% Bezier example

% This goes in a file named BezierExample.m

close all
clear all

x_nodes = [];
y_nodes = [];

% Initialize figure window

figure
hold on
xlim([0 1])
ylim([0 1])

% Collect nodes

disp('Click several points on curve. Hit enter to exit')
index = 1;
while(true)    
    [x,y,button] = ginput(1);
    
    if (isempty(x))
        break
    end
    
    if (button ~= 1)
        continue
    end
    
    % Add the new point and plot the new line segment
    
    x_nodes(index) = x(1);
    y_nodes(index) = y(1);
    if (index > 1)
        plot(x_nodes(index-1:index),y_nodes(index-1:index))
    end
    
    index = index + 1;
end

% Points have been entered. Build the collection of nodes and control
% points that define the curve

number_curves = length(x_nodes) - 1;
bezier_points = cell(number_curves,4);
for k = 1:number_curves

    % Insert the nodes
    
    bezier_points{k,1} = [x_nodes(k) y_nodes(k)];
    bezier_points{k,4} = [x_nodes(k+1) y_nodes(k+1)];
    
    % Create the control points
    
    if (k == 1)
        bezier_points{k,2} = [x_nodes(1) y_nodes(1)] + ([x_nodes(2) y_nodes(2)] - [x_nodes(1) y_nodes(1)])/3;
    else
        
        % Compute positions for control points. Arbitrarily, they will be
        % collinear with the node in between and 1/3 of the way to the next
        % node
        
        vector_1 = [x_nodes(k) y_nodes(k)] - [x_nodes(k-1) y_nodes(k-1)];
        length_1 = norm(vector_1);
        vector_1 = vector_1/length_1;
        
        vector_2 = [x_nodes(k) y_nodes(k)] - [x_nodes(k+1) y_nodes(k+1)];
        length_2 = norm(vector_2);
        vector_2 = vector_2/length_2;
        
        vector_sum = vector_1 + vector_2;
        n = vector_sum/norm(vector_sum);
        
        % If vector_1 X vector_2 is negative, reverse the direction of n
        
        if ((vector_1(1)*vector_2(2) - vector_2(1)*vector_1(2)) < 0)
            n = -n;
        end
        n_p = [-n(2) n(1)];
        
        bezier_points{k-1,3} = [x_nodes(k) y_nodes(k)] + n_p*length_1/3;
        bezier_points{k,2} = [x_nodes(k) y_nodes(k)] - n_p*length_2/3;
        
        if (k == (number_curves))
            
            bezier_points{k,3} = [x_nodes(number_curves+1) y_nodes(number_curves+1)] + ...
                                 ([x_nodes(number_curves) y_nodes(number_curves)] - [x_nodes(number_curves+1) y_nodes(number_curves+1)])/3;
        end
    end 
end

PlotBezier(bezier_points)