--- /dev/null
+%% Copyright (c) 2011, INRA
+%% 2007-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{pp} =} cbezier2poly (@var{points})
+%% @deftypefnx {Command} {Function File} {[@var{x} @var{y}] =} cbezier2poly (@var{points},@var{t})
+%% Returns the polynomial representation of the cubic Bezier defined by the control points @var{points}.
+%%
+%% With only one input argument, calculates the polynomial @var{pp} of the cubic
+%% Bezier curve defined by the 4 control points stored in @var{points}. The first
+%% point is the inital point of the curve. The segment joining the first point
+%% with the second point (first center) defines the tangent of the curve at the initial point.
+%% The segment that joints the third point (second center) with the fourth defines the tanget at
+%% the end-point of the curve, which is defined in the fourth point.
+%% @var{points} is either a 4-by-2 array (vertical concatenation of point
+%% coordinates), or a 1-by-8 array (horizotnal concatenation of point
+%% coordinates). @var{pp} is a 2-by-3 array, 1st row is the polynomial for the
+%% x-coordinate and the 2nd row for the y-coordinate. Each row can be evaluated
+%% with @code{polyval}. The polynomial @var{pp}(t) is defined for t in [0,1].
+%%
+%% When called with a second input argument @var{t}, it returns the coordinates
+%% @var{x} and @var{y} corresponding to the polynomial evaluated at @var{t} in
+%% [0,1].
+%%
+%% @seealso{drawBezierCurve, polyval}
+%% @end deftypefn
+
+function varargout = cbezier2poly (points, ti=[])
+
+
+ % 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,:);
+ elseif size(points,2) == 8
+ % 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);
+ else
+ print_usage ;
+ end
+
+ % compute coefficients of Bezier Polynomial
+ pp = zeros(2,4);
+
+ pp(:,4) = [p1(1); ...
+ p1(2)];
+ pp(:,3) = [3 * c1(1) - 3 * p1(1); ...
+ 3 * c1(2) - 3 * p1(2)];
+ pp(:,2) = [3 * p1(1) - 6 * c1(1) + 3 * c2(1); ...
+ 3 * p1(2) - 6 * c1(2) + 3 * c2(2)];
+ pp(:,1) = [p2(1) - 3 * c2(1) + 3 * c1(1) - p1(1); ...
+ p2(2) - 3 * c2(2) + 3 * c1(2) - p1(2)];
+
+ if isempty (ti)
+ varargout{1} = pp;
+ else
+ varargout{1} = polyval (pp(1,:), ti);
+ varargout{2} = polyval (pp(2,:), ti);
+ end
+
+endfunction
+
+%!demo
+%! points = [45.714286 483.79075; ...
+%! 241.65656 110.40445; ...
+%! 80.185847 741.77381; ...
+%! 537.14286 480.93361];
+%!
+%! pp = cbezier2poly(points);
+%! t = linspace(0,1,64);
+%! x = polyval(pp(1,:),t);
+%! y = polyval(pp(2,:),t);
+%! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',...
+%! points([2 3],1),points([2 3],2),'o');
+%! line(points([2 1],1),points([2 1],2),'color','r');
+%! line(points([3 4],1),points([3 4],2),'color','r');
+
+%!demo
+%! points = [0 0; ...
+%! 1 1; ...
+%! 1 1; ...
+%! 2 0];
+%!
+%! t = linspace(0,1,64);
+%! [x y] = cbezier2poly(points,t);
+%! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',...
+%! points([2 3],1),points([2 3],2),'o');
+%! line(points([2 1],1),points([2 1],2),'color','r');
+%! line(points([3 4],1),points([3 4],2),'color','r');
+
+%!test
+%! points = [0 0; ...
+%! 1 1; ...
+%! 1 1; ...
+%! 2 0];
+%! t = linspace(0,1,64);
+%!
+%! [x y] = cbezier2poly(points,t);
+%! pp = cbezier2poly(points);
+%! x2 = polyval(pp(1,:),t);
+%! y2 = polyval(pp(2,:),t);
+%! assert(x,x2);
+%! assert(y,y2);
+
+%!test
+%! points = [0 0; ...
+%! 1 1; ...
+%! 1 1; ...
+%! 2 0];
+%! t = linspace(0,1,64);
+%!
+%! p = reshape(points,1,8);
+%! [x y] = cbezier2poly(p,t);
+%! pp = cbezier2poly(p);
+%! x2 = polyval(pp(1,:),t);
+%! y2 = polyval(pp(2,:),t);
+%! assert(x,x2);
+%! assert(y,y2);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff