it's alive

checkCrossedLines.m

 % check if line segment AB intersects line segment CD
 % 
-function isInSegment = checkCrossedLines(A,B,C,D)
+function [isInSegment] = checkCrossedLines(A,B,C,D)
 
 % A = [1,1]; C = [2,2]; B = [2,1]; D = [1,2];
 

expected_value.m

+n = 100;
+k = 110;
+dists = zeros(k,1);
+cputime = zeros(k,1);
+j=1;
+for i=1:k
+tic;   
+[A,x] = shortest_path( n );
+
+[C,i_traverse,z] = traverse_graph(A,x);
+m = size(C,1);
+[B,y] = legal_paths(C,z ,i_traverse);
+
+[dist, path] = graphshortestpath(sparse(B+B'), m+1, m+2);
+
+cputime(i) = toc;
+dists(i) = dist;
+
+if dist ==Inf
+    A_inf{j} = A;
+    x_inf{j} = x;
+    y_inf{j} = y;
+    B_inf{j} = B;
+    j = j+1;
+end
+end
+
+disp(['Mean distance is ', num2str(mean(dists))])
+disp(['Standard deviation is ',num2str(std(dists))])
+disp(['Mean cpu time is ', num2str(mean(cputime))])
\ No newline at end of file

hollow_graph.m

+function [ A2,x2,J ] = hollow_graph( A,x)
+C = A'+A;
+n = size(A,1);
+delta = 1e-12;
+% nodes of degree more
+I = [];
+for i=1:n
+nonz = nnz(C(i,:));
+if nonz==1
+    I = [I,i];
+end
+end
+
+n1 = length(I);
+J = setdiff(1:n,I);
+n2 = n-n1;
+
+x2 = x(J,:);
+
+x2 = x2 + [delta,0];
+
+AI = A(J,I);
+AJ = A(J,J);
+
+A2 = zeros(n+n2);
+A2(1:n,1:n) = A;
+A2(n+1:n+n2,n+1:n+n2) = AJ;
+A2(n+1:n+n2,I) = AI;
+x3 = [x;x2];
\ No newline at end of file

launch.m

+n = 100;
+
+
+[A,x] = shortest_path( n );
+
+[C,i_traverse,z] = traverse_graph(A,x);
+m = size(C,1);
+[B,y] = legal_paths(C,z ,i_traverse);
+% [B,y] = legal_path(C,z);
+[dist, path] = graphshortestpath(sparse(B+B'), m+1, m+2);
+
+
+%%
+
+B2 = tril(B)+tril(B)';
+
+[dist, path] = graphshortestpath(sparse(B2), n+length(x2)+1, n+length(x2)+2);
+

legal_paths.m

+function [B,y] = legal_paths(C,z,i_traverse)
+%UNTITLED19 Summary of this function goes here
+%   Detailed explanation goes here
+m = size(C,1);
+y = z;
+y(m+1,:) = [0,0];
+y(m+2,:) = [0.5,0.5];
+B = zeros(m+2);
+C = C'+C;
+for i = 1:m+2
+    if i<m+1
+        neighbours_i = find((i_traverse==i_traverse(i)));
+    else
+        neighbours_i = i;
+    end
+    %Connect to possible non-neighbours
+    for j = setdiff(i:m+2,neighbours_i,'stable')
+        if j<m+1
+            neighbours_j =  find((i_traverse==i_traverse(j)));
+        else
+            neighbours_j = j;
+        end
+        [I,J] = find(C);
+
+        I1 = I(I~=i & I~=j & J~=i & J~=j); 
+        J = J(I~=i & I~=j & J~=i & J~=j);
+        I = I1;
+%         [I,indices] = setdiff(I,j,'stable');
+%         J = J(indices);
+%         [J,indices] = setdiff(J,i,'stable');
+%         I = I(indices);
+%         [J,indices] = setdiff(J,j,'stable');
+%         I = I(indices);
+        
+        crosses = 0;
+        for k = 1:length(I)
+            crosses = checkCrossedLines(y(i,:),y(j,:),y(I(k),:),y(J(k),:));
+            if crosses >0         
+                 break
+            end
+        end
+        if crosses == 0 
+            B(i,j) = sqrt(sum((y(i,:)-y(j,:)).^2));
+        end   
+    end
+    
+%     % Make neighbours obstacles i.e. Inf paths
+%     for j= neighbours_i(neighbours_i~=i)
+%         B(i,j) = Inf;
+%     end
+%     
+
+
+   
+    
+    
+    
+end
+
+
+end
+

