FourieR Group Assignment (MATLAB)
On a graph paper, each member is to write their (short-hand) name in cursive and record their x and y coordinates as data points.
From the recorded coordinates, we reconstructed each member's names using spline interpolation. The code are shown below:
- Spline Interpolation of 'Syafiqah'
% Use subplot for plotting different graphs in the same figure
subplot(4,1,1);
% Define data points for x and y coordinates
% Each line is the x and y coordinate for one letter respectively
x1 = [0 5/3 7/6 2/3 0.5 5/6 5/3 5/6 2/3 5/3 ...
2 13/6 11/4 3 35/12 17/6 7/3 2 10/3 ...
13/3 49/12 15/4 7/2 15/4 13/3 14/3 55/12 14/3 5 ...
65/12 6 35/6 65/12 17/3 37/6 23/4 11/2 11/2 19/3 ...
43/6 7 41/6 7 23/3 ...
26/3 101/12 97/12 47/6 49/6 26/3 9 107/12 9 113/12 89/10 29/3 ...
32/3 125/12 121/12 59/6 121/12 32/3 11 131/12 11 34/3 ...
12 77/6 38/3 73/6 12 145/12 149/12 51/4 13 40/3 14];
y1 = [5/3 8/3 3 8/3 13/6 1.5 1/3 0 0.5 2/3 ...
5/3 1/3 1/3 5/3 1/6 -5/6 -4/3 -1 2/3 ...
17/12 5/3 17/12 2/3 1/12 1/6 17/12 17/12 0 2/3 ...
1.5 13/6 3 5/3 0 1/3 4/3 7/5 1 2/3 ...
4/3 5/3 4/3 0 2/3 ...
17/12 5/3 17/12 2/3 0 1/6 4/3 4/3 -1 -1 0 2/3 ...
17/12 5/3 17/12 2/3 1/12 1/6 17/12 17/12 0 2/3 ...
5/3 8/3 3 8/3 5/3 0 4/3 5/3 4/3 0 2/3];
n = length(x1);
t = 0:n-1; % Parametric coordinate t
tt = 0:0.01:n-1; % More dense coordinate tt for spline interpolation
% Compute spline interpolation
xx = spline(t, x1, tt);
yy = spline(t, y1, tt);
% Plot settings
figure(1)
plot(xx, yy, 'k', 'LineWidth',1.5) % plot spline
hold on
plot(x1, y1, 'bo', 'MarkerFaceColor', 'b') % plot data points
axis([-0.2 15 -2 4])
grid on
title('Spline Interpolation of Cursive Name Syafiqah')
xlabel('x')
ylabel('y')
set(gca, 'FontSize', 10, 'LineWidth', 1)
grid on
% note: all comments are the same for the following names- Spline Interpolation of 'Fiqah'
subplot(4,1,2);
x2 = [1.6 1.2 1.1 1.1 1.1 0.9 0.8 1.1 1.5 ...
1.5 1.5 1.65 1.8 1.9 ...
2.3 2.1 1.9 2.0 2.2 2.3 2.3 2.3 2.5 2.6 2.3 2.6 ...
3.0 2.8 2.6 2.7 2.9 3.0 3.0 3.1 3.3 ...
3.3 3.5 3.4 3.3 3.3 3.3 3.5 3.67 3.8 3.9 4.0 4.1];
y2 = [2.5 2.5 2.3 1.8 1.3 1.0 1.3 1.8 1.8 ...
1.5 1.2 1.1 1.2 1.3 ...
1.8 1.9 1.3 1.1 1.3 1.8 1.0 0.4 0.2 0.4 1.0 1.3 ...
1.8 1.9 1.3 1.1 1.3 1.8 1.3 1.0 1.5 ...
