How to connect point by curve instead of line in MTALB plot

Hello, guys. I have some data points. When I plot these points in Matlab, it connects data points by line. However, I want to connect these points using a curve instead of a line graph for good representation. So please suggest to me which function we should use.

Thank you.

Answer 1

[Hassaan]

% Example data points
x = [1, 2, 3, 4, 5];
y = [1, 4, 9, 16, 25];

% Interpolate to create a smooth curve
xq = linspace(min(x), max(x), 100); % Create 100 points for a smoother curve
yq = interp1(x, y, xq, 'spline');   % 'spline' interpolation for a smooth curve

% Plotting the curve
plot(xq, yq, 'b-', x, y, 'ro'); % 'b-' for blue curve, 'ro' for red original points
xlabel('X data');
ylabel('Y data');
title('Smooth Curve Through Data Points');
legend('Interpolated Curve', 'Original Data Points');

[Ram]

@Hassaan Thank you so much for your answer. The given example by you is fitted well. Actually my data is not fitting spline. Following is my data

x y

0 0

-1.7E-05 -0.00016

-3.2E-05 2.27E-05

-4.9E-05 -0.00018

-6.1E-05 7.58E-05

-7.6E-05 -0.00021

0.000883 0.009197

0.000847 -0.00954

-0.00505 -0.04568

-0.0137 -0.0354

-0.01811 -0.00597

-0.0189 -0.00141

-0.02273 -0.03449

-0.03432 -0.07417

-0.05114 -0.08341

-0.06628 -0.05849

-0.0758 -0.03072

-0.08215 -0.02875

-0.09042 -0.04878

-0.10216 -0.06128

-0.11353 -0.04528

-0.11952 -0.01081

-0.11911 0.014622

-0.11585 0.015929

-0.11349 0.006168

-0.11196 0.008244

-0.10784 0.030304

-0.09861 0.056246

-0.08553 0.066329

-0.07239 0.056809

-0.06166 0.04375

-0.05247 0.042324

-0.04241 0.052024

-0.03072 0.057486

-0.01951 0.04753

-0.01168 0.025901

When i am fitting , i am getting like this .But it should be in circular form not like this. please help me out.

Thanks

[Walter Roberson]

I do not understand what you mean by "it should be in circular form" ??

[Ram]

@Walter Roberson . The below figure show that the exact plot . The red mark point i want to connect by curve. They are connected by lines right now.

[Hassaan]

% Define the function to compute residuals for circle fitting
function F = fit_circle(c, x, y)
    % c(1) and c(2) are the coordinates of the center of the circle
    % c(3) is the radius of the circle
    F = sqrt((x - c(1)).^2 + (y - c(2)).^2) - c(3);
end

% Example data points (x, y)
x = [-1.7E-05, -3.2E-05, -4.9E-05, -6.1E-05, -7.6E-05, 0.000883, 0.000847, -0.00505, -0.0137, -0.01811, -0.0189, -0.02273, -0.03432, -0.05114, -0.06628, -0.0758, -0.08215, -0.09042, -0.10216, -0.11353, -0.11952, -0.11911, -0.11585, -0.11349, -0.11196, -0.10784, -0.09861, -0.08553, -0.07239, -0.06166, -0.05247, -0.04241, -0.03072, -0.01951, -0.01168];
y = [-0.00016, 2.27E-05, -0.00018, 7.58E-05, -0.00021, 0.009197, -0.00954, -0.04568, -0.0354, -0.00597, -0.00141, -0.03449, -0.07417, -0.08341, -0.05849, -0.03072, -0.02875, -0.04878, -0.06128, -0.04528, -0.01081, 0.014622, 0.015929, 0.006168, 0.008244, 0.030304, 0.056246, 0.066329, 0.056809, 0.04375, 0.042324, 0.052024, 0.057486, 0.04753, 0.025901];

% Initial guess for circle parameters [x_center, y_center, radius]
initial_guess = [0, 0, 0.1];

% Fit the circle using least squares optimization
options = optimoptions('lsqnonlin', 'Display', 'off');
circle_params = lsqnonlin(@(c) fit_circle(c, x, y), initial_guess, [], [], options);

% Calculate points on the fitted circle for plotting
theta = linspace(0, 2*pi, 100);
x_fit = circle_params(1) + circle_params(3) * cos(theta);
y_fit = circle_params(2) + circle_params(3) * sin(theta);

% Plot the original data and the fitted circle
figure;
plot(x, y, 'ro'); hold on; % original data
plot(x_fit, y_fit, 'b-'); % fitted circle
axis equal; % equal scaling
legend('Original Data', 'Fitted Circle');
title('Least Squares Circle Fitting');
xlabel('X');
ylabel('Y');

Answer 2

[Image Analyst]

If you want a smooth envelope going through the convex hull points, like you showed in your example, I suggest first using convhull to find those points, and then use a spline, with a lot more "in between" points/locations to interpolate a smooth curve between them. I'm attaching a spline demo for 1-D and 3-D but it's straight forward to first spline the x data and then spline the y data and plot the new (x,y) and it will go between the convex hull points.