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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.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{v} =} polynomialCurveDerivative (@var{t}, @var{xcoef},@var{ycoef})
## @deftypefnx {Function File} {@var{v} =} polynomialCurveDerivative (@var{t}, @var{coefs})
## Compute derivative vector of a polynomial curve
##
## @var{xcoef} and @var{ycoef} are row vectors of coefficients, in the form:
## [a0 a1 a2 ... an]
## @var{v} is a 1x2 array containing direction of derivative of polynomial
## curve, computed for position @var{t}. If @var{t} is a vector, @var{v} has as many rows
## as the length of @var{t}.
##
## @var{coefs} is either a 2xN matrix (one row for the coefficients of each
## coordinate), or a cell array.
##
## @seealso{polynomialCurves2d, polynomialCurveNormal, polynomialCurvePoint,
## polynomialCurveCurvature}
## @end deftypefn
function v = polynomialCurveDerivative(t, varargin)
## Extract input parameters
# polynomial coefficients for each coordinate
var = varargin{1};
if iscell(var)
xCoef = var{1};
yCoef = var{2};
elseif size(var, 1)==1
xCoef = varargin{1};
yCoef = varargin{2};
else
xCoef = var(1,:);
yCoef = var(2,:);
end
# convert to Octave polynomial convention
xCoef = xCoef(end:-1:1);
yCoef = yCoef(end:-1:1);
# compute derivative of the polynomial
dx = polyder (xCoef);
dy = polyder (yCoef);
# numerical integration of the Jacobian of parametrized curve
v = [polyval(dx, t) polyval(dy, t)];
endfunction