template<bool simple> static void add_gradient_helper(RawArray<const Vector<int,4>> bends, RawArray<const CubicHinges<TV3>::Info> info, const T scale, RawArray<const TV3> X, SolidMatrix<TV3>& matrix) {
if (!scale) return;
for (int b=0;b<bends.size();b++) {
const auto& I = info[b];
int i0,i1,i2,i3;bends[b].get(i0,i1,i2,i3);
const T quad = -scale*I.dot;
matrix.add_entry(i0,quad*sqr(I.c[0]));
matrix.add_entry(i1,quad*sqr(I.c[1]));
matrix.add_entry(i2,quad*sqr(I.c[2]));
matrix.add_entry(i3,quad*sqr(I.c[3]));
if (simple) {
matrix.add_entry(i0,i1,quad*I.c[0]*I.c[1]);
matrix.add_entry(i0,i2,quad*I.c[0]*I.c[2]);
matrix.add_entry(i0,i3,quad*I.c[0]*I.c[3]);
matrix.add_entry(i1,i2,quad*I.c[1]*I.c[2]);
matrix.add_entry(i1,i3,quad*I.c[1]*I.c[3]);
matrix.add_entry(i2,i3,quad*I.c[2]*I.c[3]);
} else {
const T cubic = -scale*I.det;
const TV3 x0 = cubic*X[i0], x1 = cubic*X[i1], x2 = cubic*X[i2], x3 = cubic*X[i3];
matrix.add_entry(i0,i1,quad*I.c[0]*I.c[1]+cross_product_matrix(x3-x2)); // e3
matrix.add_entry(i0,i2,quad*I.c[0]*I.c[2]+cross_product_matrix(x1-x3)); // -e1
matrix.add_entry(i0,i3,quad*I.c[0]*I.c[3]+cross_product_matrix(x2-x1)); // e0
matrix.add_entry(i1,i2,quad*I.c[1]*I.c[2]+cross_product_matrix(x3-x0));
matrix.add_entry(i1,i3,quad*I.c[1]*I.c[3]+cross_product_matrix(x0-x2)); // e4
matrix.add_entry(i2,i3,quad*I.c[2]*I.c[3]+cross_product_matrix(x1-x0)); // -e2
}
}
}
template<bool definite> void SimpleShell::add_elastic_gradient_helper(SolidMatrix<TV>& matrix) const {
const int m = 3, d = 2;
Matrix<T,m> dGdD[d+1][d+1];
for (const auto& I : info) {
for (int i=0;i<d;i++)
for (int j=0;j<m;j++) {
Matrix<T,m,d> dDs;
dDs(j,i) = 1;
Matrix<T,m,d> dG = force_differential<definite>(I,dDs);
for (int k=0;k<d;k++)
dGdD[k+1][i+1].set_column(j,dG.column(k));
}
Matrix<T,m> sum;
for (int i=0;i<d;i++) {
Matrix<T,m> sum_i;
for (int j=0;j<d;j++)
sum_i -= dGdD[i+1][j+1];
dGdD[i+1][0] = sum_i;
sum -= sum_i;
}
dGdD[0][0] = sum;
for (int j=0;j<d+1;j++)
for (int i=j;i<d+1;i++)
matrix.add_entry(I.nodes[i],I.nodes[j],dGdD[i][j]);
}
}
template<class TV> void CubicHinges<TV>::
add_elastic_gradient(SolidMatrix<TV>& matrix) const {
GEODE_ASSERT(matrix.size()>=nodes_);
if (simple_hessian)
add_gradient_helper<true>(bends,info,stiffness,X,matrix);
else
add_gradient_helper<false>(bends,info,stiffness,X,matrix);
}
template<bool simple> static void add_gradient_helper(RawArray<const Vector<int,3>> bends, RawArray<const CubicHinges<TV2>::Info> info, const T scale, RawArray<const TV2> X, SolidMatrix<TV2>& matrix) {
if (!scale) return;
for (int b=0;b<bends.size();b++) {
const auto& I = info[b];
int i0,i1,i2;bends[b].get(i0,i1,i2);
const T quad = -scale*I.dot;
matrix.add_entry(i0,quad*sqr(I.c[0]));
matrix.add_entry(i1,quad*sqr(I.c[1]));
matrix.add_entry(i2,quad*sqr(I.c[2]));
if (simple) {
matrix.add_entry(i0,i1,quad*I.c[0]*I.c[1]);
matrix.add_entry(i0,i2,quad*I.c[0]*I.c[2]);
matrix.add_entry(i1,i2,quad*I.c[1]*I.c[2]);
} else {
const T a = scale*I.det;
const Matrix<T,2> anti(0,a,-a,0); // x'Ay = cross(x,y), scaled
matrix.add_entry(i0,i1,quad*I.c[0]*I.c[1]-anti);
matrix.add_entry(i0,i2,quad*I.c[0]*I.c[2]+anti);
matrix.add_entry(i1,i2,quad*I.c[1]*I.c[2]-anti);
}
}
}
template<class TV> void CubicHinges<TV>::
add_damping_gradient(SolidMatrix<TV>& matrix) const {
GEODE_ASSERT(matrix.size()>=nodes_);
add_gradient_helper<true>(bends,info,damping,X,matrix);
}
void SurfacePins::add_damping_gradient(SolidMatrix<TV>& matrix) const {
GEODE_ASSERT(matrix.size()==mass.size());
GEODE_NOT_IMPLEMENTED();
}
