Another approach —
LD1 = load('x.mat');
x = LD1.x;
LD2 = load('y.mat');
y = LD2.y;
cntrd = mean([x(:) y(:)]); % Centroid
angls = atan2(y(:)-cntrd(2), x(:)-cntrd(1)); % Angles Of Each Point W.R.T. Centroid
rads = hypot(y(:)-cntrd(2), x(:)-cntrd(1)); % Distances To Each Point From Centroid
angrad = sortrows([angls rads],1); % Sort Angles & Radii By Angles To Produce Smooth Boundary
angrad = [angrad; angrad(1,:)]; % Close Boundary
xc = (angrad(:,2).*cos(angrad(:,1)))+cntrd(1); % Boundary X-Coordinates
yc = (angrad(:,2).*sin(angrad(:,1)))+cntrd(2); % Boundary Y-Coordinates
figure
scatter(x, y, 10, 'k', 'filled') % Plot Points
hold on
plot(xc, yc, '-r') % Plot Connecting Lines
hold off
grid
axis equal
This should be reasonably robust, although if two points are essentially collinear with respect to their orientation from the centroid (have the same angle, so not all the angles are unique), it could have problems. The solution for that would be to ‘nudge’ the centroid so that all the angles are unique.
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