;+ ; 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