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polynomialCurveCentroid.m    109 lines (94 with data), 3.8 kB

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## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 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.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''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 THE AUTHOR OR CONTRIBUTORS 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; 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 centroid = polynomialCurveCentroid(tBounds, varargin)
#POLYNOMIALCURVECENTROID Compute the centroid of a polynomial curve
#
# C = polynomialCurveCentroid(T, XCOEF, YCOEF)
# XCOEF and YCOEF are row vectors of coefficients, in the form:
# [a0 a1 a2 ... an]
# T is a 1x2 row vector, containing the bounds of the parametrization
# variable: T = [T0 T1], with T taking all values between T0 and T1.
# C contains coordinate of the polynomial curve centroid.
#
# C = polynomialCurveCentroid(T, COEFS)
# COEFS is either a 2xN matrix (one row for the coefficients of each
# coordinate), or a cell array.
#
# C = polynomialCurveCentroid(..., TOL)
# TOL is the tolerance fo computation (absolute).
#
# Example
# polynomialCurveCentroid
#
# See also
# polynomialCurves2d, polynomialCurveLength
#
#
# ------
# Author: David Legland
# e-mail: david.legland@gignon.inra.fr
# Created: 2007-02-23
# Copyright 2007 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.
## Extract input parameters
# parametrization bounds
t0 = tBounds(1);
t1 = tBounds(end);
# polynomial coefficients for each coordinate
var = varargin{1};
if iscell(var)
xCoef = var{1};
yCoef = var{2};
varargin(1) = [];
elseif size(var, 1)==1
xCoef = varargin{1};
yCoef = varargin{2};
varargin(1:2)=[];
else
xCoef = var(1,:);
yCoef = var(2,:);
varargin(1)=[];
end
# tolerance
tol = 1e-6;
if ~isempty(varargin)
tol = varargin{1};
end
## compute length by numerical integration
# compute derivative of the polynomial
dx = polynomialDerivate(xCoef);
dy = polynomialDerivate(yCoef);
# convert to polyval format
dx = dx(end:-1:1);
dy = dy(end:-1:1);
cx = xCoef(end:-1:1);
cy = yCoef(end:-1:1);
# compute curve length by integrating the Jacobian
L = quad(@(t)sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol);
# compute first coordinate of centroid
xc = quad(@(t)polyval(cx, t).*sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol);
# compute first coordinate of centroid
yc = quad(@(t)polyval(cy, t).*sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol);
# divide result of integration by total length of the curve
centroid = [xc yc]/L;