How to Draw the USA Flag with Nelson!

[Nelson-numerical-software]

usaFlag.m

function usaFlag()
  % Define flag dimensions and colors
  flagWidth = 1.9;            % Width of the flag relative to its height
  flagHeight = 1;             % Height of the flag (set to 1 for scaling)
  stripeHeight = flagHeight / 13; % Height of each stripe (13 total stripes)
  unionWidth = 0.76;          % Width of the blue union section relative to flag height
  unionHeight = 7 * stripeHeight; % Height of the blue union section (covers 7 stripes)
  red = [0.698, 0.133, 0.133]; % RGB color for the red stripes
  blue = [0.234, 0.233, 0.430]; % RGB color for the blue union
  white = [1, 1, 1];          % RGB color for the white stripes and stars
  
  % Create figure for the flag
  figure;
  hold on;
  axis equal;                 % Ensures the flag proportions are correct
  axis off;                   % Hides axes for a cleaner display
  
  % Draw the 13 stripes of the flag
  for i = 0:12
    if mod(i, 2) == 0
      color = red;        % Red stripes on even indices
    else
      color = white;      % White stripes on odd indices
    end
    y = i * stripeHeight;   % Vertical position of the current stripe
    h = fill([0, flagWidth, flagWidth, 0], [y, y, y + stripeHeight, y + stripeHeight], color);
    h.EdgeColor = 'none';   % Removes edges for seamless stripes
  end
  
  % Draw the blue union rectangle
  h = fill([0, unionWidth, unionWidth, 0], [6 * stripeHeight, 6 * stripeHeight, 13 * stripeHeight, 13 * stripeHeight], blue);
  h.EdgeColor = 'none';       % Removes edges for a cleaner look
  
  % Draw stars in the blue union
  starRadius = 0.5 * stripeHeight; % Radius of each star (adjust to scale)
  rows = 9;                   % Number of rows of stars
  cols = 11;                  % Number of columns of stars
  xOffset = unionWidth / cols / 2; % Horizontal offset for centering stars in each cell
  yOffset = unionHeight / rows / 2; % Vertical offset for centering stars in each cell
  
  % Loop through rows and columns to position each star
  for row = 0:rows - 1
    for col = 0:cols - 1
      if mod(row, 2) == mod(col, 2) % Alternate star positions for staggered pattern
        x = col * unionWidth / cols + xOffset; % X-coordinate of the star
        y = flagHeight - row * unionHeight / rows - yOffset; % Y-coordinate of the star
        drawStar(starRadius, x, y, white); % Call to function to draw each star
      end
    end
  end
  
  hold off; % Release the hold on the figure
end

drawStar.m

function drawStar(radius, centerX, centerY, color)
    % drawStar: Function to create a 5-pointed star shape using patches
    % 
    % Parameters:
    %   radius  - Radius of the star (controls the size of the star)
    %   centerX - X-coordinate for the center of the star
    %   centerY - Y-coordinate for the center of the star
    %   color   - Color of the star (typically white for the American flag)
    
    % Define angles for the outer points of the star
    outerAngles = linspace(0.3 * pi, 2.3 * pi, 6); % 5 points around a circle, slightly rotated

    % Calculate coordinates for the outer points of the star
    outerX = (radius / 2) * cos(outerAngles); % X-coordinates for outer points, scaled by radius
    outerY = (radius / 2) * sin(outerAngles); % Y-coordinates for outer points, scaled by radius
    
    % Define angles for the inner points of the star, with slight rotation for alignment
    innerAngles = outerAngles + 0.2 * pi;

    % Calculate coordinates for the inner points of the star
    innerX = (radius / 6) * cos(innerAngles); % X-coordinates for inner points (about 1/3 of outer radius)
    innerY = (radius / 6) * sin(innerAngles); % Y-coordinates for inner points (about 1/3 of outer radius)
    
    % Combine outer and inner coordinates to form the star shape
    starXCoordinates = [outerX; innerX]; % Stack X-coordinates of outer and inner points
    starYCoordinates = [outerY; innerY]; % Stack Y-coordinates of outer and inner points

    % Create a filled patch (polygon) to draw the star shape
    starPatch = patch(starXCoordinates(:) + centerX, starYCoordinates(:) + centerY, color); 
    starPatch.EdgeColor = 'none'; % Remove edges for a seamless star appearance
end