Distance based interpolation along a general curve in space
Updated 16 Aug 2012

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A common request is to interpolate a set of points at fixed distances along some curve in space (2 or more dimensions.) The user typically has a set of points along a curve, some of which are closely spaced, others not so close, and they wish to create a new set which is uniformly spaced along the same curve.

When the interpolation is assumed to be piecewise linear, this is easy. However, if the curve is to be a spline, perhaps interpolated as a function of chordal arclength between the points, this gets a bit more difficult. A nice trick is to formulate the problem in terms of differential equations that describe the path along the curve. Then the interpolation can be done using an ODE solver.

As an example of use, I'll pick a random set of points around a circle in the plane, then generate a new set of points that are equally spaced in terms of arc length along the curve, so around the perimeter of the circle.

theta = sort(rand(15,1))*2*pi;
theta(end+1) = theta(1);
px = cos(theta);
py = sin(theta);

100 equally spaced points, using a spline interpolant.

pt = interparc(100,px,py,'spline');

% Plot the result
axis([-1.1 1.1 -1.1 1.1])
axis equal
grid on
xlabel X
ylabel Y
title 'Points in blue are uniform in arclength around the circle'

You can now also return a function handle to evaluate the curve itself at any point. As well, CSAPE is an option for periodic (closed) curves, as long as it is available in your matlab installation.

[~,~,foft] = interparc([],px,py,'spline');
ans =
0.98319 0.18257
-0.19064 0.98151
-0.98493 -0.17486
0.18634 -0.98406
0.98319 0.18257

Cite As

John D'Errico (2024). interparc (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Fix for dudt at the proper points.

Fixed bug in recognizing contractions

Add csape for periodic fits, and return a function handle for external evaluation.