bht_round_rectangle(t,der,varargin)

function y = bht_round_rectangle(t,der,varargin)
% BHT_ROUND_RECTANGLE
% 
% Define a rectangle-shaped boundary.
% 
% Syntax
% 
%     y = BHT_ROUND_RECTANGLE(t,der,settings)
% 
% Description
% 
%     This function defines a rectangle-shaped boundary as a parameterized
%     closed line over [0,2*pi[. The input variable t (the parameter) is a
%     vector with all of its elements within [0,2*pi[. The function
%     returns, depending on the flag der:
% 
%     * der = 0: the coordinates of the points corresponding to the
%       parameters t(k). 
%     * der = 1: the coordinates of the tangent vectors
%       (the first derivatives of the parameterization). 
%     * der = 2: the second derivatives of the parameterization.
% 
%     The input variable settings is a row vector with six elements: 
%     *  the rectangle is centered at the point of coordinates settings(3:4). 
%     *  Its width is 2*settings(1) and its height is 2*settings(2).
%     *  Since boundaries have to be twice continuously differentiable lines within
%        BhT, rectangle's corners are smoothed. Thus, settings(5) has to be
%        within ]0,1] and is the smoothing parameter. 
%     *  At last, settings(6) is a flag (-1 or 1) for the orientation of the 
%        boundary: 1 means that the boundary has counterclockwise orientation
%        and -1 clockwise orientation.
% 
% See also BHT_BOUNDARY_CHECK

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                         %
%                      BIOHYDRODYNAMICS MATLAB TOOLBOX                    %
%                                                                         %
%                         A. MUNNIER and B. PINCON                        %
%                                                                         %
% [e-mail]        [e-mail]   %
% http://www.iecn.u-nancy.fr/~munnier  http://www.iecn.u-nancy.fr/~pincon %
%                                                                         %
%                                                                         %
%                      INSTITUT ELIE CARTAN, NANCY 1                      %
%                       http://www.iecn.u-nancy.fr/                       %
%                                                                         %
%                      INRIA Lorraine, Projet CORIDA                      %
%                    http://www.iecn.u-nancy.fr/~corida/                  %
%                                                                         %  
%                                                                         %  
%                                                                         %
%                                                                         %
%                            August 15th 2008                             %
%                                                                         %
%                                               GNU GPL v3 licence        %
%                                                                         %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%##########################################################################
% Reading settings
if isempty(varargin)
    error('Boundary''s parameters (row vector of at least six elements) are missing.')
else
parameters = varargin{1};
end

if length(parameters) ~= 6
    error('Boundary''s parameter vector must have at least six elements');
end

% =========================================================================
% smoothing parameter
epsilon = parameters(5);
if epsilon <=0 || epsilon > 1
    error('Fifth element of parameter vector is the smoothing parameter (must be between 0 and 1)') 
end
epsilon = epsilon*pi/4;
% =========================================================================
% rectangle's size
L = parameters(3);
l = parameters(4);
% center
center = reshape(parameters(1:2),2,1);
% =========================================================================
orient = parameters(6); % -1 for ext and 1 for int
if orient^2 ~= 1
    error('Last element of parameter vector must be 1 (fluid outside) or -1 (fluid inside)')
end
% =========================================================================
n = length(t);
t = reshape(t,1,n); % assure la forme ligne  

[x1,dx1,ddx1] = bht_step1(t,pi/4+epsilon,L);
x1 = x1 + center (1)*ones(1,n);
[x2,dx2,ddx2] = bht_step2(t,pi/4+epsilon,-orient*l);
x2 = x2 + center(2)*ones(1,n);

if der == 0
  y = [x1; x2];
elseif der == 1
  y = [dx1; dx2];
elseif der == 2
  y = [ddx1; ddx2];
else
  error('der doit etre 0, 1 ou 2')
end