Compute the Maximum Points Values in Optimum Tetrahedral Volume (update:29-07-07)

optimization analysis with cyclic-permutation

Description:

In the one point-system, we suppose a optimum tetrahedral volume and this volume should be contain maximum points in the selected point-system. Extarly, this tetrahedral volume's of boundary conditions should be depend only four-node in point-system.

Also, this sub-program running of similarly cyclic-permutation technique than not more-speedly. This program's cyclic-permutation run-time is depend matlab main function as -nchoosek-. Plainly, If you selected more 50 point than solution time possible be few minute. This program's low-order-level of run-time not depent is my program's base-algorithm.

I selected new algorithm this sub-function. This algorithm is; random nodes be control in-side or out-side in tetrahedral volume with four-homogen axis system boundary conditions as vectoral matlab solutions.

Syntax:
random_nodes = selected three-dimensional point-system .
random_nodes_in = in-side points in optimum tetrahedral volume.
random_nodes_out = out-side points in optimum tetrahedral volume.

Example:

warning: This function analysis need nodes matrix
Runing automatic example:
maxnodetrn(rand(20,2))<--| Example:

random_nodes_permutation =

1 2 3 4
1 2 3 5
1 2 3 6
%....... ..... ......
% 14 15 17 19
% 14 15 17 20

Total.cyclicper.--active.per.----in.node---optimum.node.position.matrix
4845 1 5 1 2 3 4
Total.cyclicper.--active.per.----in.node---optimum.node.position.matrix
4845 111 6 1 2 11 14
Total.cyclicper.--active.per.----in.node---optimum.node.position.matrix
4845 247 7 1 3 11 14
Total.cyclicper.--active.per.----in.node---optimum.node.position.matrix
4845 765 8 1 9 11 17
Total.cyclicper.--active.per.----in.node---optimum.node.position.matrix
4845 4407 9 9 11 13 17

Tetrahedral volume in-side points
A =
node value x{i} y{i} z{i}
2.0000 0.2973 0.4577 0.4662
5.0000 0.2639 0.4939 0.3625
6.0000 0.4577 0.4175 0.7308
7.0000 0.8437 0.2923 0.6497
9.0000 0.7000 0.7538 0.0076
11.0000 0.9745 0.0769 0.9452
13.0000 0.1313 0.7649 0.7829
17.0000 0.0430 0.3062 0.1785
18.0000 0.4792 0.3707 0.5294

Tetrahedral volume out-side points
B =
1.0000 0.7729 0.9523 0.8137
3.0000 0.1779 0.5369 0.7223
4.0000 0.6908 0.0665 0.9949
8.0000 0.8815 0.2897 0.6813
10.0000 0.7557 0.0968 0.6541
12.0000 0.4022 0.7209 0.6133
14.0000 0.7247 0.6579 0.0032
15.0000 0.8995 0.8104 0.7970
16.0000 0.1707 0.3742 0.6418
19.0000 0.0939 0.7067 0.2187
20.0000 0.6500 0.1684 0.5481

Run-times:
tic;[A,B]=maxnodetetra(rand(5,3)) ;toc ,Elapsed time is 0.031401 s.
tic;[A,B]=maxnodetetra(rand(10,3)) ;toc ,Elapsed time is 0.118064 s.
tic;[A,B]=maxnodetetra(rand(20,3)) ;toc ,Elapsed time is 1.899223 s.
tic;[A,B]=maxnodetetra(rand(30,3)) ;toc ,Elapsed time is 10.60622 s.
tic;[A,B]=maxnodetetra(rand(40,3)) ;toc ,Elapsed time is 36.15070 s.
tic;[A,B]=maxnodetetra(rand(50,3)) ;toc ,Elapsed time is 92.99520 s.
tic;[A,B]=maxnodetetra(rand(60,3)) ;toc ,Elapsed time is 201.53488s.
tic;[A,B]=maxnodetetra(rand(70,3)) ;toc ,Elapsed time is 394.61013s.
tic;[A,B]=maxnodetetra(rand(80,3)) ;toc ,Elapsed time is 626.83163s.