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## Copyright (C) 2024 David Legland
## 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.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = drawParabola(varargin)
%DRAWPARABOLA 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.
%
% drawParabola(AX, ...);
% Specifies handle of the axis to draw on.
%
% H = drawParabola(...);
% Returns an handle to the created graphical object.
%
%
% Example:
% figure(1); clf; hold on;
% axis equal; axis([0 100 0 100])
% % draw parabola with default parameterization bounds
% drawParabola([50 50 .2 30]);
% % draw parabola with more specific bounds and drawing style
% drawParabola([50 50 .2 30], [-3 3], 'color', 'r', 'linewidth', 2);
%
%
% See also
% drawCircle, drawEllipse
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-06-02
% Copyright 2006-2023 INRA - TPV URPOI - BIA IMASTE
% Extract parabola
if nargin < 1
error('MatGeom:geom2d:drawParabola:IllegalArgument', ...
'Please specify parabola representation');
end
% extract handle of axis to draw on
if isAxisHandle(varargin{1})
ax = varargin{1};
varargin(1) = [];
else
ax = gca;
end
% input parabola is given as a packed array
parabola = varargin{1};
varargin(1) = [];
x0 = parabola(:,1);
y0 = parabola(:,2);
a = parabola(:,3);
% check if parabola orientation is specified
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 array
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(ax, xt, yt, varargin{:});
end
% process output arguments
if nargout > 0
varargout = {h};
end
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