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| author | Martin Miller | 2017-04-04 12:31:50 -0500 |
|---|---|---|
| committer | Martin Miller | 2017-04-04 12:31:50 -0500 |
| commit | f03177359d0d592c41b8c6412b65ecbed49a64e4 (patch) | |
| tree | ad482d3f299d6583f3a2314ffbbced20f9a20d13 | |
| parent | f683e1e8be18de841c714f3bf8ec15d2d0b68a75 (diff) | |
| download | refslam-f03177359d0d592c41b8c6412b65ecbed49a64e4.zip refslam-f03177359d0d592c41b8c6412b65ecbed49a64e4.tar.gz | |
Update Feature class to use FULLSTATE.
The Jacobian of the measurement model, Hx and Hy were updated using code
generated with matlab's ccode() function. This generates a number of
intermediate values, which are an optimization by the function's
description, before setting the final values. In any case, it's not
necessarily more readable, but it does eliminate the incredbily long
lines used previously.
| -rw-r--r-- | src/feature.cpp | 523 | ||||
| -rw-r--r-- | src/feature.h | 1 |
2 files changed, 477 insertions, 47 deletions
diff --git a/src/feature.cpp b/src/feature.cpp index c9cdda1..8f6fd12 100644 --- a/src/feature.cpp +++ b/src/feature.cpp @@ -444,26 +444,296 @@ Feature::Hx ( const Vector3d &pos, const Quaterniond &q ) qb0w3=q0.z(); qb0w4=q0.w(); +#ifdef FULLSTATE + Matrix<double,Dynamic,13,0,6,13> H; + H = Matrix<double,6,13>::Zero(); +#else Matrix<double,Dynamic,9,0,6,9> H; H = Matrix<double,6,9>::Zero(); +#endif - hx11 = -(2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx12 = (pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx13 = -(2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx21 = -(2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx22 = (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx23 = (pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) - ((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hx33 = (4 * qbw1*qbw4 + 4 * qbw2*qbw3) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) + ((4 * qbw1*qbw3 - 4 * qbw2*qbw4)*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + ((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) , 2); - - hx43 = ((4 * qbw1*qbw3 - 4 * qbw2*qbw4)*((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) + (2 * qbw1*qbw4 - 2 * qbw2*qbw3)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) + (pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) , 2) - (2 * pow(qbw1 , 2) + 2 * pow(qbw2 , 2) - 2 * pow(qbw3 , 2) - 2 * pow(qbw4 , 2)) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))); - - H.block<4,3>(2,0) << hx11, hx12, hx13, hx21, hx22, hx23,0,0,hx33,0,0,hx43; + // Matlab generated C code. + double t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20, + t21,t22,t23,t24,t25,t26,t27,t28,t29,t30,t31,t32,t33,t34,t35,t36,t37, + t38,t39,t40,t41,t42,t43,t44,t45,t46,t47,t48,t49,t50,t51,t52,t53,t54, + t55,t56,t57,t58,t59,t60,t61,t62,t63,t64,t65,t66,t67,t68,t69,t70,t71, + t72,t73,t74,t75,t76,t77,t78,t79,t80,t81,t82,t83,t84,t85,t86,t87,t88, + t89,t90,t91,t92,t93,t94,t95,t96,t97,t98,t99,t100,t101,t102,t103,t104, + t105,t106,t107,t108,t109,t110,t111,t112,t113,t114,t115,t116,t117,t118, + t119,t120,t121,t122,t123,t124,t125,t126,t127,t128,t129,t130,t131,t132, + t133,t134,t135,t136,t137,t138,t139,t140,t141,t142,t143,t144,t145,t146, + t147,t148,t149,t150,t151,t152,t153,t154,t155,t156,t157,t158,t159,t160, + t161,t162,t163,t164,t165,t166,t167,t168,t169,t170,t171,t172,t173,t174, + t175,t176,t177,t178,t179,t180,t181,t182,t183,t184,t185,t186,t187,t188, + t189,t190,t191,t192,t193,t194,t195,t196,t197,t198,t199,t200,t201,t202, + t203,t204,t205,t206,t207,t208,t209,t210,t211,t212,t213,t214,t215,t216, + t217,t218,t219,t220,t221,t222,t223,t224,t225,t226,t227,t228,t229,t230, + t231,t232; + + t2 = qb0w1*qb0w2*2.0; + t3 = qb0w1*qb0w1; + t4 = qb0w2*qb0w2; + t5 = qb0w3*qb0w3; + t6 = qb0w4*qb0w4; + t7 = t3-t4-t5+t6; + t8 = qb0w3*qb0w4*2.0; + t9 = t2+t8; + t10 = qb0w1*qb0w3*2.0; + t13 = qb0w2*qb0w4*2.0; + t11 = t10-t13; + t12 = 1.0/pib3; + t14 = qbw1*qbw1; + t15 = qbw2*qbw2; + t16 = qbw3*qbw3; + t17 = qbw4*qbw4; + t18 = qbw1*qbw2*2.0; + t19 = qbw3*qbw4*2.0; + t20 = qbw1*qbw4*2.0; + t21 = qbw2*qbw3*2.0; + t22 = qbw1*qbw3*2.0; + t23 = xb0w1-xbw1; + t24 = t7*t23; + t25 = xb0w2-xbw2; + t26 = t9*t25; + t27 = xb0w3-xbw3; + t28 = t11*t27; + t29 = t14-t15-t16+t17; + t30 = t7*t29; + t31 = t18+t19; + t32 = t9*t31; + t33 = qbw2*qbw4*2.0; + t34 = t20+t21; + t35 = t11*t34; + t36 = t14-t15+t16-t17; + t37 = t18-t19; + t38 = t7*t37; + t55 = t9*t36; + t39 = t35+t38-t55; + t40 = t20-t21; + t41 = t9*t40; + t42 = t14+t15-t16-t17; + t43 = t11*t42; + t44 = t22+t33; + t56 = t7*t44; + t45 = t41+t43-t56; + t46 = pib2*t12*t45; + t47 = t2-t8; + t48 = qb0w1*qb0w4*2.0; + t49 = qb0w2*qb0w3*2.0; + t50 = t48+t49; + t51 = t22-t33; + t52 = t3-t4+t5-t6; + t53 = t11*t51; + t54 = t30+t32+t53; + t58 = t12*t54; + t59 = pib1*t12*t39; + t57 = t24+t26+t28+t46-t58-t59; + t60 = 1.0/(t57*t57); + t61 = t25*t52; + t62 = t50*t51; + t63 = t29*t47; + t79 = t31*t52; + t64 = t62+t63-t79; + t65 = t12*t64; + t66 = t36*t52; + t67 = t37*t47; + t68 = t34*t50; + t69 = t66+t67+t68; + t70 = pib1*t12*t69; + t71 = t44*t47; + t72 = t40*t52; + t80 = t42*t50; + t73 = t71+t72-t80; + t74 = pib2*t12*t73; + t77 = t23*t47; + t78 = t27*t50; + t75 = t61+t65+t70+t74-t77-t78; + t76 = 1.0/t57; + t81 = qbw1*t52*2.0; + t82 = qbw2*t47*2.0; + t83 = qbw4*t50*2.0; + t84 = t81+t82+t83; + t85 = qbw1*t47*2.0; + t86 = qbw3*t50*2.0; + t98 = qbw2*t52*2.0; + t87 = t85+t86-t98; + t88 = qbw2*t7*2.0; + t89 = qbw4*t11*2.0; + t112 = qbw1*t9*2.0; + t90 = t88+t89-t112; + t91 = qbw1*t7*2.0; + t92 = qbw2*t9*2.0; + t93 = qbw3*t11*2.0; + t94 = t91+t92+t93; + t95 = qbw4*t52*2.0; + t96 = qbw3*t47*2.0; + t109 = qbw1*t50*2.0; + t97 = t95+t96-t109; + t99 = qbw3*t52*2.0; + t100 = qbw2*t50*2.0; + t108 = qbw4*t47*2.0; + t101 = t99+t100-t108; + t102 = qbw1*t11*2.0; + t103 = qbw4*t9*2.0; + t111 = qbw3*t7*2.0; + t104 = t102+t103-t111; + t105 = qbw4*t7*2.0; + t106 = qbw3*t9*2.0; + t110 = qbw2*t11*2.0; + t107 = t105+t106-t110; + t113 = t10+t13; + t114 = t48-t49; + t115 = t3+t4-t5-t6; + t116 = t27*t115; + t117 = t25*t114; + t118 = t31*t114; + t119 = t51*t115; + t132 = t29*t113; + t120 = t118+t119-t132; + t121 = t37*t113; + t122 = t36*t114; + t134 = t34*t115; + t123 = t121+t122-t134; + t124 = pib1*t12*t123; + t125 = t42*t115; + t126 = t44*t113; + t127 = t40*t114; + t128 = t125+t126+t127; + t129 = pib2*t12*t128; + t131 = t23*t113; + t133 = t12*t120; + t130 = t116+t117+t124+t129-t131-t133; + t135 = t12*t94; + t136 = pib1*t12*t90; + t137 = t135+t136-pib2*t12*t104; + t138 = qbw1*t114*2.0; + t139 = qbw2*t113*2.0; + t159 = qbw4*t115*2.0; + t140 = t138+t139-t159; + t141 = qbw3*t115*2.0; + t142 = qbw2*t114*2.0; + t151 = qbw1*t113*2.0; + t143 = t141+t142-t151; + t144 = pib1*t12*t94; + t145 = pib2*t12*t107; + t146 = t144+t145-t12*t90; + t147 = qbw1*t115*2.0; + t148 = qbw3*t113*2.0; + t149 = qbw4*t114*2.0; + t150 = t147+t148+t149; + t152 = qbw2*t115*2.0; + t153 = qbw4*t113*2.0; + t158 = qbw3*t114*2.0; + t154 = t152+t153-t158; + t155 = t12*t104; + t156 = pib2*t12*t94; + t157 = t155+t156-pib1*t12*t107; + t160 = t12*t107; + t161 = pib1*t12*t104; + t162 = pib2*t12*t90; + t163 = t160+t161+t162; + t164 = xbw3*2.0; + t165 = t12*t51; + t166 = pib1*t12*t34; + t178 = pib2*t12*t42; + t167 = t164+t165+t166-t178; + t168 = t51*t167; + t169 = pib1*t12*t36; + t170 = pib2*t12*t40; + t179 = t12*t31; + t171 = t169+t170-t179; + t172 = t31*t171; + t173 = t12*t29; + t174 = pib1*t12*t37; + t175 = pib2*t12*t44; + t176 = t173+t174+t175; + t180 = t29*t176; + t177 = t168+t172-t180; + t181 = 1.0/t177; + t182 = 1.0/(t177*t177); + t183 = t37*t176; + t184 = t36*t171; + t199 = t34*t167; + t185 = t183+t184-t199; + t186 = pib1*qbw1*t12*2.0; + t187 = pib2*qbw4*t12*2.0; + t196 = qbw2*t12*2.0; + t188 = t186+t187-t196; + t189 = qbw3*t12*2.0; + t190 = pib1*qbw4*t12*2.0; + t205 = pib2*qbw1*t12*2.0; + t191 = t189+t190-t205; + t192 = qbw1*t12*2.0; + t193 = pib1*qbw2*t12*2.0; + t194 = pib2*qbw3*t12*2.0; + t195 = t192+t193+t194; + t197 = qbw3*t167*2.0; + t198 = qbw2*t171*2.0; + t200 = qbw4*t12*2.0; + t201 = pib2*qbw2*t12*2.0; + t206 = pib1*qbw3*t12*2.0; + t202 = t200+t201-t206; + t203 = qbw1*t171*2.0; + t204 = qbw2*t176*2.0; + t207 = qbw1*t167*2.0; + t208 = qbw3*t176*2.0; + t209 = qbw4*t171*2.0; + t210 = qbw2*t167*2.0; + t211 = qbw4*t176*2.0; + t212 = qbw1*qbw3*4.0; + t213 = t212-qbw2*qbw4*4.0; + t214 = t44*t176; + t215 = t40*t171; + t216 = t42*t167; + t217 = t214+t215+t216; + t218 = t31*t188; + t219 = t51*t191; + t226 = qbw1*t176*2.0; + t220 = t197+t198+t218+t219-t226-t29*t195; + t221 = t31*t195; + t222 = t51*t202; + t223 = qbw4*t167*2.0; + t224 = t29*t188; + t225 = -t203-t204+t221+t222+t223+t224; + t227 = t51*t195; + t228 = t29*t191; + t229 = t207+t208+t209+t227+t228-t31*t202; + t230 = t31*t191; + t231 = t29*t202; + t232 = t210+t211+t230+t231-qbw3*t171*2.0-t51*t188; + + H(2,0) = -t47/(t24+t26+t28+t46-t12*(t30+t32+t11*(t22-qbw2*qbw4*2.0))-pib1*t12*t39)-t7*t60*t75; + H(2,1) = t52*t76-t9*t60*t75; + H(2,2) = -t50*t76-t11*t60*t75; +#ifdef FULLSTATE + H(2,6) = -t76*(t12*t87+pib1*t12*t84+pib2*t12*t97)-t60*t75*t137; + H(2,7) = t76*(t12*t84-pib1*t12*t87+pib2*t12*t101)-t60*t75*t146; + H(2,8) = -t76*(-t12*t97+pib2*t12*t87+pib1*t12*t101)-t60*t75*t157; + H(2,9) = t76*(t12*t101-pib2*t12*t84+pib1*t12*t97)-t60*t75*t163; +#endif + H(3,0) = -t76*t113-t7*t60*t130; + H(3,1) = t76*t114-t9*t60*t130; + H(3,2) = t76*t115-t11*t60*t130; +#ifdef FULLSTATE + H(3,6) = -t76*(-t12*t143+pib1*t12*t140+pib2*t12*t150)-t60*t130*t137; + H(3,7) = t76*(t12*t140+pib1*t12*t143-pib2*t12*t154)-t60*t130*t146; + H(3,8) = t76*(t12*t150+pib2*t12*t143+pib1*t12*t154)-t60*t130*t157; + H(3,9) = -t76*(t12*t154+pib2*t12*t140-pib1*t12*t150)-t60*t130*t163; +#endif + H(4,2) = t181*(qbw1*qbw4*4.0+qbw2*qbw3*4.0)+t182*t185*t213; +#ifdef FULLSTATE + H(4,6) = -t181*(t203+t204-qbw4*t167*2.0+t36*t188-t34*t191+t37*t195)+t182*t185*t220; + H(4,7) = t181*(t197+t198-qbw1*t176*2.0-t37*t188+t36*t195-t34*t202)-t182*t185*t225; + H(4,8) = t181*(t210+t211-qbw3*t171*2.0+t37*t191+t34*t195+t36*t202)+t182*t185*t229; + H(4,9) = t181*(t207+t208+t209+t34*t188+t36*t191-t37*t202)-t182*t185*t232; +#endif + H(5,2) = -t181*(t14*2.0+t15*2.0-t16*2.0-t17*2.0)+t182*t213*t217; +#ifdef FULLSTATE + H(5,6) = -t181*(t207+t208+t209+t40*t188+t42*t191+t44*t195)+t182*t217*t220; + H(5,7) = -t181*(t210+t211-qbw3*t171*2.0+t44*t188-t40*t195-t42*t202)-t182*t217*t225; + H(5,8) = t181*(t197+t198-t226+t44*t191-t42*t195+t40*t202)+t182*t217*t229; + H(5,9) = -t181*(t203+t204-t223+t42*t188-t40*t191+t44*t202)-t182*t217*t232; +#endif return H; } /* ----- end of method Feature::Hx ----- */ @@ -502,37 +772,191 @@ Feature::Hy ( const Vector3d &pos, const Quaterniond &q ) Matrix<double,6,3> H; H = Matrix<double,6,3>::Zero(); - - hy11 = -((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / (pib3*((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) - (((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / (pib3*pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2)); - - hy12 = (((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / (pib3*pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2)) - ((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / (pib3*((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)); - - hy13 = (((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pow(pib3 , 2) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pow(pib3 , 2) + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pow(pib3 , 2)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) + ((((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pow(pib3 , 2) + (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pow(pib3 , 2) - (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pow(pib3 , 2))*(((2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(xb0w3 - xbw3) - (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(xb0w1 - xbw1) + (xb0w2 - xbw2)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) + pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w4)+2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w2)-2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hy21 = -((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / (pib3*((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) - (((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / (pib3*pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2)); - - hy22 = (((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / (pib3*pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2)) - ((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / (pib3*((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)); - - hy23 = ((pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pow(pib3 , 2) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pow(pib3 , 2) + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pow(pib3 , 2)) / ((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) + ((((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pow(pib3 , 2) + (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pow(pib3 , 2) - (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pow(pib3 , 2))*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(xb0w2 - xbw2) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(xb0w1 - xbw1) - ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4)) / pib3 + (xb0w3 - xbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (pib1*((2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw2 - 2 * qbw3*qbw4))) / pib3 + (pib2*((pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))*(pow((qb0w1) , 2) + pow((qb0w2) , 2) - pow((qb0w3) , 2) - pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w3)+2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 + 2 * qbw2*qbw4) + (2 * (qb0w1)*(qb0w4)-2 * (qb0w2)*(qb0w3))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3)) / pow(((2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(xb0w2 - xbw2) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(xb0w3 - xbw3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw2 + 2 * qbw3*qbw4) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw3 - 2 * qbw2*qbw4)) / pib3 + (xb0w1 - xbw1)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (pib1*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) - (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)) + (2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(2 * qbw1*qbw4 + 2 * qbw2*qbw3))) / pib3 + (pib2*((2 * (qb0w1)*(qb0w3)-2 * (qb0w2)*(qb0w4))*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2)) - (2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow((qb0w1) , 2) - pow((qb0w2) , 2) - pow((qb0w3) , 2) + pow((qb0w4) , 2)) + (2 * (qb0w1)*(qb0w2)+2 * (qb0w3)*(qb0w4))*(2 * qbw1*qbw4 - 2 * qbw2*qbw3))) / pib3) , 2); - - hy31 = ((((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - ((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) / pib3 + ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3)*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + ((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) , 2) - (pow((2 * qbw1*qbw2 - 2 * qbw3*qbw4) , 2) / pib3 - pow( (2 * qbw1*qbw4 + 2 * qbw2*qbw3) , 2) / pib3 + pow( (pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)), 2) / pib3) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))); - - hy32 = -(((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + ((2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + ((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) - ((((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + ((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) / pib3 - ((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + ((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) , 2); - - hy33 = ((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pow(pib3 , 2) + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pow(pib3 , 2) + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pow(pib3 , 2)) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*((2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pow(pib3 , 2) - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pow(pib3 , 2) + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pow(pib3 , 2)) + ((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pow(pib3 , 2) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pow(pib3 , 2) + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pow(pib3 , 2))*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) - (((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) - (2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + ((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2)))*((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pow(pib3 , 2) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pow(pib3 , 2) + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pow(pib3 , 2)) + (2 * qbw1*qbw3 - 2 * qbw2*qbw4)*((2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pow(pib3 , 2) - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pow(pib3 , 2) + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pow(pib3 , 2)) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pow(pib3 , 2) + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pow(pib3 , 2) + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pow(pib3 , 2))*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1 , 2) + pow(qbw2 , 2) - pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1 , 2) - pow(qbw2 , 2) + pow(qbw3 , 2) - pow(qbw4 , 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1 , 2) - pow(qbw2 , 2) - pow(qbw3 , 2) + pow(qbw4 , 2))) , 2); - - hy41 = ((((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - ((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))) / pib3 + ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3)*((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) + (2 * qbw1*qbw4 - 2 * qbw2*qbw3)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) + (pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))), 2) - (((2 * qbw1*qbw4 - 2 * qbw2*qbw3)*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + ((2 * qbw1*qbw4 + 2 * qbw2*qbw3)*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + ((2 * qbw1*qbw2 - 2 * qbw3*qbw4)*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))); - - hy42 = -(pow((2 * qbw1*qbw3 + 2 * qbw2*qbw4), 2) / pib3 + pow((2 * qbw1*qbw4 - 2 * qbw2*qbw3), 2) / pib3 - pow((pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2)) , 2) / pib3) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))) - ((((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + ((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))) / pib3 - ((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3)*((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) + (2 * qbw1*qbw4 - 2 * qbw2*qbw3)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) + (pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))), 2); - - hy43 = ((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pow(pib3, 2) + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pow(pib3, 2) + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pow(pib3, 2)) + (2 * qbw1*qbw4 - 2 * qbw2*qbw3)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pow(pib3, 2) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pow(pib3, 2) + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pow(pib3, 2)) + ((2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pow(pib3, 2) - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pow(pib3, 2) + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pow(pib3, 2))*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / ((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))) - (((2 * qbw1*qbw3 + 2 * qbw2*qbw4)*((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3) + (2 * qbw1*qbw4 - 2 * qbw2*qbw3)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) + (pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3))*((2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pow(pib3, 2) - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pow(pib3, 2) + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pow(pib3, 2)) + (2 * qbw1*qbw3 - 2 * qbw2*qbw4)*((2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pow(pib3, 2) - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pow(pib3, 2) + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pow(pib3, 2)) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pow(pib3, 2) + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pow(pib3, 2) + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pow(pib3, 2))*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)))) / pow(((2 * qbw1*qbw3 - 2 * qbw2*qbw4)*(2 * xbw3 + (2 * qbw1*qbw3 - 2 * qbw2*qbw4) / pib3 - (pib2*(pow(qbw1, 2) + pow(qbw2, 2) - pow(qbw3, 2) - pow(qbw4, 2))) / pib3 + (pib1*(2 * qbw1*qbw4 + 2 * qbw2*qbw3)) / pib3) + (2 * qbw1*qbw2 + 2 * qbw3*qbw4)*((pib1*(pow(qbw1, 2) - pow(qbw2, 2) + pow(qbw3, 2) - pow(qbw4, 2))) / pib3 - (2 * qbw1*qbw2 + 2 * qbw3*qbw4) / pib3 + (pib2*(2 * qbw1*qbw4 - 2 * qbw2*qbw3)) / pib3) - ((pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2)) / pib3 + (pib1*(2 * qbw1*qbw2 - 2 * qbw3*qbw4)) / pib3 + (pib2*(2 * qbw1*qbw3 + 2 * qbw2*qbw4)) / pib3)*(pow(qbw1, 2) - pow(qbw2, 2) - pow(qbw3, 2) + pow(qbw4, 2))), 2); - H << 1,0,0, - 0,1,0, - hy11,hy12,hy13, - hy21,hy22,hy23, - hy31,hy32,hy33, - hy41,hy42,hy43; + // Matlab generated code + double t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20, + t21,t22,t23,t24,t25,t26,t27,t28,t29,t30,t31,t32,t33,t34,t35,t36,t37, + t38,t39,t40,t41,t42,t43,t44,t45,t46,t47,t48,t49,t50,t51,t52,t53,t54, + t55,t56,t57,t58,t59,t60,t61,t62,t63,t64,t65,t66,t67,t68,t69,t70,t71, + t72,t73,t74,t75,t76,t77,t78,t79,t80,t81,t82,t83,t84,t85,t86,t87,t88, + t89,t90,t91,t92,t93,t94,t95,t96,t97,t98,t99,t100,t101,t102,t103,t104, + t105,t106,t107,t108,t109,t110,t111,t112,t113,t114,t115,t116,t117,t118, + t119,t120,t121,t122,t123,t124,t125,t126,t127,t128,t129,t130,t131,t132, + t133,t134,t135,t136,t137,t138,t139,t140,t141,t142,t143,t144,t145,t146, + t147,t148,t149,t150,t151,t152,t153,t154,t155,t156,t157,t158; + + t2 = qb0w1*qb0w1; + t3 = qb0w2*qb0w2; + t4 = qb0w3*qb0w3; + t5 = qb0w4*qb0w4; + t6 = qb0w1*qb0w2*2.0; + t7 = 1.0/pib3; + t8 = t2-t3-t4+t5; + t9 = qbw1*qbw1; + t10 = qbw2*qbw2; + t11 = qbw3*qbw3; + t12 = qbw4*qbw4; + t13 = qb0w3*qb0w4*2.0; + t14 = t6+t13; + t15 = qbw1*qbw2*2.0; + t16 = qb0w1*qb0w3*2.0; + t18 = qb0w2*qb0w4*2.0; + t17 = t16-t18; + t19 = qbw1*qbw4*2.0; + t20 = qbw2*qbw3*2.0; + t21 = t19+t20; + t22 = t9-t10+t11-t12; + t23 = qbw3*qbw4*2.0; + t24 = qbw1*qbw3*2.0; + t25 = t15-t23; + t26 = t17*t21; + t27 = t8*t25; + t40 = t14*t22; + t28 = t26+t27-t40; + t29 = xb0w1-xbw1; + t30 = t8*t29; + t31 = xb0w2-xbw2; + t32 = t14*t31; + t33 = xb0w3-xbw3; + t34 = t17*t33; + t35 = t9-t10-t11+t12; + t36 = t8*t35; + t37 = t15+t23; + t38 = t14*t37; + t39 = qbw2*qbw4*2.0; + t41 = t19-t20; + t42 = t14*t41; + t43 = t9+t10-t11-t12; + t44 = t17*t43; + t45 = t24+t39; + t63 = t8*t45; + t46 = t42+t44-t63; + t47 = pib2*t7*t46; + t48 = t2-t3+t4-t5; + t49 = t6-t13; + t50 = qb0w1*qb0w4*2.0; + t51 = qb0w2*qb0w3*2.0; + t52 = t50+t51; + t53 = t24-t39; + t54 = t22*t48; + t55 = t25*t49; + t56 = t21*t52; + t57 = t54+t55+t56; + t58 = t45*t49; + t59 = t41*t48; + t74 = t43*t52; + t60 = t58+t59-t74; + t61 = t17*t53; + t62 = t36+t38+t61; + t65 = t7*t62; + t66 = pib1*t7*t28; + t64 = t30+t32+t34+t47-t65-t66; + t67 = 1.0/(t64*t64); + t68 = t31*t48; + t69 = t52*t53; + t70 = t35*t49; + t77 = t37*t48; + t71 = t69+t70-t77; + t72 = t7*t71; + t73 = pib1*t7*t57; + t75 = pib2*t7*t60; + t80 = t29*t49; + t81 = t33*t52; + t76 = t68+t72+t73+t75-t80-t81; + t78 = 1.0/(pib3*pib3); + t79 = 1.0/t64; + t82 = t2+t3-t4-t5; + t83 = t16+t18; + t84 = t50-t51; + t85 = t25*t83; + t86 = t22*t84; + t97 = t21*t82; + t87 = t85+t86-t97; + t88 = t43*t82; + t89 = t45*t83; + t90 = t41*t84; + t91 = t88+t89+t90; + t92 = t33*t82; + t93 = t31*t84; + t94 = t37*t84; + t95 = t53*t82; + t101 = t35*t83; + t96 = t94+t95-t101; + t98 = pib1*t7*t87; + t99 = pib2*t7*t91; + t105 = t29*t83; + t106 = t7*t96; + t100 = t92+t93+t98+t99-t105-t106; + t102 = t62*t78; + t103 = pib1*t28*t78; + t104 = t102+t103-pib2*t46*t78; + t107 = xbw3*2.0; + t108 = t7*t53; + t109 = pib1*t7*t21; + t121 = pib2*t7*t43; + t110 = t107+t108+t109-t121; + t111 = t53*t110; + t112 = pib1*t7*t22; + t113 = pib2*t7*t41; + t122 = t7*t37; + t114 = t112+t113-t122; + t115 = t37*t114; + t116 = t7*t35; + t117 = pib1*t7*t25; + t118 = pib2*t7*t45; + t119 = t116+t117+t118; + t123 = t35*t119; + t120 = t111+t115-t123; + t124 = 1.0/t120; + t125 = 1.0/(t120*t120); + t126 = t25*t119; + t127 = t22*t114; + t129 = t21*t110; + t128 = t126+t127-t129; + t130 = pib1*t22*t78; + t131 = pib2*t41*t78; + t154 = t37*t78; + t132 = t130+t131-t154; + t133 = t53*t78; + t134 = pib1*t21*t78; + t155 = pib2*t43*t78; + t135 = t133+t134-t155; + t136 = t35*t78; + t137 = pib1*t25*t78; + t138 = pib2*t45*t78; + t139 = t136+t137+t138; + t140 = t7*t22*t41; + t141 = t7*t21*t43; + t142 = t7*t25*t45; + t143 = t140+t141+t142; + t144 = t7*t22*t37; + t145 = t7*t21*t53; + t146 = t144+t145-t7*t25*t35; + t147 = t7*t43*t53; + t148 = t7*t35*t45; + t149 = t147+t148-t7*t37*t41; + t150 = t45*t119; + t151 = t41*t114; + t152 = t43*t110; + t153 = t150+t151+t152; + t156 = t37*t132; + t157 = t53*t135; + t158 = t156+t157-t35*t139; + + H(0,0) = 1.0; + H(1,1) = 1.0; + H(2,0) = -(t7*t57)/(t30+t32+t34+t47-t7*(t36+t38+t17*(t24-qbw2*qbw4*2.0))-pib1*t7*t28)-t7*t28*t67*t76; + H(2,1) = -t7*t60*t79+t7*t46*t67*t76; + H(2,2) = t79*(t71*t78+pib1*t57*t78+pib2*t60*t78)+t67*t76*t104; + H(3,0) = -t7*t79*t87-t7*t28*t67*t100; + H(3,1) = -t7*t79*t91+t7*t46*t67*t100; + H(3,2) = t79*(-t78*t96+pib1*t78*t87+pib2*t78*t91)+t67*t100*t104; + H(4,0) = -t124*(-t7*(t21*t21)+t7*(t22*t22)+t7*(t25*t25))+t125*t128*t146; + H(4,1) = -t124*t143-t125*t128*t149; + H(4,2) = t124*(t22*t132-t21*t135+t25*t139)-t125*t128*t158; + H(5,0) = -t124*t143+t125*t146*t153; + H(5,1) = -t124*(t7*(t41*t41)-t7*(t43*t43)+t7*(t45*t45))-t125*t149*t153; + H(5,2) = t124*(t41*t132+t43*t135+t45*t139)-t125*t153*t158; return H ; } /* ----- end of method Feature::Hy ----- */ @@ -656,8 +1080,13 @@ Feature::inFOV ( ) } /* ----- end of method Feature::inFOV ----- */ bool +#ifdef FULLSTATE +Feature::isInlier(const measurement_t &z, const Matrix<double,13,13> &Pxx, + const Matrix<double,13,3> &Pxy, const Matrix<double,3,3> &Pyy, +#else Feature::isInlier(const measurement_t &z, const Matrix<double,9,9> &Pxx, const Matrix<double,9,3> &Pxy, const Matrix<double,3,3> &Pyy, +#endif const Vector3d &pos, const Quaterniond &q, double thr) { Matrix<double,Dynamic,Dynamic,0,6,6> s; diff --git a/src/feature.h b/src/feature.h index 6260d71..56e0835 100644 --- a/src/feature.h +++ b/src/feature.h @@ -17,6 +17,7 @@ #define RANSAC_LI_THRESHOLD 4e-5 /* */ #define RANSAC_HI_THRESHOLD 5e-2 /* */ #define INITDEPTH +#define FULLSTATE using Eigen::Dynamic; |