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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 = cubicBezierToPolyline(points, varargin)
%CUBICBEZIERTOPOLYLINE Compute equivalent polyline from bezier curve control.
%
% POLY = cubicBezierToPolyline(POINTS, N)
% Creates a polyline with N edges from the coordinates of the 4 control
% points stored in POINTS.
% POINTS is either a 4-by-2 array (vertical concatenation of point
% coordinates), or a 1-by-8 array (horizontal concatenation of point
% coordinates).
% The result is a (N-1)-by-2 array.
%
% POLY = cubicBezierToPolyline(POINTS)
% Assumes N = 64 edges as default.
%
% [X Y] = cubicBezierToPolyline(...)
% Returns the result in two separate arrays for X and Y coordinates.
%
%
% Example
% poly = cubicBezierToPolyline([0 0;5 10;10 5;10 0], 100);
% drawPolyline(poly, 'linewidth', 2, 'color', 'g');
%
% See also
% drawBezierCurve, drawPolyline
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-10-06, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% default number of discretization steps
N = 64;
% check if discretization step is specified
if ~isempty(varargin)
var = varargin{1};
if length(var) == 1 && isnumeric(var)
N = round(var);
end
end
% parametrization variable for bezier (use N+1 points to have N edges)
t = linspace(0, 1, N+1)';
% rename points
if size(points, 2)==2
% case of points given as a 4-by-2 array
p1 = points(1,:);
c1 = points(2,:);
c2 = points(3,:);
p2 = points(4,:);
else
% case of points given as a 1-by-8 array, [X1 Y1 CX1 CX2..]
p1 = points(1:2);
c1 = points(3:4);
c2 = points(5:6);
p2 = points(7:8);
end
% compute coefficients of Bezier Polynomial, using polyval ordering
coef(4, 1) = p1(1);
coef(4, 2) = p1(2);
coef(3, 1) = 3 * c1(1) - 3 * p1(1);
coef(3, 2) = 3 * c1(2) - 3 * p1(2);
coef(2, 1) = 3 * p1(1) - 6 * c1(1) + 3 * c2(1);
coef(2, 2) = 3 * p1(2) - 6 * c1(2) + 3 * c2(2);
coef(1, 1) = p2(1) - 3 * c2(1) + 3 * c1(1) - p1(1);
coef(1, 2) = p2(2) - 3 * c2(2) + 3 * c1(2) - p1(2);
% compute position of vertices
x = polyval(coef(:, 1), t);
y = polyval(coef(:, 2), t);
if nargout <= 1
varargout = {[x y]};
else
varargout = {x, y};
end
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