// LSCM equation, geometric form :
// (Z1 - Z0)(U2 - U0) = (Z2 - Z0)(U1 - U0)
// Where Uk = uk + i.vk is the complex number
// corresponding to (u,v) coords
// Zk = xk + i.yk is the complex number
// corresponding to local (x,y) coords
void MeshPara::setup_conformal_map_relations(Mesh::FHandle fh)
{
int id[3];
Vec3f p[3];
auto fv = mesh_.fv_begin(fh);
for (int i = 0; i < 3; i++, fv++)
{
p[i] = mesh_.point(*fv);
id[i] = (*fv).idx();
}
Vec2f z[3];
project_triangle(p[0], p[1], p[2], z[0], z[1], z[2]);
Vec2f z01 = z[1] - z[0];
Vec2f z02 = z[2] - z[0];
double a = z01[0];
double b = z01[1];
double c = z02[0];
double d = z02[1];
assert(b == 0.0);
// Note : 2*id + 0 --> u
// 2*id + 1 --> v
int u0_id = 2 * id[0];
int v0_id = 2 * id[0] + 1;
int u1_id = 2 * id[1];
int v1_id = 2 * id[1] + 1;
int u2_id = 2 * id[2];
int v2_id = 2 * id[2] + 1;
// Note : b = 0
// Real part
nlBegin(NL_ROW);
nlCoefficient(u0_id, -a + c);
nlCoefficient(v0_id, b - d);
nlCoefficient(u1_id, -c);
nlCoefficient(v1_id, d);
nlCoefficient(u2_id, a);
nlEnd(NL_ROW);
// Imaginary part
nlBegin(NL_ROW);
nlCoefficient(u0_id, -b + d);
nlCoefficient(v0_id, -a + c);
nlCoefficient(u1_id, -d);
nlCoefficient(v1_id, -c);
nlCoefficient(v2_id, a);
nlEnd(NL_ROW);
}
void leastSquaresSystem::solve(double *vs)
{
int i;
Node *n;
coeffIndexPair *f;
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE) ;
nlSolverParameteri(NL_MAX_ITERATIONS, 1000) ;
nlSolverParameterd(NL_THRESHOLD, 1e-10) ;
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++)
{
nlSetVariable(i, vs[i]);
if (locks[i]) nlLockVariable(i);
}
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[0][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
nlSolve();
for (i=0; i<num_variables; i++) vs[i] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
}
void sparse3System::solve(double *vs)
{
int i, j;
Node *n;
coeffIndexPair *f;
for (j=0; j<3; j++)
{
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++)
{
nlSetVariable(i, vs[i*3 + j]);
if (locks[i]) nlLockVariable(i);
}
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[j][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
nlSolve();
for (i=0; i<num_variables; i++) vs[i*3 + j] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
}
}
// Solves the system for j'th component of B
bool sparseSystem::solve(double *x, int j)
{
int i;
Node *n;
coeffIndexPair *f;
nlNewContext();
nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
nlSolverParameteri(NL_NB_VARIABLES, num_variables);
nlBegin(NL_SYSTEM);
for (i=0; i<num_variables; i++) nlSetVariable(i, x[i]);
nlBegin(NL_MATRIX);
for (i=0; i<num_equations; i++)
{
nlRowParameterd(NL_RIGHT_HAND_SIDE, known_term[j][i]);
nlBegin(NL_ROW);
for (n=rows[i].cips.head(); n!=NULL; n=n->next())
{
f = (coeffIndexPair *)n->data;
nlCoefficient(f->index, f->coeff);
}
nlEnd(NL_ROW);
}
nlEnd(NL_MATRIX);
nlEnd(NL_SYSTEM);
bool success = (bool)nlSolve();
if (success) for (i=0; i<num_variables; i++) x[i] = nlGetVariable(i);
nlDeleteContext(nlGetCurrent());
return success;
}
