Tetra: initialized Z in higher dim algo, loose bounds on size

Research/Edge Intersection/Tetrahedra/Higher dimensions/ALGO_simplices_IntersectSimplices_v1_20211216.m

@@ -36,12 +36,12 @@ if prod(sum(S,2))==0   % if there is a given coordinate where all X values are n
   Z=[];
   return
 end
-S=prod(S);
-Z=U(:,S==1);
+S=prod(S); m=sum(S==1); Z=U(:,S==1);
 
 %--Intersections--%
 global D
 D=zeros(2^n,2^(n+1)); % storage for determinants
+Z=[Z,zeros(n-1,2^n * n)]; % is this the actual number of possible intersections? surely we can prove a tighter bound
 H=cell(1); J=H; T=H;
 H{1}=X; J{1}=eye(n); T{1}=zeros(n,1);
 for i=1:n-2
@@ -50,19 +50,21 @@ for i=1:n-2
     return
   end
   for j=1:length(T)     % given this unpacking it is probably more efficient to do this step within the subfunctions
-    Hj=H{j}; S=prod(Hj>=0); Z=[Z,A*Hj(2:end,S==1)+v0];
+    H1=H{j}; S=prod(H1>=0); mj=sum(S==1);
+    Z(:,m+(1:mj))=A*H1(2:end,S==1)+v0; m=m+mj;
     if sum(S)~=0             % check which hyperplanes of V intersect with edges of U
       ind=1:n; ind=ind(T{j}==1)-1; ind(ind==0)=n;
       nhbrs(ind)=1;
     end
   end
 end
+Z=Z(:,1:m);
 
 %--Vertices of Y in X--%
 binV=zeros(n,1); indV=binV; % another probably terrible way of doing things... see notes on v1 of Unfold and v2 of Orphan for thoughts
 while ~isempty(H)
   H1=H{1}; T1=T{1};
-  indT=1:n; indT=indT(T1==0); % at most two values in ind
+  indT=1:n; indT=indT(T1==0); % at most two values in indT
   for i=indT
     if indV(i)==0
       j=indT(indT~=i);

Research/Edge Intersection/Tetrahedra/Higher dimensions/SUB_simplices_Orphan_v2_20211214.m

-function [H_new,J_new,T_new] = SUB_simplices_Orphan_v2_20211214(H,J,T,y)
+function [H_new,J_new,T_new,m_new] = SUB_simplices_Orphan_v2_20211214(H,J,T,y)
 % ORPHAN determines adjacent intersections and generates index set
 %   [H_new,J_new,T_new] = Orphan(H,J,T,A,y,X) finds all intersections
 %   H_new between the n-simplex X and the hyperplanes indexed by T and y.