Using splines and plotting them

given x = 1 2 2.5 3 4 5 and y = 1 5 7 8 2 1

I am suppose to use the spline function built into MATLAB with not-a-knot end conditions. I am having an issue with plotting this. I am trying to plot it on the same plot as two other functions and I am returned an error saying that the dimensions don't line up.

Answer 1

[Image Analyst]

For whatever it's worth, here's one of my spline demos:

% 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)

Answer 2

[Image Analyst]

And here's my other demo, where you interactively place the knots:

% function SmoothSplineCurve()
clc;  % Clear command window.
clear;  % Delete all variables.
close all;  % Close all figure windows except those created by imtool.
imtool close all;  % Close all figure windows created by imtool.
workspace;  % Make sure the workspace panel is showing.
fontSize = 20;

% Change the current folder to the folder of this m-file.
if(~isdeployed)
        cd(fileparts(which(mfilename)));
end
set(gcf, 'Position', get(0,'Screensize')); % Enlarge figure to full screen.
set(gcf,'name','Spline Image Analysis Demo','numbertitle','off') 

axis([0 10 0 10])
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Spline Demo', 'FontSize', fontSize);
hold on
% Initially, the list of points is empty.
knots = [];
numberOfPointsClicked = 0;
% Prompt the user
message = sprintf('Left click to draw some vertex points.\nRight click the final point to finish drawing.');
uiwait(msgbox(message));
buttonThatWasClicked = 1;
% Enter a loop asking user to click on the knot vertexes.
while buttonThatWasClicked == 1
    [xKnot, yKnot, buttonThatWasClicked] = ginput(1);
    plot(xKnot, yKnot, 'ro', 'LineWidth', 2)
    numberOfPointsClicked = numberOfPointsClicked+1;
  % Make this coordinate a new column.
    knots(:, numberOfPointsClicked) = [xKnot; yKnot];
end

% Calculate the area within the blue spline curve.
% You do not need to connect the last point back to the first point.
x = knots(1, :);
y = knots(2, :);
areaOfPolygon = polyarea(x,y);

% Interpolate with a spline curve and finer spacing.
originalSpacing = 1 : numberOfPointsClicked;
% Make 9 points in between our original points that the user clicked on.
finerSpacing = 1 : 0.1 : numberOfPointsClicked;
% Do the spline interpolation.
splineXY = spline(originalSpacing, knots, finerSpacing);

% Plot the interpolated curve.
hold off;
plot(knots(1, :), knots(2, :), 'ro',...
  splineXY(1, :), splineXY(2, :), 'b+-', 'LineWidth', 2, 'MarkerSize', 16);
title('Blue Spline Between Red Knots', 'FontSize', fontSize);
legend('Knots', 'Spline');
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
grid on;
hold off;
% Calculate the area within the blue spline curve.
% You do not need to connect the last point back to the first point.
x = splineXY(1, :);
y = splineXY(2, :);
areaInsideSplineCurve = polyarea(x,y);

% Give the area calculations.
message = sprintf('The area inside the polygon you drew is %.2f.\nThe area inside the blue spline curve is %.2f', ...
  areaOfPolygon, areaInsideSplineCurve);
fprintf(1, '%s', message); % Print to command window.
msgbox(message); % Show user via a popup message box.