1.5 2.2 2.4 2.2 1.5 1.0 1.5 1.7 1.5 1.2 1.0 1.2];
n = length(x2);
t = 0:n-1;
tt = 0:0.01:n-1;
xx = spline(t, x2, tt);
yy = spline(t, y2, tt);
figure(1)
plot(xx, yy, 'k', 'LineWidth', 1.5)
hold on
plot(x2, y2, 'bo', 'MarkerFaceColor', 'b')
axis([-0.2 6 -0.2 3])
grid on
title('Spline Interpolation of Cursive Name Fiqah')
xlabel('x')
ylabel('y')
set(gca, 'FontSize', 10, 'LineWidth', 1)
grid on- Spline Interpolation of 'Bazilah'
subplot(4,1,3);
x3 = [1.0 1.5 1.90 1.55 2.0 1.75 1.25 1.3 1.4 ...
3.05 2.7 2.3 2.40 2.75 3.1 3.05 3.40 3.70 ...
3.70 3.95 4.15 3.95 3.70 4.15 4.0 3.60 3.90 4.4 4.70 ...
4.70 4.65 4.7 5.0 5.325 ...
5.325 5.55 5.5 5.4 5.3 5.5 5.9 ...
6.65 6.3 5.9 6.00 6.40 6.7 6.60 6.85 7.214 ...
7.214 7.5 7.40 7.3 7.15 7.55 7.8 7.9 7.95 8.4];
y3 = [1.6 1.9 1.80 1.40 1.2 0.85 0.85 1.3 1.7 ...
1.50 1.6 1.2 0.85 1.05 1.6 0.95 1.05 1.45 ...
1.45 1.50 1.55 1.25 0.95 0.90 0.4 0.45 0.75 1.1 1.45 ...
1.45 1.00 0.8 0.9 1.25 ...
1.250 1.90 2.0 1.6 0.9 0.8 1.2 ...
1.50 1.6 1.2 0.85 1.05 1.6 0.95 0.90 1.236 ...
1.236 1.8 2.00 1.6 0.80 1.40 1.5 1.2 0.90 1.2];
n = length(x3);
t = 0:n-1;
tt = 0:0.01:n-1;
xx = spline(t, x3, tt);
yy = spline(t, y3, tt);
figure(1)
plot(xx, yy, 'k', 'LineWidth',1.5)
hold on
plot(x3, y3, 'bo', 'MarkerFaceColor', 'b')
axis([0 9 0 3])
grid on
title('Spline Interpolation of Cursive Name Bazilah')
xlabel('x')
ylabel('y')
set(gca, 'FontSize', 10, 'LineWidth', 1)
grid on- Spline Interpolation of 'Hilal'
subplot(4,1,4);
x4 = [0.3 0.55 0.5 0.25 0.3 0.55 1.25 1.6 1.4 1.25 ...
1.6 1.9 2.05 1.95 1.8 1.9 2.1 2.35 2.6 2.8 3 2.8 2.6 2.8 3.03 3.55 ...
4.35 4.65 4.4 3.3 3.12 4.35 4.65 4.7 4.9 5.1 5.3 5.5 5.3 5.1 5.3 5.4 5.5];
y4 = [3.3 1.5 0.85 0.3 1 1.5 1.65 2.5 3.3 1.65 0.3 1.3 1.85 ...
2.15 1.85 1.3 0.5 0.3 0.8 1.5 2.8 3.3 2.8 1.5 0.576 0.11 0.3 ...
1.1 1.9 1.9 0.38 0.3 1.1 0.5 0.3 0.6 1.5 2.6 3.3 2.6 1.5 0.7 0.3];
n = length(x4);
t = 0:n-1;
tt = 0:0.01:n-1;
xx = spline(t, x4, tt);
yy = spline(t, y4, tt);
figure(1)
plot(xx, yy, 'k', 'LineWidth', 1.5)
hold on
plot(x4, y4, 'bo', 'MarkerFaceColor', 'b')
axis([-0.2 6 -0.2 4.5])
grid on
title('Spline Interpolation of Cursive Name Hilal')
xlabel('x')
ylabel('y')
set(gca, 'FontSize', 10, 'LineWidth', 1)
grid onThe outcome will look like this:
We created a function using containers.Map to combine letters into words. The function code are shown below:
function plotWord(word)
% use containers.Map to contain all letters' data
Letter = containers.Map;
Letter('a') = [0 2/3; 2.5 1.75; 1.75 2; 0.75 1.75; 0 0.75; 0.75 0.25; ...
