Spline Interpolation

What is Spline Interpolation?

Spline interpolation methods create smooth and continuous curves by dividing the data range into smaller intervals and fitting separate piece-wise polynomial functions (splines) to each interval. These splines join together at the intersection points so the entire curve looks smooth and natural.

Spline your name

A fun and interesting way to use spline!

Function to write cursive names

This code defines a MATLAB function plotWord.m that takes an input string, and outputs the corresponding cursive-written word(s). The input string is converted to lowercase for consistent plotting. The code iterates through each character in the input string and uses a "switch-case" statement to define the coordinates for the corresponding cursive letters. The primary purpose of this code is to generate a plot of cursive letters based on the input string using spline interpolation.

Below is the code for our function:

function plotWord(inputString)
% Initialize figure to plot letters
figure;
hold on;

% Initialize a variable to keep track of the end position of x
% Initially, endposx = 0 as it starts from x = 0
endposx = 0;

inputString = lower(inputString);

for i = 1:length(inputString)
    letter = inputString(i);


    switch letter
            case 'a'
                x = [4.2 3.8 2.95 2.6 3 3.8 4.53 4.7 4.05 4.4 5.3] + endposx;
                y = [3.5 3.9 3.35 2.4 2.25 3.1 3.86 3.7 2.3 2.16 2.8];
            case 'b'
                x = [4 5.5 5.45 4.56 3.54 3.96 4.54 4 3.54 3.96 5] + endposx;
                y = [3.76 6.3 6.53 5.2 2.76 2.2 3.1 3.76 2.76 2.2 3.4];
            case 'c'
                x = [4.6 4.94 4.5 3.1 3.57 5.15] + endposx;
                y = [3.34 3.8 4.24 2.76 2.1 2.77];
            case 'd'
                x = [5.4 5.2 4.7 3.9 3.56 3.95 4.8 5.5 6.1 6.9 7.3 5.5 5.06 5.5 6.0] + endposx;
                y = [3.2 3.75 3.75 3.15 2.36 2.07 2.3 3.2 4.4 5.65 5.56 3.2 1.34 0.73 1];
            case 'e'
                x = [3.35 4.0 4.37 4.03 3.35 3.2 3.54 4.4] + endposx;
                y = [3 3.1 3.45 3.65 3 2.4 2.1 2.5];
            case 'f'
                x = [3.8 6 5.8 4.6 3.8 3.14 3.54 3.7 3.25 3.8 5.4] + endposx;
                y = [2.6 6 6.44 4.6 2.6 0.85 1.1 2.03 2.5 2.6 2.8];
            case 'g'
                x = [3.75 3.3 2.45 2.7 4.4 4.3 2.25 1.75 3.25 5.55] + endposx;
                y = [3.8 4.4 3.7 3.2 4.4 3.25 0.5 0.75 2.55 4.05];
            case 'h'
                x = [4.85 2.4 2.65 3.95 4.5 3.95 4.4 6.2] + endposx;
                y = [7.1 2.45 2.15 3.9 3.4 1.85 1.5 2.9];
            case 'i'
                x = [2.6 3.5 3.45 2.2 2.55 3.75] + endposx;
                y = [4 4.5 4.85 2.4 2.1 2.55];
            case 'j'
                x = [3.25 4.5 4.2 2.35 1.45 2] + endposx;
                y = [4.4 5.5 5.7 0.2 0.25 1.5];
            case 'k'
                x = [1.1 5.1 2.7 3.6 5 2.95 3.2 6.05] + endposx;
                y = [1.55 7.7 4 4.6 5.5 4.3 2.8 3];
