Interpolating values on a 2D plot when NOT a function (i.e. a looped shape)
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Hi maestros,
I have a shape in x,y, that loops back on itself and meanders (without intersecting itself). An example would be a circle, a heart shape or the top view of a race car track.
I wish to find the values of y (usually there would be more than 1) for a given x value (or set of x values). I am aware that the spline function could help me if this was a function. I am also aware that a parameter 't' could be made to find (x,y,) in terms of 't', but don't see how this could help me.
Here is an example set of points in x,y if you want it:
x= [-0.2073 0.5721 1.4722 2.2293 2.6327 3.0899 3.7784 4.5382 5.5277 6.9211 8.3167 9.2896 9.0604 7.8213 6.6720 5.9258 5.1584 4.3335 3.8667 4.1657 5.3247 5.9008 5.0912 3.0462 0.6883 -0.9153 -1.9870 -3.2646 -4.0178 -4.6815 -6.2504 -7.6611 -8.3864 -8.6373 -8.3692 -7.5111 -6.5901 -6.3305 -6.6416 -7.2034 -7.1405 -6.1491 -4.8732 -3.8070 -3.0348 -2.4280 -1.5272 -0.8534 -0.4118 0.2505]
y = [ -2.3595 -2.9712 -3.0852 -2.7334 -2.2111 -1.6185 -1.3093 -1.3964 -1.6764 -1.9983 -1.8301 -0.9510 0.0921 0.7508 0.8846 0.5857 0.2114 0.1446 0.4953 1.1859 1.8096 2.5017 2.8755 2.7823 2.3773 1.7967 1.2743 1.2158 1.7293 2.3063 2.5951 2.4283 1.8694 1.1793 0.6032 0.2349 -0.0044 -0.3900 -1.1001 -1.7027 -2.3185 -2.7130 -2.6429 -2.1655 -1.6388 -1.4356 -1.4135 -1.6123 -2.1106 -2.7784]
Any help would be greatly appreciated, as I have spent a LONG time searching.
Mike
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Answers (3)
Image Analyst
on 3 Sep 2013
Mike: Do you want something like this, where I parameterized x and y and fit a spline to both?
% function SmoothSplineCurve()
clc; % Clear command window.
clear; % Delete all variables.
close all; % Close all figure windows except those 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.
6 Comments
Ryan Spencer
on 6 Jan 2022
Hello Image Analyst. Fantastic code! Could you describe how to superimpose an image as the background?You can then use your code to trace/outline a geometry within the image. Thank you!
Image Analyst
on 6 Jan 2022
Not sure what you mean. Start a new question and give an example of your inputs and your desired output.
Bjorn Gustavsson
on 4 Sep 2013
Pseudo-coded stab at this:
1, find all indices for which x(i1) < x_current and x(i1+1) > x_current
and x(i1) > x_current and x(i1+1) < x_current and x(i1) == x_current
2, Interpolate between the point-pairs
HTH
0 Comments
gaoliming gao
on 2 Jul 2020
You may want to refer to this exchange file https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc
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