Tetra: driver for intersection of simplices, inelegant

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

+function [Z]=ALGO_simplices_IntersectSimplices_v1_20211216(U,V)
+% INTERSECTSIMPLICES calculates the intersection between two simplices of
+% arbitrary dimension
+
+% Important note: this version, and the related subfunctions, do not
+% include a formal treatment of the signs of each component. A version that
+% is in keeping with the principles laid out in the paper would feature an
+% in-depth network of connections between signs, as well as tests for the
+% same sign of components of previous intersections in the event that the
+% m-face of X does not have a maximum number of intersections at a given
+% step.
+
+n=length(U); % there are n vertices of U (and V) which means the dimension
+             %  of the space is n-1
+             
+%--Change of Coordinates--%
+v0=V(:,n); A=V(:,1:n-1)-V(:,n);
+X=A \ (U-v0);
+X=[X; 1-ones(1,n-1)*X]; % tack on the x*e_0 'coordinates'
+
+%--Vertices of X in Y--%
+S=X>=0;
+if prod(prod(S,2))==0   % if there is a given coordinate where all X values are negative
+  disp('Simplices do not intersect') % then there is a hyperplane that entirely divides X and Y
+  Z=[];
+  return
+end
+S=prod(S);
+Z=U(:,S==1);
+
+%--Intersections--%
+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);
+  if isempty(H)         % if no intersections are calculated for a given step then there are no more intersections to be found
+    return
+  end
+  S=prod(H>=0); Z=[Z,A*H(1:n,S==1)+v0];
+end
+
+%--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 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
+  for i=indT
+    if indV(i)==0
+      j=indT(indT~=i);
+      if sign(max(H1(j,:)))~=sign(min(H1(j,:)))
+        binV(i)=1;
+      end
+      indV(i)=1;
+    end
+  end
+  m=length(T); indT=zeros(m,1);
+  for i=1:m
+    if nnz(indV | T{i})==n
+      indT(i)=1;
+    end
+  end
+  H=H{indT==0}; T=T{indT==0};
+end
+Z=[Z,V(:,binV)];
\ No newline at end of file

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

@@ -20,7 +20,7 @@ function [H_new,J_new,T_new] = SUB_simplices_Unfold_v1_20211214(H_all,J_all,T_al
 %   - is there not a faster/less involved way to remove dupliate
 %       combinations?
 
-T=T_all{1}; n=length(T); d=nnz(T); m_max=nchoosek(n,d);
+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;
 while ~isempty(H_all)
     H=H_all{1}; J=J_all{1}; T=T_all{1};