# 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
Ah, ok, I kind of just ignored the inner black lines thinking they wee just part of the things being bounded.

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. :)
Jukka Koskinen on 12 Dec 2016
Actually I contacted support and the answer was pretty same: relax the shrinking factory.