no approximation we're so good

check_corner.m

-function corner = check_corner(i0,i1,A,y)
+function corner = check_corner(i0,i1,A,y, inc)
 m = size(y,1);
 C = zeros(m);
 C(1:m-2,1:m-2) = A;
@@ -6,7 +6,9 @@ D = C'+C;
 
 % going from x0 to x1
 [~,nodes] = find(D(i1,:)); 
-nodes = nodes(nodes~=i0); %remove existing edge if it exists
+if inc==1
+    nodes = nodes(nodes~=i0); %remove existing edge if it exists
+end
 j = 1;
 theta = zeros(length(nodes),1);
 for k=nodes

legal_path.m

@@ -35,8 +35,8 @@ for i=1:n+2
             corners = 1;
         else
            % check if outgoing nodes are corners
-           node_corner = check_corner(i,node,A+A',x);
-           outgoing_corner = check_corner(node,i,A+A',x);
+           node_corner = check_corner(i,node,A+A',x,1);
+           outgoing_corner = check_corner(node,i,A+A',x,0);
            corners = node_corner | outgoing_corner;
         end
             

make_plot.m

@@ -5,4 +5,17 @@ hold on
 G2 = graph(A+A');
 plot(G2, 'XData',x(:,1),'YData',x(:,2))
 xlim([0,1])
-ylim([0,1])
\ No newline at end of file
+ylim([0,1])
+
+%% 
+
+figure
+
+plot(G2, 'XData',x(:,1),'YData',x(:,2));
+A_path = zeros(n+2);
+for i=1:length(path)-1
+   A_path(path(i),path(i+1)) = 1; 
+end
+hold on
+G3 = graph(A_path+A_path');
+plot(G3, 'XData',y(:,1),'YData',y(:,2),'LineWidth',1.5,'EdgeColor','g');