            case 'l'
                x = [4.5 3.65 2.75] + endposx;
                y = [8.7 6.7 2.1];
            case 'm'
                x = [2.1 1.75 2.35 3.5 3.7 2.9 3.65 4.3 4.1 4.35 5.3 6.3] + endposx;
                y = [4.05 3.05 3.45 4.55 4.4 2.85 3.05 3.3 2.25 2.05 2.4 3.45];
            case 'n'
                x = [2.4 2.3 3 3.7 3.95 3.8 4.05 5.15 5.8] + endposx;
                y = [3.8 2.75 3.5 3.5 3.15 2.2 2.05 2.7 3.5];
            case 'o'
                x = [2.8 3.5 3.8 3.45 2.9 2.65 2.7 3.4 3.7 3.75 4.55] + endposx;
                y = [3.15 3.75 3.5 2.4 2.05 2.2 2.9 3.8 3.7 2.95 2.9];
            case 'p'
                x = [2.9 4.2 3.75 1.75 3.1 4.3 4.95 4.65 3.5 3.3 4.5 6.05] + endposx;
                y = [3.35 5.6 5.15 0.3 3.15 4.4 4.15 3.25 2.3 2.65 3.45 4.1];
            case 'q'
                x = [4.5 4.45 3.85 2.9 3.1 4.8 2.95 4.9 5.85] + endposx;
                y = [3.95 4.65 5.05 4.25 3.6 4.1 0.25 1.7 1.95];
            case 'r'
                x = [2.85 3.55 3.1 3 3.65 4.2 4.55 5.25] + endposx;
                y = [2.5 3.65 3.15 2.25 3.45 3.4 2.85 2.9];
            case 's'
                x = [4.65 4.8 4.05 3.45 3.85 3.1 2.7 3.45 5.4] + endposx;
                y = [4.35 4.9 4.95 4.35 3.05 2.1 2.6 3.15 4];
            case 't'
                x = [7.4 1.7 5.0 6.0 4.6 3.35 5.5] + endposx;
                y = [5.4 5.5 5.4 6.9 4.7 1.80 0.1];
            case 'u'
                x = [2.85 2.25 4.0 3.9 3.8 5.7] + endposx;
                y = [3.90 2.20 3.2 3.4 2.2 3.0];
            case 'v'
                x = [3.55 3.50 3.1 4.6 4.55 4.75 5.6] + endposx;
                y = [3.80 3.95 2.1 3.3 3.40 2.95 3.0];
            case 'w'
                x = [3.25 3.1 2.25 4.1 4.0 3.9 5.3 5.15 6.2] + endposx;
                y = [3.70 3.8 2.80 3.2 3.3 2.1 3.7 3.75 3.0];  
            case 'x'
                x = [2.95 4.20 3.8 2.9 3.6 3.5 3.45 3.9 5.1] + endposx;
                y = [2.10 3.70 3.4 2.2 3.0 3.7 3.30 2.3 2.2];  
            case 'y'
                x = [3.1 2.6 4.6 4.4 2.8 2.5 4.6] + endposx;
                y = [3.8 2.9 3.7 3.8 0.5 0.6 2.9];  
            case 'z'
                x = [3.1 4.2 3.3 3.2 4.05 3.45 3.3 4.7 5.8] + endposx;
                y = [3.4 4.0 2.2 2.3 2.15 0.10 0.3 2.5 3.3];                
    end
    
    n = length(x);
    t = 0:n-1; % Paremetric coordinate t
    tt = 0:0.01:n-1; % More dense coordinate tt for spline interpolation

    % Compute spline interpolation
    xx = spline(t, x, tt);
    yy = spline(t, y, tt);

    % Plot the cursive letter
    plot(xx, yy, 'k', 'Linewidth', 1.5);

    % Update the end position for the next letter
    endposx = max(xx) - 2.5;
end

% Set plot properties
grid on;
    title('Spline Interpolation of Cursive Letters');
    xlabel('x');
    ylabel('y');
    set(gca, 'FontSize', 10, 'LineWidth', 1);
    
    hold off;
end

Example:

Improvements

• spacing
• capital letters
• special characters
• connecting the letters

Thank you for reading me!