / (t1(1)-t1(0)) / 2
avgslopey = (y1(1)-y1(0) + y1(nc)-y1(nc-1)) / (t1(1)-t1(0)) / 2
dx1 = Spl_Init(t, x_in, yp0=avgslopex, ypn_1=avgslopex)
dy1 = Spl_Init(t, y_in, yp0=avgslopey, ypn_1=avgslopey)
x1 = Spl_Interp(t, x_in, dx1, t1)
y1 = Spl_Interp(t, y_in, dy1, t1)
; Compute cumulative path length.
ds = SQRT((x1(1:*)-x1)^2 + (y1(1:*)-y1)^2)
ss = [0d, Total(ds, /Cumulative)]
; Invert this curve, solve for TX, which should be evenly sampled in
; the arc length space.
sx = DIndgen(points) * Max(ss)/points + phase
tx = Spl_Interp(ss, t1, Spl_Init(ss, t1), sx)
; Reinterpolate the original points using the new values of TX.
x_out = Spl_Interp(t, x_in, dx1, tx)
y_out = Spl_Interp(t, y_in, dy1, tx)
x_out = [x_out, x_out[0]]
y_out = [y_out, y_out[0]]
END