%-------------------------------------------------------------------------------------------------------------------%
%
% IB2d is an Immersed Boundary Code (IB) for solving fully coupled non-linear 
% 	fluid-structure interaction models. This version of the code is based off of
%	Peskin's Immersed Boundary Method Paper in Acta Numerica, 2002.
%
% Author: Nicholas A. Battista
% Email:  nick.battista@unc.edu
% Date Created: May 27th, 2015
% Institution: UNC-CH
%
% This code is capable of creating Lagrangian Structures using:
% 	1. Springs
% 	2. Beams (*torsional springs)
% 	3. Target Points
%	4. Muscle-Model (combined Force-Length-Velocity model, "HIll+(Length-Tension)")
%
% One is able to update those Lagrangian Structure parameters, e.g., spring constants, resting %%	lengths, etc
% 
% There are a number of built in Examples, mostly used for teaching purposes. 
% 
% If you would like us %to add a specific muscle model, please let Nick (nick.battista@unc.edu) know.
%
%--------------------------------------------------------------------------------------------------------------------%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: creates the BEAM-EXAMPLE geometry and prints associated input files
%
% PYTHON INDEXING!!!
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function BeamCurve()

%
% Grid Parameters (MAKE SURE MATCHES IN input2d !!!)
%
Nx =  32;        % # of Eulerian Grid Pts. in x-Direction (MUST BE EVEN!!!)
Ny =  32;        % # of Eulerian Grid Pts. in y-Direction (MUST BE EVEN!!!)
Lx = 1.0;        % Length of Eulerian Grid in x-Direction
Ly = 1.0;        % Length of Eulerian Grid in y-Direction


% Immersed Structure Geometric / Dynamic Parameters %
N = 2*Nx;        % Number of Lagrangian Pts. (2x resolution of Eulerian grid)
a = 0.5;         % Length of beam (only in x-coordinate)
struct_name = 'BeamCurve'; % Name for .vertex, .spring, .beam, .target, etc files.


% Call function to construct geometry
[xLag,yLag] = give_Me_Immsersed_Boundary_Geometry(N,Lx,a);


% Plot Geometry to test
plot(xLag,yLag,'r-'); hold on;
plot(xLag,yLag,'*'); hold on;
xlabel('x'); ylabel('y');
axis square;


% Prints .vertex file!
print_Lagrangian_Vertices(xLag,yLag,struct_name);

% Prints .beam file! (TORSIONAL SPRINGS)
%k_Beam = 7.5e10; C = 0.0;
%print_Lagrangian_Beams(xLag,yLag,k_Beam,C,struct_name);

% Prints .nonInv_beam file! (NON-INVARIANT))
k_Beam = 1e10; 
print_Lagrangian_nonInv_Beams(xLag,yLag,k_Beam,struct_name)

% Prints .target file! 
k_Target = 2e8;
print_Lagrangian_Target_Pts(xLag,k_Target,struct_name)



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: prints VERTEX points to a file called rubberband.vertex
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function print_Lagrangian_Vertices(xLag,yLag,struct_name)

    N = length(xLag);

    vertex_fid = fopen([struct_name '.vertex'], 'w');

    fprintf(vertex_fid, '%d\n', N );

    %Loops over all Lagrangian Pts.
    for s = 1:N
        X_v = xLag(s);
        Y_v = yLag(s);
        fprintf(vertex_fid, '%1.16e %1.16e\n', X_v, Y_v);
    end

    fclose(vertex_fid); 
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: prints Vertex points to a file called rubberband.vertex
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function print_Lagrangian_Target_Pts(xLag,k_Target,struct_name)

    N = length(xLag);

    target_fid = fopen([struct_name '.target'], 'w');

    fprintf(target_fid, '%d\n', 2 );

    fprintf(target_fid, '%d %1.16e\n', 1-1, k_Target);
    fprintf(target_fid, '%d %1.16e\n', N-1, k_Target);

    fclose(target_fid); 
 
    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: prints BEAM (NON-INVARIANT) points to a file called rubberband.nonInv_beam
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function print_Lagrangian_nonInv_Beams(xLag,yLag,k_Beam,struct_name)

    % k_Beam: beam stiffness
    % C: beam curvature
    
    N = length(xLag); % NOTE: Total number of beams = Number of Total Lag Pts. - 2

    beam_fid = fopen([struct_name '.nonInv_beam'], 'w');

    fprintf(beam_fid, '%d\n', N-2 );

    %spring_force = kappa_spring*ds/(ds^2);

    %BEAMS BETWEEN VERTICES
    for s = 2:N-1
            if  s <= N-1         
                fprintf(beam_fid, '%d %d %d %1.16e %1.16e %1.16e\n',s-1-1, s-1, s+1-1, k_Beam, 0, 0);  
            else
                %Case s=N
                fprintf(beam_fid, '%d %d %d %1.16e %1.16e %1.16e\n',s-1-1, s-1, 1-1,   k_Beam, 0, 0);  
            end
    end
    fclose(beam_fid); 
    
    
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: prints BEAM (Torsional Spring) points to a file called rubberband.beam
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function print_Lagrangian_Beams(xLag,yLag,k_Beam,C,struct_name)

    % k_Beam: beam stiffness
    % C: beam curvature
    
    N = length(xLag); % NOTE: Total number of beams = Number of Total Lag Pts. - 2

    beam_fid = fopen([struct_name '.beam'], 'w');

    fprintf(beam_fid, '%d\n', N-2 );

    %spring_force = kappa_spring*ds/(ds^2);

    %BEAMS BETWEEN VERTICES
    for s = 2:N-1
            if  s <= N-1         
                fprintf(beam_fid, '%d %d %d %1.16e %1.16e\n',s-1, s, s+1, k_Beam, C);  
            else
                %Case s=N
                fprintf(beam_fid, '%d %d %d %1.16e %1.16e\n',s-1, s, 1,   k_Beam, C);  
            end
    end
    fclose(beam_fid); 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: prints SPRING points to a file called rubberband.spring
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function print_Lagrangian_Springs(xLag,yLag,k_Spring,ds_Rest,struct_name)

    N = length(xLag);

    spring_fid = fopen([struct_name '.spring'], 'w');

    fprintf(spring_fid, '%d\n', N );

    %spring_force = kappa_spring*ds/(ds^2);

    %SPRINGS BETWEEN VERTICES
    for s = 1:N
            if s < N         
                fprintf(spring_fid, '%d %d %1.16e %1.16e\n', s, s+1, k_Spring, ds_Rest);  
            else
                %Case s=N
                fprintf(spring_fid, '%d %d %1.16e %1.16e\n', s, 1,   k_Spring, ds_Rest);  
            end
    end
    fclose(spring_fid); 
    
    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FUNCTION: creates the Lagrangian structure geometry
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [xLag,yLag] = give_Me_Immsersed_Boundary_Geometry(N,Lx,a)

% The immsersed structure is a curved line %
ds = a/(N-1);

xLag(1) = -a/2;%Lx/2-a/2;
yLag(1) = 0.0;
for i=2:N
    
    xLag(i) = xLag(i-1) + ds;
    x = xLag(i);
    yLag(i) = -2*( (x)^2 - (a/2)^2 );

end

xLag = xLag + Lx/2;
yLag = yLag + Lx/2;
