This is the problem I'm having trouble with. I really don't know where to start with it, so if someone could get me some pointers that would be amazing.
MATLAB: I need to make a plot using spline interpolation
forceinterplinterpolationspline interpolation
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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.
Try my demo:
% Demo to show spline interpolation.
% Clean up / initialize
clc; close all; clear all; workspace; % Display workspace panel.
% Create the original knot points.
x = 1:10;y = rand (10,1);% 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, 10, 10 * 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)
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