make_plot.m

@@ -12,10 +12,45 @@ ylim([0,1])
 figure
 
 plot(G2, 'XData',x(:,1),'YData',x(:,2));
-A_path = zeros(n+2);
+A_path = zeros(m+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');
+
+%%
+
+figure 
+G4 = graph(A2+A2');
+x3 = [x;x2];
+plot(G4, 'XData',x3(:,1),'YData',x3(:,2));
+
+%%
+figure
+G5 = graph(C+C');
+plot(G5, 'XData',z(:,1),'YData',z(:,2));
+
+%% 
+figure
+G5 = graph(C+C');
+plot(G5, 'XData',z(:,1),'YData',z(:,2));
+hold on
+G2 = graph(A+A');
+plot(G2, 'XData',x(:,1),'YData',x(:,2))
+xlim([0,1])
+ylim([0,1])
+
+%%
+figure
+G5 = graph(C+C');
+plot(G5, 'XData',z(:,1),'YData',z(:,2));
+
+A_path = zeros(m+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');
\ No newline at end of file

minimum_angle.m

+function [ i_next,angle] = minimum_angle(i0,i1,A,x)
+%
+D = A'+A;
+
+% going from x0 to x1
+[~,nodes] = find(D(i1,:)); 
+if length(nodes) >1
+    nodes = nodes(nodes ~=i0);
+end
+j = 1;
+theta = zeros(length(nodes),1);
+for k=nodes
+    theta0 = acos(dot(x(i0,:)-x(i1,:), x(k,:)-x(i1,:))/(sqrt(sum(abs(x(i0,:)-x(i1,:)).^2))*D(k,i1)));
+    thecross = cross([x(i0,:)-x(i1,:),0], [x(k,:)-x(i1,:),0]);
+    thesign = sign(thecross(3));
+    if thesign<0
+        theta(j) = 2*pi-theta0;
+    else
+        theta(j) = theta0;
+    end
+    j=j+1;
+end
+
+[angle,i_next] = min(theta);
+i_next = nodes(i_next);
+end
+

traverse_graph.m

+function [B, i_traverse,y] = traverse_graph( A,x )
+delta = 1e-5;
+C = A'+A;
+nonz=2;
+i=1;
+while nonz>1
+    nonz = nnz(C(i,:));
+    if nonz==1
+         current_node = i;
+    end
+    i=i+1;
+end
+i_traverse(1) = current_node;
+y(1,:) = x(current_node,:);
+next_node = find(C(current_node,:));
+j = 2;
+while next_node ~= i_traverse(1)
+    [node_temp,angle] = minimum_angle(current_node,next_node,A,x);
+    if node_temp == current_node
+        y(j,:) = x(next_node,:);
+    elseif angle<pi
+        y(j,:) = x(next_node,:) + delta*(x(current_node,:) + x(node_temp,:) - 2*x(next_node,:));
+    elseif angle>=pi
+        y(j,:) = x(next_node,:) - delta*(x(current_node,:) + x(node_temp,:) - 2*x(next_node,:));
+    end
+    current_node = next_node;
+    i_traverse(j) = current_node;
+    next_node = node_temp;
+    j = j+1;
+end
+m = length(i_traverse);
+B = zeros(m);
+for i=1:m-1
+    B(i,i+1) = C(i_traverse(i),i_traverse(i+1));
+    % Make blocks between neighbours
+    for j=find(i_traverse==i_traverse(i))
+        if (j~=i)
+            B(i,j) =Inf;
+        end
+    end
+    % Fill in the Polygon
+    for j=find(i_traverse==i_traverse(i+1))
+        if (j~=i+1)
+            B(i,j) =Inf;
+        end
+    end
+end
+for i=2:m
+    % Fill in the Polygon
+    for j=find(i_traverse==i_traverse(i-1))
+        if (j~=i-1)
+            B(i,j) =Inf;
+        end
+    end    
+end
+B(m,1) = C(i_traverse(m),i_traverse(1));
+
+% y = x(i_traverse,:);
+end