[Octave-bug-tracker] [bug #60818] delaunayn - 2D code path vectorization doesn't match nD algorithm

[Nicholas Jankowski]

Follow-up Comment #20, bug #60818 (project octave):

stepping through the nD code, using a 3D example, it seems to be missing one
of the zero volume tets:

Matlab:

A = [0 0 0;
1 0 0;
0 1 0;
0 0 1;
1 1 0;
1 0 1;
0 1 1;
1 1 1;
0.5 0.5 0.5];

B = delaunay(A)
B =
     3     4     1     9
     3     7     9     5
     8     9     7     5
     8     6     9     5
     8     6     7     9
     9     7     4     6
     3     7     4     9
     3     9     2     5
     9     6     2     5
     9     4     2     6
     9     4     1     2
     3     9     1     2

size(B)
ans =
    12     4


Octave old code:

>> A = [0 0 0; 1 0 0; 0 1 0; 0 0 1; 1 1 0; 1 0 1; 0 1 1; 1 1 1; 0.5 0.5 0.5]
A =

        0        0        0
   1.0000        0        0
        0   1.0000        0
        0        0   1.0000
   1.0000   1.0000        0
   1.0000        0   1.0000
        0   1.0000   1.0000
   1.0000   1.0000   1.0000
   0.5000   0.5000   0.5000

>> B = delaunayn(A)
B =

   5   9   2   1
   5   9   3   1
   6   9   2   1
   6   9   4   1
   6   5   9   2
   6   5   8   9
   7   9   3   1
   7   9   4   1
   7   5   9   3
   7   5   8   9
   7   6   9   4
   7   6   8   9

>> size(B)
ans =

   12    4


new code, using LU decomp for 3D:


>> B = delaunayn(A)
B =

   5   3   2   1
   5   9   3   1
   6   4   2   1
   6   9   2   1
   6   9   4   1
   6   5   8   2
   6   5   9   2
   7   9   3   1
   7   9   4   1
   7   5   9   3
   7   5   8   9
   7   6   9   4
   7   6   8   9

>> size(B)
ans =

   13    4

>> p12 = A(B(:,1),:)-A(B(:,2),:); p23 = A(B(:,2),:)-A(B(:,3),:); p34 =
A(B(:,3),:)-A(B
(:,4),:);
>> vol = dot (p12, cross (p23, p34, 2), 2)
vol =

        0
  -0.5000
        0
  -0.5000
   0.5000
        0
   0.5000
   0.5000
  -0.5000
  -0.5000
  -0.5000
   0.5000
   0.5000


so, it left in the three 0 vol tets but dropped 2 others.  will look through
to see if it's something obvious.

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