/usr/share/octave/packages/geometry-1.7.0/polynomialCurves2d/polynomialCurveCentroid.m is in octave-geometry 1.7.0-1build1.
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## 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
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{c} =} polynomialCurveCentroid (@var{t}, @var{xcoef}, @var{ycoef})
## @deftypefnx {Function File} {@var{c} =} polynomialCurveCentroid (@var{t}, @var{coefs})
## @deftypefnx {Function File} {@var{c} =} polynomialCurveCentroid (@dots{}, @var{tol})
## Compute the centroid of a polynomial curve
##
## @var{xcoef} and @var{ycoef} are row vectors of coefficients, in the form:
## [a0 a1 a2 ... an]
## @var{t} is a 1x2 row vector, containing the bounds of the parametrization
## variable: @var{t} = [T0 T1], with @var{t} taking all values between T0 and T1.
## @var{c} contains coordinate of the polynomial curve centroid.
##
## @var{coefs} is either a 2xN matrix (one row for the coefficients of each
## coordinate), or a cell array.
##
## @var{tol} is the tolerance fo computation (absolute).
##
## @seealso{polynomialCurves2d, polynomialCurveLength}
## @end deftypefn
function centroid = polynomialCurveCentroid(tBounds, varargin)
## Extract input parameters
# parametrization bounds
t0 = tBounds(1);
t1 = tBounds(end);
# polynomial coefficients for each coordinate
var = varargin{1};
if iscell(var)
cx = var{1};
cy = var{2};
varargin(1) = [];
elseif size(var, 1)==1
cx = varargin{1};
cy = varargin{2};
varargin(1:2)=[];
else
cx = var(1,:);
cy = var(2,:);
varargin(1)=[];
end
# convert to Octave polyval format
cx = cx(end:-1:1);
cy = cy(end:-1:1);
# tolerance
tol = 1e-6;
if ~isempty(varargin)
tol = varargin{1};
end
## compute length by numerical integration
# compute derivative of the polynomial
dx = polyder (cx);
dy = polyder (cy);
# 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;
endfunction
%!demo
%! bounds = [-1 1];
%! coefs = [0 1 1; 0 -1 2];
%! c = polynomialCurveCentroid (bounds, coefs);
%!
%! drawPolynomialCurve (bounds, coefs(1,:), coefs(2,:));
%! hold on
%! plot (c(1),c(2),'sr')
%! hold off
%! # -------------------------------------------------
%! # Centriod of a polynomial curve
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