Polycut2

POLYCUT2(lat,long) connects the contour and holes of polygons. In contrast to POLYCUT, POLYCUT2 finds an output polygon with smaller total contour length and avoids cases where the cuts interesect with the polygon contours.
Example:
% outer contour
ov = [0,0; 0,1; 2,1; 2,2; 0,2; 0,3; 3,3; 3,0];
% hole 1
iv1 = [0.5,0.3; 1.5,0.3; 1.5,0.7; 0.5,0.7];
% hole 2
iv2 = [0.5,2.3; 1.5,2.3; 1.5,2.7; 0.5,2.7];
v = [ov;nan(1,2);iv1;nan(1,2);iv2];
[v1(:,1),v1(:,2)] = polycut(v(:,1),v(:,2));
[v2(:,1),v2(:,2)] = polycut2(v(:,1),v(:,2));

% red is old method, blue is new one
figure;
line(v1(:,1),v1(:,2),'Color','red');
figure;
line(v2(:,1),v2(:,2),'Color','blue');