Tetra: algo v1 for higher dim

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

@@ -29,10 +29,11 @@ S=prod(S);
 Z=U(:,S==1);
 
 %--Intersections--%
+D=zeros(2^n,2^(n+1)); % storage for determinants
 H=cell(1); J=H; T=H;
 H{1}=X; J{1}=eye(n); T{1}=zeros(n,1);
 for i=1:n-1
-  [H,J,T]=SUB_simplices_Unfold_v1_20211214(H,J,T,X);
+  [H,J,T]=SUB_simplices_Unfold_v1_20211214(H,J,T,X,D);
   if isempty(H)         % if no intersections are calculated for a given step then there are no more intersections to be found
     return
   end

Research/Edge Intersection/Tetrahedra/Higher dimensions/SUB_simplices_IntersectHyperplane_v1_20211217.m

+function [h,D]=SUB_simplices_IntersectHyperplane_v1_20211217(D,J,T,X)
+% INTERSECTHYPERPLANE computes the intersection of an m-face of X and a
+% collection of hyperplanes of Y
+
+% Uses Cramer's rule with a look-up table to find determinants indexed by J
+% and T
+
+%--Initialize outputs--%
+n=length(T); m=nnz(T)+1;
+h=zeros(n,1);
+
+%--Determine which coordinates of the intersection are needed--%
+indT=1:n; indT=indT(T==0);
+
+%--Denominator is the same for all--%
+j=bit2int(J,n);
+k1=bit2int([1;T],n+1);
+if D(j,k1)==0
+    D(j,k1)=det([ones(m,1), X(J==1,T==1)]); % could also be calculated with other entries of D now that they're indexed with binary
+end
+
+for i=indT
+    %--Convert T with i to coordinates of D--%
+    T_new=T; T_new(i)=1;
+    k=bit2int([0;T_new],n+1);
+    if D(j,k)==0
+        D(j,k)=det(X(J==1,T_new==1));
+    end
+    h(i)=(-1)^(i-1) * D(j,k)/D(j,k1); % need to multiply by a sign to indicate column swaps between num and denom
+end
\ No newline at end of file

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,X)
+function [H_new,J_new,T_new,D] = SUB_simplices_Orphan_v2_20211214(H,J,T,y,D,X)
 % 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.
@@ -27,7 +27,7 @@ for i=1:m-1
             % calculate intersection
                 m_new=m_new+1;
                 J_new(:,m_new)=J(:,i) | J(:,j);
-%             H_new(:,m_new)=SUB_simplices_Intersection_v1_?(X,J_new(:,m_new),T_new);
+                [H_new(:,m_new),D]=SUB_simplices_IntersectHyperplane_v1_20211217(D,J_new(:,m_new),T_new,X);
             end
         end
     end

Research/Edge Intersection/Tetrahedra/Higher dimensions/SUB_simplices_Unfold_v1_20211214.m

-function [H_new,J_new,T_new] = SUB_simplices_Unfold_v1_20211214(H_all,J_all,T_all,X)
+function [H_new,J_new,T_new] = SUB_simplices_Unfold_v1_20211214(H_all,J_all,T_all,X,D)
 % UNFOLD marches through combinations of hyperplane intersections
 %   [H_new,J_new,T_new]=Unfold(H_all,J_all,T_all) computes the new set of
 %   intersections H_new with indices of X J_new and indices of Y T_new.
@@ -22,12 +22,13 @@ function [H_new,J_new,T_new] = SUB_simplices_Unfold_v1_20211214(H_all,J_all,T_al
 
 T=T_all{1}; n=length(T); d=nnz(T)+1; m_max=nchoosek(n,d);
 H_new=cell(m_max,1); J_new=H_new; T_new=H_new; m_new=0;
+% D=zeros(m_max,nchoosek(n+1,d)); % possibly a faster way to get second input from first
 while ~isempty(H_all)
     H=H_all{1}; J=J_all{1}; T=T_all{1};
     indy=1:n; indy=indy(T==0);
     for y=indy
         m_new=m_new+1;      % how many new hyperplane combos have we computed?
-        [H_new{m_new},J_new{m_new},T_new{m_new}]=SUB_simplices_Orphan_v2_20211214(H,J,T,y,X);
+        [H_new{m_new},J_new{m_new},T_new{m_new},D]=SUB_simplices_Orphan_v2_20211214(H,J,T,y,D,X);
     end
     m=length(T_all); indT=zeros(m,1);
     for i=1:m