# Find only interior points from set of points

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I have a collection of interior and exterior points and need to remove all exterior points from the set. The points can be in any order and any shape. The exterior shape does not have to match the interior shape. However, the inner shape NEVER intersects the outer shape. Both shapes share a common "center" point and I have that data. For example, I could have the points like...

t1 = linspace(0,2*pi, 100);

t2 = wrapTo2Pi(t1 + 0.05);

r1 = 5;

r2 = 10;

r3 = 7;

r4 = 12;

x1 = r1*cos(t1);

y1 = r2*sin(t1);

x2 = r3*cos(t2);

y2 = r4*sin(t2);

xGiven = [x1, x2];

yGiven = [y1, y2];

figure()

scatter(xGiven , yGiven);

Assume, that the only information provided is xGiven, and yGiven. No information on how they were constructed is provided.

Here, I only want the points of the interior ring. The common point shared is [0,0] since both shapes are symmetric about that point.

The only toolbox I have access to is the signal processing toolbox.

Any suggestions would be greatly appreciated.

##### 0 Comments

### Accepted Answer

Image Analyst
on 18 Apr 2023

Try this:

% Demo by Image Analyst separate point sets using the convex hull.

clc; % Clear the command window.

close all; % Close all figures (except those of imtool.)

clear; % Erase all existing variables. Or clearvars if you want.

workspace; % Make sure the workspace panel is showing.

format short g;

format compact;

fontSize = 16;

markerSize = 16;

t1 = linspace(0,2*pi, 100);

t2 = wrapTo2Pi(t1 + 0.05);

r1 = 5;

r2 = 10;

r3 = 7;

r4 = 12;

x1 = r1*cos(t1);

y1 = r2*sin(t1);

x2 = r3*cos(t2);

y2 = r4*sin(t2);

xGiven = [x1, x2];

yGiven = [y1, y2];

figure()

subplot(3, 1, 1);

scatter(xGiven , yGiven, 'filled');

xlim([-8, 8]);

title('All Points', 'FontSize', fontSize);

grid on;

% First get exterior points. They are the convex hull.

chIndexes = convhull(xGiven , yGiven);

xExterior = xGiven(chIndexes);

yExterior = yGiven(chIndexes);

% Now get the interior points. They are whatever is not the convex hull

interiorIndexes = setdiff(1:length(xGiven), chIndexes);

xInterior = xGiven(interiorIndexes);

yInterior = yGiven(interiorIndexes);

% Plot red dots for the exterior points

subplot(3, 1, 2);

plot(xExterior, yExterior, 'r.', 'MarkerSize', markerSize);

xlim([-8, 8]);

grid on;

title('Exterior Points', 'FontSize', fontSize);

% Plot magenta dots for the interior points.

subplot(3, 1, 3);

plot(xInterior, yInterior, 'm.', 'MarkerSize', markerSize);

xlim([-8, 8]);

grid on;

title('Interior Points', 'FontSize', fontSize);

##### 2 Comments

Image Analyst
on 18 Apr 2023

### More Answers (1)

Akira Agata
on 18 Apr 2023

The following is an example:

% Sample data

rng('default');

x = rand(100, 1);

y = rand(100, 1);

% Identiry exterior points

k = boundary(x, y);

% Create index

idxExterior = false(size(x));

idxExterior(k) = true;

idxInterior = ~idxExterior;

% Show the result

figure

tiledlayout('flow')

ax1 = nexttile;

scatter(x,y, 'b.')

daspect([1 1 1])

title('All points')

ax2 = nexttile;

scatter(x(idxExterior), y(idxExterior), 'r.')

daspect([1 1 1])

title('Exterior points')

ax3 = nexttile;

scatter(x(idxInterior), y(idxInterior), 'm.')

daspect([1 1 1])

title('Interior points')

linkaxes([ax1, ax2, ax3], 'xy')

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