Compute Approximate Medial Axis of Polygonal Domain

Create an approximate Medial Axis of a polygonal domain using a constrained Delaunay triangulation. The Medial Axis of a polygon is defined by the locus of the center of a maximal disk within the polygon interior.

Construct a constrained Delaunay triangulation of a sample of points on the domain boundary.

load trimesh2d
dt = delaunayTriangulation(x,y,Constraints);
inside = isInterior(dt);

Construct a triangulation to represent the domain triangles.

tr = triangulation(dt(inside,:),dt.Points);

Construct a set of edges that join the circumcenters of neighboring triangles. The additional logic constructs a unique set of such edges.

numt = size(tr,1);
T = (1:numt)';
neigh = neighbors(tr);
cc = circumcenter(tr);
xcc = cc(:,1);
ycc = cc(:,2);
idx1 = T < neigh(:,1);
idx2 = T < neigh(:,2);
idx3 = T < neigh(:,3);
neigh = [T(idx1) neigh(idx1,1); T(idx2) neigh(idx2,2); T(idx3) neigh(idx3,3)]';

Plot the domain triangles in green, the domain boundary in blue, and the medial axis in red.

clf
triplot(tr,"g")
hold on
plot(xcc(neigh),ycc(neigh),"-r",LineWidth=1.5)
axis([-10 310 -10 310])
axis equal
plot(x(Constraints'),y(Constraints'),"-b",LineWidth=1.5)
xlabel("Medial Axis of Polygonal Domain",FontWeight="b")
hold off