User:Dora Gustafson/llRotBetween alternatives

llRotBetween, some alternatives and considerations

Under construction

Scope

Four scripts are covered, They are

1. llRotBetween( vector a, vector b); // The built in function
2. RotBetween( vector a, vector b); // The replacement outlined in the wiki
3. rotV2V( vector a, vector b); // The shortest replacement
4. rotbetween( vector a, vector b); // Using a Vector to rotation function

Tests

First the rotation solutions were compared and they didn't compare at all. Testing rotations is a bad idea since there is no single solution, but an infinite number of solutions. All 4 functions provide different valid solutions. So the sensible thing to do is to test how the solution affects a vector:

Test with random, normalized vectors

<lsl> cycles = 0; record = []; while ( cycles++ < nLimit && llGetListLength( record) < 30) {

   u = llVecNorm(< llFrand( 2.0)-1.0, llFrand( 2.0)-1.0, llFrand( 2.0)-1.0 >);
   v = llVecNorm(< llFrand( 2.0)-1.0, llFrand( 2.0)-1.0, llFrand( 2.0)-1.0 >);
   solution = rotbetween( u, v);
   if ( llVecDist( u*solution, v) > epsilon ) record += [cycles, u, v];

}</lsl>

Results for function 1. llRotBetween

Errors > 1E-7 / number of test cycles

10/13, 10/14

Errors > 1E-6 / number of test cycles

7/1000, 3/1000, 8/1000

Results for function 2. RotBetween

Errors > 1E-7 / number of test cycles

10/18, 10/21, 10/27

Errors > 1E-6 / number of test cycles

0/1000, 0/10000

Results for function 3. rotV2V

Errors > 1E-7 / number of test cycles

10/15, 10/22, 10/14

Errors > 1E-6 / number of test cycles

0/1000, 1/10000, 0/10000

Results for function 4. rotbetween

Errors > 1E-7 / number of test cycles

10/16, 10/23, 10/13

Errors > 1E-6 / number of test cycles

0/1000, 0/10000

Test with close to parallel and anti parallel vectors

<lsl> cycles = 0; record = []; while ( cycles++ < nLimit && llGetListLength( record) < 30) {

   u = llVecNorm(< llFrand( 2.0)-1.0, llFrand( 2.0)-1.0, llFrand( 2.0)-1.0 >);
   v = < llFrand( 2E-3)-1E-3, llFrand( 2E-3)-1E-3, llFrand( 2E-3)-1E-3 >;
   if ( llFrand(1.0) < 0.5 ) v -= u;
   else v += u;
   solution = rotbetween( u, v);
   if ( llVecDist( u*solution, v) > epsilon ) record += [cycles, u, v];

}</lsl>

Results for function 1. llRotBetween

Errors > 1E-3 / number of test cycles

10/16, 10/15, 10/27

Errors > 1E-2 / number of test cycles

0/1000, 0/10000

Results for function 2. RotBetween

Errors > 1E-3 / number of test cycles

10/98, 10/96, 10/109

Errors > 1E-2 / number of test cycles

0/1000, 0/10000

Results for function 3. rotV2V

Errors > 1E-3 / number of test cycles

10/222, 10/89, 10/99

Errors > 1E-2 / number of test cycles

0/1000, 0/10000

Results for function 4. rotbetween

Errors > 1E-3 / number of test cycles

10/192, 10/164, 10/75

Errors > 1E-2 / number of test cycles

0/1000, 0/10000

Conclusion

Functions 2, 3 and 4 have similar performances Function 1, the built-in has the lowest performance