2.5 0.25; 3.5 1.75; 3.25 1.75; 3.5 0; 4.5 1; 5 2/3];
Letter('b') = [0 2/3; 1 2.5; 2 3.5; 1 3.5; 1 0; 2 2; 4 2; 3.5 0.125; 1.5 0.5; 6 2/3];
Letter('c') = [0 2/3; 2 1.5; 5 2.25; 2 1.5; 2.5 0.25; 5 0.25; 5 0.25; 7 2/3];
Letter('d') = [0 2/3; 1 1.5; 3.5 2; 2 1.5; 2 0.25; 3.5 0.5; 4.5 3.5; 3.5 3.5; ...
4 2; 4.5 0; 5 2/3];
Letter('e') = [0 2/3; 0.5 2; 2 2; 2 3; 1 2; 1 0.5; 2.5 1; 3 2/3];
Letter('f') = [0 2/3; 64/6 3; 12 10/3; 35/3 4; 65/6 13/3; 34/3 0; 37/3 2/3; 23/2 8/3; 11 14/5; 11 2; 38/3 2/3];
Letter('g') = [0 2/3; 1 3/2; 2.5 4/2; 1.5 4/2; 1.5 1/2; 2.5 1/2; 3 3.5/2; 3 0; ...
2.5 -3/2; 1.5 -3/2; 3 0; 4 2/3];
Letter('h') = [0 2/3; 1 6/3; 3.5 9/3; 3 10/3; 1.5 9/3; 1 6/3; 1.25 0; 2.25 5/3; ...
3.25 6/3; 4 5/3; 5 0; 6 2/3];
Letter('i') = [0 2/3; 1.25 2/3; 2 4/3; 1.5 5/3; 1 4/3; 1.5 0; 6 2/3];
Letter('j') = [0 2/3; 1 3/3; 2 4/3; 3 5/3; 3 0; 3 -2/3; 2.5 -3/3; 2 -2/3; 4 2/3];
Letter('k') = [0 2/3; 3 3/2; 3.375 6.5/2; 3 6.5/2; 3 0.75/2; 3 0.75/2; 3.75 4/2; ...
4.5 4/2; 3.5 2.5/2; 3.5 2.5/2; 4.5 0; 6 2/3];
Letter('l') = [0 2/3; 1 0; 2 1/1.5; 2.5 5/1.5; 1.5 5/1.5; 2 1/1.5; 3 0; 4 2/3];
Letter('m') = [0 2/3; 2 3.5/2; 2 3.5/2; 2 0.5/2; 2 0.5/2; 3 3.5/2; 4 3.5/2; ...
4 0.5/2; 4 0.5/2; 5 3.5/2; 6 3.5/2; 6 0.5/2; 8 2/3];
Letter('n') = [0 2/3; 2 3.5/2; 2 3.5/2; 2 0.5/2; 2 0.5/2; 3 3.5/2; 4 3.5/2; ...
4 0.5/2; 6 2/3];
Letter('o') = [0 2/3; 3 4/3; 3 0.5/2; 4.5 0.5/2; 4.5 3.5/2; 3.375 3.5/2; 6 2/3];
Letter('p') = [0 2/3; 1.5 4/2.5; 1.5 4/2.5; 1.5 -2/2.5; 1.5 -2/2.5; 2.25 4/2.5; 3.75 4/2.5; 3.75 0.75/2.5; ...
