I have a x vector 25×1 and a y vector 25×1. I want to spline between the points to extend the vector to 96×1 points. Is there a way to do this without using interp point by point… such as using x(2,1)–> x(3,1) y(2,1)–>y(3,1) to add 3 points and move on to the next point and add three until I get 96 points. I want the the original 25 points to remain in the 96×1 vector. Thanks in advance for your help, John
MATLAB: Spline fitting a set of data
interpninterpolationscatterspline
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With your data, my demo would become this:
% Create the original knot points.
xInitial = [1.6 1.1 .6 .1 .4 .9 1.4 1.9];yInitial = [1 1.5 2 2.5 3 3.5 4 4.5];lengthX = length(xInitial);% flip sideways so there is only 1 y for every x
x = yInitial;y = xInitial;% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);grid on;set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;newXSamplePoints = linspace(min(x), max(x), lengthX * samplingRateIncrease);smoothedY = spline(x, y, newXSamplePoints);% Now flip back
ySmooth = newXSamplePoints;xSmooth = smoothedY;% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(newXSamplePoints, smoothedY, '-ob');title('Spline Interpolation Demo', 'FontSize', 20);legend('Original Points', 'Spline Points');figure;plot(xInitial, yInitial, '-sr', 'LineWidth', 2);% Plot smoothedY and show how the line is% smooth, and has no sharp bends.hold on; % Don't destroy the first curve we plotted.plot(xSmooth, ySmooth, '-ob');grid on;
You can also use a Savitzky-Golay filter to smooth curves, and I attach a demo for that.
Like Matt J says, the usual solution is to get evenly spaced intervals using interpolation, such as interp1() or spline().
Here's a spline demo if you want to do a cubic fit between the points:
% Demo to show spline interpolation.
% Clean up / initialize
clc; close all; clear all; workspace; % Display workspace panel.
% Create the original knot points.
lengthX = 10;x = 1:lengthX;y = rand (lengthX,1);% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;newXSamplePoints = linspace(1, lengthX, lengthX * samplingRateIncrease);smoothedY = spline(x, y, newXSamplePoints);% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(newXSamplePoints, smoothedY, '-ob');title('Spline Interpolation Demo', 'FontSize', 20);legend('Original Points', 'Spline Points');% Mathworks Demo code from their Help
% x = 0:10;
% y = sin(x);
% xx = 0:.25:10;
% yy = spline(x,y,xx);
% plot(x,y,'o',xx,yy)
The input points don't need to be uniformly spaced like I did in the demo.
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