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Mantis#1598. Thank you kindly, Matth for a patch that addresses: 

The previous implementation of llEuler2Rot was not mathematically 
incorrect, but it was an awkward way of posing the problem that 
led to a few degenerate cases which were not handled correctly - 
for example, PI rotations around X and Z axes were wrong. I put 
some comments in the source about how I arrived at the current 
implementation, which I think is easier to read, and gives 
results that match SL.
0.6.0-stable
Charles Krinke 2008-07-17 19:11:56 +00:00
parent 6084a7ea3e
commit 26fd0595d7
2 changed files with 103 additions and 53 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

78
OpenSim/Region/ScriptEngine/Common/LSL_BuiltIn_Commands.cs
View File

@ -354,48 +354,72 @@ namespace OpenSim.Region.ScriptEngine.Common
return new LSL_Types.Vector3(0.0, -Math.PI / 2, NormalizeAngle(Math.Atan2((r.z * r.s + r.x * r.y), 0.5 - t.x - t.z)));
}
// Xantor's newer llEuler2Rot() *try the second* inverted quaternions (-x,-y,-z,w) as LL seems to like
// New and improved, now actually works as described. Prim rotates as expected as does llRot2Euler.
/* From wiki:
The Euler angle vector (in radians) is converted to a rotation by doing the rotations around the 3 axes
in Z, Y, X order. So llEuler2Rot(<1.0, 2.0, 3.0> * DEG_TO_RAD) generates a rotation by taking the zero rotation,
a vector pointing along the X axis, first rotating it 3 degrees around the global Z axis, then rotating the resulting
vector 2 degrees around the global Y axis, and finally rotating that 1 degree around the global X axis.
*/
/* How we arrived at this llEuler2Rot
*
* Experiment in SL to determine conventions:
* llEuler2Rot(<PI,0,0>)=<1,0,0,0>
* llEuler2Rot(<0,PI,0>)=<0,1,0,0>
* llEuler2Rot(<0,0,PI>)=<0,0,1,0>
*
* Important facts about Quaternions
* - multiplication is non-commutative (a*b != b*a)
* - http://en.wikipedia.org/wiki/Quaternion#Basis_multiplication
*
* Above SL experiment gives (c1,c2,c3,s1,s2,s3 as defined in our llEuler2Rot):
* Qx = c1+i*s1
* Qy = c2+j*s2;
* Qz = c3+k*s3;
*
* Rotations applied in order (from above) Z, Y, X
* Q = (Qz * Qy) * Qx
* ((c1+i*s1)*(c2+j*s2))*(c3+k*s3)
* (c1*c2+i*s1*c2+j*c1*s2+ij*s1*s2)*(c3+k*s3)
* (c1*c2+i*s1*c2+j*c1*s2+k*s1*s2)*(c3+k*s3)
* c1*c2*c3+i*s1*c2*c3+j*c1*s2*c3+k*s1*s2*c3+k*c1*c2*s3+ik*s1*c2*s3+jk*c1*s2*s3+kk*s1*s2*s3
* c1*c2*c3+i*s1*c2*c3+j*c1*s2*c3+k*s1*s2*c3+k*c1*c2*s3 -j*s1*c2*s3 +i*c1*s2*s3 -s1*s2*s3
* regroup: x=i*(s1*c2*c3+c1*s2*s3)
* y=j*(c1*s2*c3-s1*c2*s3)
* z=k*(s1*s2*c3+c1*c2*s3)
* s= c1*c2*c3-s1*s2*s3
*
* This implementation agrees with the functions found here:
* http://lslwiki.net/lslwiki/wakka.php?wakka=LibraryRotationFunctions
* And with the results in SL.
*
* It's also possible to calculate llEuler2Rot by direct multiplication of
* the Qz, Qy, and Qx vectors (as above - and done in the "accurate" function
* from the wiki).
* Apparently in some cases this is better from a numerical precision perspective?
*/
public LSL_Types.Quaternion llEuler2Rot(LSL_Types.Vector3 v)
{
m_host.AddScriptLPS(1);
double x,y,z,s,s_i;
double x,y,z,s;
double c1 = Math.Cos(v.x/2.0);
double c2 = Math.Cos(v.y/2.0);
double c3 = Math.Cos(v.z/2.0);
double s1 = Math.Sin(v.x/2.0);
double s2 = Math.Sin(v.y/2.0);
double s3 = Math.Sin(v.z/2.0);
double cosX = Math.Cos(v.x);
double cosY = Math.Cos(v.y);
double cosZ = Math.Cos(v.z);
double sinX = Math.Sin(v.x);
double sinY = Math.Sin(v.y);
double sinZ = Math.Sin(v.z);
s = Math.Sqrt(cosY * cosZ - sinX * sinY * sinZ + cosX * cosZ + cosX * cosY + 1.0f) * 0.5f;
if (Math.Abs(s) < 0.00001) // null rotation
{
x = 0.0f;
y = 1.0f;
z = 0.0f;
}
else
{
s_i = 1.0f / (4.0f * s);
x = - (-sinX * cosY - cosX * sinY * sinZ - sinX * cosZ) * s_i;
y = - (-cosX * sinY * cosZ + sinX * sinZ - sinY) * s_i;
z = - (-cosY * sinZ - sinX * sinY * cosZ - cosX * sinZ) * s_i;
}
x = s1*c2*c3+c1*s2*s3;
y = c1*s2*c3-s1*c2*s3;
z = s1*s2*c3+c1*c2*s3;
s = c1*c2*c3-s1*s2*s3;
return new LSL_Types.Quaternion(x, y, z, s);
}
public LSL_Types.Quaternion llAxes2Rot(LSL_Types.Vector3 fwd, LSL_Types.Vector3 left, LSL_Types.Vector3 up)
{
m_host.AddScriptLPS(1);

