Difference between revisions of "User:Dora Gustafson/llRotBetween alternatives"
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== Conclusion == | == Conclusion == | ||
Functions 2, 3 and 4 have similar performances. | Functions 2, 3 and 4 have similar performances. | ||
Function 1, the built-in, has a lower performance | Function 1, the built-in, has a lower performance.<br> | ||
All four functions are very good except with parallel and anti parallel vectors.<br> | |||
The rotation found is not always what you expect.<br> | |||
: The rotation will point a vector in the right direction, i.e. the rotation's ''forward'' is all right. | |||
: The rotations ''left'' direction is in the plane given by the two vectors, which is not always what you want or expect | |||
: Function 4 is different, it returns a rotation with ''left'' in the horizontal plane | |||
== Scripts and functions == | == Scripts and functions == |
Revision as of 15:34, 26 December 2012
llRotBetween, some alternatives and considerations
Scope
Four functions are covered, They are
- llRotBetween( vector a, vector b); // The built in function
- RotBetween( vector a, vector b); // The replacement outlined in the wiki
- rotV2V( vector a, vector b); // The shortest replacement
- 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 are no single solutions, but infinite numbers of solutions. All 4 functions provide valid, but different solutions. So the sensible thing to do is to test how the solution rotates 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>
Errors / test cycles | Function 1 | Function 2 | Function 3 | Function 4 |
---|---|---|---|---|
llRotBetween | RotBetween | rotV2V | rotbetween | |
abs error > 1e-7 | 10 / 13 | 10 / 18 | 10 / 15 | 10 / 16 |
10 / 14 | 10 / 21 | 10 / 22 | 10 / 23 | |
10 / 27 | 10 / 14 | 10 / 13 | ||
abs error > 1e-6 | 7 / 1000 | 0 / 1000 | 0 / 1000 | 0 / 1000 |
3 / 1000 | 0 / 10000 | 1 / 10000 | 0 / 10000 | |
8 / 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>
Errors / test cycles | Function 1 | Function 2 | Function 3 | Function 4 |
---|---|---|---|---|
llRotBetween | RotBetween | rotV2V | rotbetween | |
abs error > 1e-3 | 10 / 16 | 10 / 98 | 10 / 222 | 10 / 192 |
10 / 15 | 10 / 96 | 10 / 89 | 10 / 164 | |
10 / 27 | 10 / 109 | 10 / 99 | 10 / 75 | |
abs error > 1e-2 | 0 / 1000 | 0 / 1000 | 0 / 1000 | 0 / 1000 |
0 / 10000 | 0 / 10000 | 0 / 10000 | 0 / 10000 |
Conclusion
Functions 2, 3 and 4 have similar performances.
Function 1, the built-in, has a lower performance.
All four functions are very good except with parallel and anti parallel vectors.
The rotation found is not always what you expect.
- The rotation will point a vector in the right direction, i.e. the rotation's forward is all right.
- The rotations left direction is in the plane given by the two vectors, which is not always what you want or expect
- Function 4 is different, it returns a rotation with left in the horizontal plane
Scripts and functions
- Function 1, llRotBetween()
- This is the built in function, see llRotBetween
- Function 2, RotBetween()
- This is the suggested replacement for llRotBetween
- Function 3, rotV2V()
<lsl>rotation rotV2V( vector a, vector b) {
a = llVecNorm(a); b = llVecNorm(b); vector c = b; while ( llFabs(a*c) > 0.999999 ) c = llVecNorm(< llFrand( 2.0)-1.0, llFrand( 2.0)-1.0, llFrand( 2.0)-1.0 >); c = llVecNorm(a%c); return ZERO_ROTATION/llAxes2Rot( a, c, a%c)*llAxes2Rot( b, c, b%c);
} </lsl>
- Function 4, rotbetween()
<lsl>rotation Vec2Rot( vector a) {
a = llVecNorm(a); vector c = < 0.0, 0.0, 1.0 >; if ( llFabs(a*c) > 0.999999 ) c = llVecNorm(< llFrand( 2.0)-1.0, llFrand( 2.0)-1.0, 0.0 >); vector b = llVecNorm(c%a); return llAxes2Rot( a, b, a%b);
}
rotation rotbetween( vector a, vector b) {
return ZERO_ROTATION/Vec2Rot(a)*Vec2Rot(b);
} </lsl>