void static calcRotEqs(const Rod& r, const VecXe& rot, const std::vector<Vec3e>& curveBinorm,
VecXe& grad, std::vector<Triplet>& triplets) {
Eigen::Matrix<real, 2, 2> J;
J << 0.0, -1.0, 1.0, 0.0;
for (int i=1; i<r.numEdges()-1; i++) {
Vec3e m1 = cos(rot(i)) * r.next().u[i] + sin(rot(i)) * r.next().v(i);
Vec3e m2 = -sin(rot(i)) * r.next().u[i] + cos(rot(i)) * r.next().v(i);
Vec2e curvePrev(curveBinorm[i-1].dot(m2), -curveBinorm[i-1].dot(m1)); // omega ^i _i
Vec2e curveNext(curveBinorm[i].dot(m2), -curveBinorm[i].dot(m1)); // omega ^i _i+1
real dWprev = 1.0 / r.restVoronoiLength(i) *
curvePrev.dot(J * r.getCS()[i].bendMat() * (curvePrev - r.restCurveNext(i)));
real dWnext = 1.0 / r.restVoronoiLength(i+1) *
curveNext.dot(J * r.getCS()[i+1].bendMat() * (curveNext - r.restCurvePrev(i+1)));
real twistPrev = rot(i) - rot(i-1) + r.next().refTwist(i);
real twistNext = rot(i+1) - rot(i) + r.next().refTwist(i+1);
grad(i-1) = -(dWprev + dWnext + 2.0 * r.getCS()[i].twistCoeff() *
(twistPrev/r.restVoronoiLength(i) - twistNext/r.restVoronoiLength(i+1)));
real hess = 2.0*(r.getCS()[i].twistCoeff()/r.restVoronoiLength(i) +
r.getCS()[i+1].twistCoeff()/r.restVoronoiLength(i+1));
hess += 1.0 / r.restVoronoiLength(i) *
(curvePrev.dot(J.transpose() * r.getCS()[i].bendMat() * J * curvePrev)
- curvePrev.dot(r.getCS()[i].bendMat() * (curvePrev - r.restCurveNext(i))));
hess += 1.0 /r.restVoronoiLength(i+1) *
(curveNext.dot(J.transpose() * r.getCS()[i+1].bendMat() * J * curveNext)
- curveNext.dot(r.getCS()[i+1].bendMat() * (curveNext - r.restCurvePrev(i+1))));
triplets.push_back(Triplet(i-1, i-1, hess));
}
}
IMEXIntegrator::IMEXIntegrator(std::vector<RodEnergy*>& energies, Rod& r) :
Integrator(r, energies) {
// Fill hess base
std::vector<Triplet> triplets;
for (int i=1; i < r.numEdges()-1; i++) {
if (i > 1) {
triplets.push_back(Triplet(i-1, i-2, -2.0*r.getCS()[i].twistCoeff()/r.restVoronoiLength(i)));
}
if (i < r.numEdges()-2) {
triplets.push_back(Triplet(i-1, i, -2.0*r.getCS()[i+1].twistCoeff()/r.restVoronoiLength(i+1)));
}
}
hessBase = Eigen::SparseMatrix<real>(r.numEdges()-2, r.numEdges()-2);
hessBase.setFromTriplets(triplets.begin(), triplets.end());
}