2.25 0.75/2.5; 6 2/3];
Letter('q') = [0 2/3; 2.5 4.25/2.5; 1.75 5/2.5; 0.75 4.25/2.5; 0 2/2.5; 1 0; ...
2.5 0.5/2.5; 3.5 4/2.5; 3.25 4/2.5; 3.5 -3/2.5; 4 -3/2.5; 3.45 0; 5 2/3];
Letter('r') = [0 2/3; 1.5 1/2; 2.25 4/2; 2.25 4/2; 3.75 3/2; 3.75 3/2; 4.5 0.5; 6 2/3];
Letter('s') = [0 2/3; 4 4/2.25; 2.5 4.5/2.25; 1 4/2.25; 0.5 3.25/2.25; 1.5 2.25/2.25; 4 0.5/2.25; ...
1.5 0; 1 0.75/2.25; 6 2/3];
Letter('t') = [0 2/3; 2.25 0; 3 2.5/1.75; 3.375 5/1.75; 3 6/1.75; 2.625 5/1.75; 2.7 3/1.75; ...
3 3/1.75; 4.5 3/1.75; 1.5 3/1.75; 1.5 3/1.75; 2.7 3/1.75; 2.7 2.5/1.75; 3.75 0; 6 2/3];
Letter('u') = [0 2/3; 2 3.5/2; 2 3.5/2; 2.5 0.75/2; 4 0.75/2; 4.5 3.5/2; ...
4.5 3.5/2; 5 0.5/2; 6 2/3];
Letter('v') = [0 2/3; 2 1.75; 2 1.75; 4 0.25; 4 0.25; 6 1.75; 6 1.75; 8 2/3];
Letter('w') = [0 2/3; 2.5 3.5/2; 2.5 3.5/2; 3.125 0.75/2; 3.75 0.75/2; 4.375 3.5/2; ...
4.375 3.5/2; 5 0.75/2; 5.625 0.75/2; 6.25 3.5/2; 6.25 3.5/2; ...
6.875 0.5/2; 10 2/3];
Letter('x') = [0 2/3; 2 4/2; 2 4/2; 3.5 2/2; 2 0.5/2; 2 0.5/2; 6 4/2; 6 4/2; 4 2/2; ...
6 0.5/2; 8 2/3];
Letter('y') = [0 2/3; 1 5/2.5; 1.5 1/2.5; 3.25 1/2.5; 4 5/2.5; 3.75 0.5/2.5; 3.5 -2.5/2.5; ...
2 -4/2.5; 1 -3/2.5; 6 2/3];
Letter('z') = [0 2/3; 2 4/2; 6 4/2; 4 2/2; 4 2/2; 6 2/2; 6 -1/2; 2 -2/2; 8 2/3];
% Check for uppercase letters before proceeding
if any(isstrprop(word, 'upper'))
disp('Error : Uppercase letter does not exist.')
return;
end
figure;
hold on;
% Initialize the gap and current point
gap = 0; % make sure there is no gap between letters
currentX = 0;
xx = zeros(currentX);
yy = zeros(currentX);
for i = 1:length(word)
letter = lower(word(i)); % lowercase the letter
if isKey(Letter, letter)
points = Letter(letter);
points(:, 1) = points(:, 1) + currentX;
t = linspace(1, size(points, 1), 100);
xx = spline(1:size(points, 1), points(:, 1), t);
yy = spline(1:size(points, 1), points(:, 2), t);
plot(xx, yy, 'LineWidth', 1.5);
if i < length(word)
nextLetter = lower(word(i + 1));
nextPoints = Letter(nextLetter);
xx = [xx, nextPoints(:, 1)'];
yy = [yy, nextPoints(:, 2)'];
currentX = max(xx) + gap; % update starting x-coordinate
end
end
end
% Plot settings
plot(xx, yy, 'k', 'LineWidth', 1.5);
title(word); % outputs the title to be the word called
xlabel('x');
ylabel('y');
grid on;
hold off