// http://en.wikipedia.org/wiki/Inertia_tensor_of_triangle
Matrix3r woo::Volumetric::triangleInertia(const Vector3r& v0, const Vector3r& v1, const Vector3r& v2){
Matrix3r V; V<<v0.transpose(),v1.transpose(),v2.transpose(); // rows!
Real a=((v1-v0).cross(v2-v0)).norm(); // twice the triangle area
Matrix3r S; S<<2,1,1, 1,2,1, 1,1,2; S*=(1/24.);
Matrix3r C=a*V.transpose()*S*V;
return Matrix3r::Identity()*C.trace()-C;
};
Matrix3r MeasureCapStress::matBp_BodyGlob(Real alpha,Real wettAngle, Real radius,Vector3r vecN){ // matrix B prime (the surface tension coefficient excepted), defined at body scale (see (3.49) p.65), expressed in global framework
Matrix3r Bp_BodyGlob ;
Bp_BodyGlob << - pow(sin(alpha),2) * cos(alpha+wettAngle) , 0 , 0 ,
0 , - pow(sin(alpha),2) * cos(alpha+wettAngle) , 0 ,
0 , 0 , sin(2*alpha) * sin(alpha+wettAngle);
Bp_BodyGlob *= Mathr::PI * pow(radius,2.0);
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * Bp_BodyGlob * globToLocRet.transpose() ;
}
Matrix3r MeasureCapStress::matLG_bridgeGlob(Real nn11,Real nn33, Vector3r vecN){
Matrix3r LG_bridgeGlob ;
LG_bridgeGlob << nn11 + nn33 , 0 , 0 , // useless to write lgArea - nn11 = 2*nn11 + nn33 - nn11
0 , nn11 + nn33 , 0 ,
0 , 0 , 2*nn11; // trace = 2*(2*nn11 + nn33) = 2*lgArea
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * LG_bridgeGlob * globToLocRet.transpose() ;
}
Matrix3r MeasureCapStress::matA_BodyGlob(Real alpha,Real radius,Vector3r vecN){
Matrix3r A_BodyGlob ;
A_BodyGlob << pow( 1 - cos(alpha),2) * (2 + cos(alpha)) , 0 , 0 ,
0 , pow( 1 - cos(alpha),2) * (2 + cos(alpha)) , 0 ,
0 , 0 , 2 * ( 1-pow(cos(alpha),3) );
A_BodyGlob *= Mathr::PI * pow(radius,3.0)/3.0;
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * A_BodyGlob * globToLocRet.transpose() ;
}
/*! @brief Recalculate body's inertia tensor in rotated coordinates.
*
* @param I inertia tensor in old coordinates
* @param T rotation matrix from old to new coordinates
* @return inertia tensor in new coordinates
*/
Matrix3r woo::Volumetric::inertiaTensorRotate(const Matrix3r& I,const Matrix3r& T){
/* [http://www.kwon3d.com/theory/moi/triten.html] */
return T.transpose()*I*T;
}
Matrix3r inertiaRotate(const Matrix3r& I, const Matrix3r& T){
return T.transpose()*I*T;
}