78
OpenSim/Region/ScriptEngine/Shared/Api/Implementation/LSL_Api.cs
View File

@ -341,46 +341,72 @@ namespace OpenSim.Region.ScriptEngine.Shared.Api
return new LSL_Types.Vector3(0.0, -Math.PI / 2, NormalizeAngle(Math.Atan2((r.z * r.s + r.x * r.y), 0.5 - t.x - t.z)));
}
// Xantor's newer llEuler2Rot() *try the second* inverted quaternions (-x,-y,-z,w) as LL seems to like
// New and improved, now actually works as described. Prim rotates as expected as does llRot2Euler.
/* From wiki:
The Euler angle vector (in radians) is converted to a rotation by doing the rotations around the 3 axes
in Z, Y, X order. So llEuler2Rot(<1.0, 2.0, 3.0> * DEG_TO_RAD) generates a rotation by taking the zero rotation,
a vector pointing along the X axis, first rotating it 3 degrees around the global Z axis, then rotating the resulting
vector 2 degrees around the global Y axis, and finally rotating that 1 degree around the global X axis.
*/
/* How we arrived at this llEuler2Rot
*
* Experiment in SL to determine conventions:
* llEuler2Rot(<PI,0,0>)=<1,0,0,0>
* llEuler2Rot(<0,PI,0>)=<0,1,0,0>
* llEuler2Rot(<0,0,PI>)=<0,0,1,0>
*
* Important facts about Quaternions
* - multiplication is non-commutative (a*b != b*a)
* - http://en.wikipedia.org/wiki/Quaternion#Basis_multiplication
*
* Above SL experiment gives (c1,c2,c3,s1,s2,s3 as defined in our llEuler2Rot):
* Qx = c1+i*s1
* Qy = c2+j*s2;
* Qz = c3+k*s3;
*
* Rotations applied in order (from above) Z, Y, X
* Q = (Qz * Qy) * Qx
* ((c1+i*s1)*(c2+j*s2))*(c3+k*s3)
* (c1*c2+i*s1*c2+j*c1*s2+ij*s1*s2)*(c3+k*s3)
* (c1*c2+i*s1*c2+j*c1*s2+k*s1*s2)*(c3+k*s3)
* c1*c2*c3+i*s1*c2*c3+j*c1*s2*c3+k*s1*s2*c3+k*c1*c2*s3+ik*s1*c2*s3+jk*c1*s2*s3+kk*s1*s2*s3
* c1*c2*c3+i*s1*c2*c3+j*c1*s2*c3+k*s1*s2*c3+k*c1*c2*s3 -j*s1*c2*s3 +i*c1*s2*s3 -s1*s2*s3
* regroup: x=i*(s1*c2*c3+c1*s2*s3)
* y=j*(c1*s2*c3-s1*c2*s3)
* z=k*(s1*s2*c3+c1*c2*s3)
* s= c1*c2*c3-s1*s2*s3
*
* This implementation agrees with the functions found here:
* http://lslwiki.net/lslwiki/wakka.php?wakka=LibraryRotationFunctions
* And with the results in SL.
*
* It's also possible to calculate llEuler2Rot by direct multiplication of
* the Qz, Qy, and Qx vectors (as above - and done in the "accurate" function
* from the wiki).
* Apparently in some cases this is better from a numerical precision perspective?
*/
public LSL_Types.Quaternion llEuler2Rot(LSL_Types.Vector3 v)
{
m_host.AddScriptLPS(1);
double x,y,z,s,s_i;
double x,y,z,s;
double c1 = Math.Cos(v.x/2.0);
double c2 = Math.Cos(v.y/2.0);
double c3 = Math.Cos(v.z/2.0);
double s1 = Math.Sin(v.x/2.0);
double s2 = Math.Sin(v.y/2.0);
double s3 = Math.Sin(v.z/2.0);
double cosX = Math.Cos(v.x);
double cosY = Math.Cos(v.y);
double cosZ = Math.Cos(v.z);
double sinX = Math.Sin(v.x);
double sinY = Math.Sin(v.y);
double sinZ = Math.Sin(v.z);
s = Math.Sqrt(cosY * cosZ - sinX * sinY * sinZ + cosX * cosZ + cosX * cosY + 1.0f) * 0.5f;
if (Math.Abs(s) < 0.00001) // null rotation
{
x = 0.0f;
y = 1.0f;
z = 0.0f;
}
else
{
s_i = 1.0f / (4.0f * s);
x = - (-sinX * cosY - cosX * sinY * sinZ - sinX * cosZ) * s_i;
y = - (-cosX * sinY * cosZ + sinX * sinZ - sinY) * s_i;
z = - (-cosY * sinZ - sinX * sinY * cosZ - cosX * sinZ) * s_i;
}
x = s1*c2*c3+c1*s2*s3;
y = c1*s2*c3-s1*c2*s3;
z = s1*s2*c3+c1*c2*s3;
s = c1*c2*c3-s1*s2*s3;
return new LSL_Types.Quaternion(x, y, z, s);
}
public LSL_Types.Quaternion llAxes2Rot(LSL_Types.Vector3 fwd, LSL_Types.Vector3 left, LSL_Types.Vector3 up)
{
m_host.AddScriptLPS(1);