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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{h} = } drawParabola (@var{parabola})
## @deftypefnx {Function File} {@var{h} = } drawParabola (@var{parabola}, @var{t})
## @deftypefnx {Function File} {@var{h} = } drawParabola (@dots{}, @var{param}, @var{value})
## Draw a parabola on the current axis.
##
## drawParabola(PARABOLA);
## Draws a vertical parabola, defined by its vertex and its parameter.
## Such a parabola admits a vertical axis of symetry.
##
## The algebraic equation of parabola is given by:
## (Y - YV) = A * (X - VX)^2
## Where XV and YV are vertex coordinates and A is parabola parameter.
##
## A parametric equation of parabola is given by:
## x(t) = t + VX;
## y(t) = A * t^2 + VY;
##
## PARABOLA can also be defined by [XV YV A THETA], with theta being the
## angle of rotation of the parabola (in degrees and Counter-Clockwise).
##
## drawParabola(PARABOLA, T);
## Specifies which range of 't' are used for drawing parabola. If T is an
## array with only two values, the first and the last values are used as
## interval bounds, and several values are distributed within this
## interval.
##
## drawParabola(..., NAME, VALUE);
## Can specify one or several graphical options using parameter name-value
## pairs.
##
## H = drawParabola(...);
## Returns an handle to the created graphical object.
##
##
## Example:
## @example
## figure(1); clf; hold on;
## drawParabola([50 50 .2 30]);
## drawParabola([50 50 .2 30], [-1 1], 'color', 'r', 'linewidth', 2);
## axis equal;
## @end example
##
## @seealso{drawCircle, drawEllipse}
## @end deftypefn
function varargout = drawParabola(varargin)
# Extract parabola
if nargin<1
error('geom2d:IllegalArgument', ...
'Please specify parabola representation');
end
# input parabola is given as a packed array
parabola = varargin{1};
varargin(1) = [];
x0 = parabola(:,1);
y0 = parabola(:,2);
a = parabola(:,3);
if size(parabola, 2)>3
theta = parabola(:, 4);
else
theta = zeros(length(a), 1);
end
# extract parametrisation bounds
bounds = [-100 100];
if ~isempty(varargin)
var = varargin{1};
if isnumeric(var)
bounds = var;
varargin(1) = [];
end
end
# create parametrisation
if length(bounds)>2
t = bounds;
else
t = linspace(bounds(1), bounds(end), 100);
end
# create handle array (in the case of several parabola)
h = zeros(size(x0));
# draw each parabola
for i=1:length(x0)
# compute transformation
trans = ...
createTranslation(x0(i), y0(i)) * ...
createRotation(deg2rad(theta(i))) * ...
createScaling(1, a);
# compute points on the parabola
[xt yt] = transformPoint(t(:), t(:).^2, trans);
# draw it
h(i) = plot(xt, yt, varargin{:});
end
# process output arguments
if nargout>0
varargout{1}=h;
end
endfunction

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