Generates string for Bezier curves in GeoGebra

curveString.m

% Generates Bezier polynomials in x and y for use in Geogebra                                      
%                                       
%                                       
% Input(s)                              
%   n: Degree of Bezier curve                                    
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% Output(s)                             
%   cStr: String used to define Bezier curve in Geogebra                                    
%                                       
% Example:                              
% Start Geogebra, select number of points n, and place n points on the Geogebra 
% grid. In this example, n = 5.                                     
% Run curveString: 
% cStr = curveString(5)
% Copy and paste string into Geogebra, then move points as desired to shape
% the Bezier curve. Points in Geogebra are now control points for the
% Bezier curve.                                      
%
%
% See also: BezierHull                            
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% Dependencies: None                        
                                        
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%                                       
% Written by: John Peach 30-Sep-2020    
% Marakesh Sailing Analysis and Design  
%                                       
% Revisions:                            
                                        
                                        
function cStr = curveString(n)
    
    % First n upper case letters of the alphabet
    alpha = upper(char(65:64+n));
    
    % Binomial coefficients
    coeff = binomial(n-1);
    
    % Generate x,y polynomial strings
    x = ['x(A)(1-t)^' num2str(n-1) ' + '];
    y = ['y(A)(1-t)^' num2str(n-1) ' + '];
    for k = 2:n-1
        c = num2str(coeff(k));
        if k > 2
            p0 = ['^' num2str(k-1)];
        else
            p0 = '';
        endif
        
        if n-k > 1
            p1 = ['^' num2str(n-k)];
        else
            p1 = '';
        endif
        
        Ltr = alpha(k);
        
        x = [x c 'x(' Ltr ')' '(1-t)' p1 '*t' p0 ' + '];
        y = [y c 'y(' Ltr ')' '(1-t)' p1 '*t' p0 ' + '];
    endfor
    
    x = [x 'x(' alpha(end) ')' 't^' num2str(n-1)];
    y = [y 'y(' alpha(end) ')' 't^' num2str(n-1)];
    
    % Combine into curve definition
    cStr = ['curve[' x ', ' y ',t,0,1]'];
    
    % Display string
    fprintf('%s\n', cStr)

endfunction