# Boundary function fails, R2016b

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Jukka Koskinen
on 1 Dec 2016

Commented: Jukka Koskinen
on 12 Dec 2016

I try to make a concave hull type boundary around several overlapping shapes (four circles in this case) by the boundary function. The following code illustrates the problem. The boundary is drawn in black color (better seen in attached file). It doesn't look good... It seems that there is a bug in the function?

if true

clear all;

close all;

r_1 = 5;

r_2 = 3;

r_3 = 2;

r_4 = 2;

center_1 = [2 2];

center_2 = [2 -2];

center_3 = [5 5];

center_4 = [-3 5];

alpha = 0:(2*pi)/120:2*pi;

circle_1 = [center_1(1)+r_1*sin(alpha)' center_1(2)+r_1*cos(alpha)'];

circle_2 = [center_2(1)+r_2*sin(alpha)' center_2(2)+r_2*cos(alpha)'];

circle_3 = [center_3(1)+r_3*sin(alpha)' center_3(2)+r_3*cos(alpha)'];

circle_4 = [center_4(1)+r_4*sin(alpha)' center_4(2)+r_4*cos(alpha)'];

shape = [circle_1

circle_2

circle_3

circle_4];

k = boundary(shape(:,2), shape(:,1), 1);

figure(1)

plot(circle_1(:,1), circle_1(:,2), 'r')

hold on;

grid on;

plot(circle_2(:,1), circle_2(:,2), 'b')

plot(circle_3(:,1), circle_3(:,2), 'g')

plot(circle_4(:,1), circle_4(:,2), 'm')

plot(shape(k,1), shape(k,2), 'k')

axis([-10 10 -10 10])

end

##### 3 Comments

Adam
on 2 Dec 2016

### Accepted Answer

Massimo Zanetti
on 7 Dec 2016

Hi Jukka, if you look at the plot of the boundary without superimposing it to the circles you can see (see first image below) that the shrinking is extreme. You set it to the maximum value of 1 with k = boundary(shape(:,2), shape(:,1), 1);. Thus, the algorithm finds points also in the interior of the major circle.

To solve for this, just relax the shrinking factor by setting it to .5 (the default value). So, invoke k = boundary(shape(:,2), shape(:,1), .5);. The result is shown in the second image. I think that is the one you need. :)

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