How to Discretize a Polygon boundary in to equally spaced points?

The following code plots a polygon (Rectangle with curved corners).

%%
clc
clear all
close all
%%

h=polybuffer( polyshape([0.15  0 -0.15 -0.15 -0.15 0 0.15 0.15], [0.25 0.25 0.25 0.10 -0.05 -0.05 -0.05 0.10]),0.1);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

pgon1 = polyshape({h.Vertices(:,1)}, {h.Vertices(:,2)});
xb = (pgon1.Vertices(:,1))';
yb = (pgon1.Vertices(:,2))';
xb = xb(:);
yb = yb(:);


figure
plot(xb, yb, 'DisplayName','All Data')

axis([-0.4 0.4 -0.2 0.4])

Currently, I have a set of points near the curved region and very limited over the straight portions. I want to generate a set of boundary points for this polyshape that are equally spaced. How do I do that?

Answer 1

[Suraj Kumar]

Hi @Prasanna Routray,

Based on my understanding you want to discretize the boundary of a polygon into equally spaced points.

To achieve this, you can refer to the following steps:

1. After defining the polygon, extract its vertices and calculate the Euclidean distances between consecutive vertices.You can use the function 'cumsum' to get the cumulative distances along the boundary.

xb = (pgon1.Vertices(:,1))';
yb = (pgon1.Vertices(:,2))';
distances = [0; cumsum(sqrt(diff(xb).^2 + diff(yb).^2))];

2. Choose the number of equally spaced points and use `linspace` to generate target distances along the perimeter.

numPoints = 30;
equalSpacedDistances = linspace(0, distances(end), numPoints);

3. Then apply `interp1` to interpolate the x and y coordinates at these distances, yielding points uniformly distributed along the boundary.

xEqualSpaced = interp1(distances, xb, equalSpacedDistances);
yEqualSpaced = interp1(distances, yb, equalSpacedDistances);

You can refer to the attached output for a better understanding:

To learn more about 'cumsum' and 'interp1' functions in MATLAB, please refer to the following links:

• https://www.mathworks.com/help/matlab/ref/double.cumsum.html
• https://www.mathworks.com/help/matlab/ref/double.interp1.html

Happy Coding!

Answer 2

[Walter Roberson]

See John D'errico file exchange contribution interparc https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc