%% 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>
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%% -*- 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);
