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////////////////////////////////////////////////////////////////////////////////
//
// RegularityCheck.cc
//
// produced: 2001/10/28 jr
// last change: 2001/10/28 jr
//
////////////////////////////////////////////////////////////////////////////////
#include "RegularityCheck.hh"
// constructors:
RegularityCheck::RegularityCheck(const PointConfiguration& points,
const Chirotope& chiro,
const SimplicialComplex& t) :
_pointsptr(&points),
_chiroptr (&chiro),
_triangptr(&t) {
// we build the coefficient matrix from the chirotope and the triangulation t:
// for all simplices in the triangulation t ...:
for (SimplicialComplex::const_iterator iter1 = t.begin();
iter1 != t.end();
++iter1) {
const Simplex& simp1(*iter1);
SimplicialComplex::const_iterator iter2 = iter1;
while (++iter2 != t.end()) {
// ... look for an adjacent simplex:
const Simplex& simp2(*iter2);
Simplex ridge(simp1);
ridge *= simp2;
if (ridge.card() != _chiroptr->rank() - 1) {
continue;
}
// simp2 is adjacent, build new constraint:
Vector new_col(_chiroptr->no());
// build the matrix of all points corresponding to simp1:
StairCaseMatrix basis_matrix;
for (basis_type::const_iterator basis_iter = simp1.begin();
basis_iter != simp1.end();
++basis_iter) {
basis_matrix.augment((*_pointsptr)[*basis_iter]);
}
const size_type new_index = *((simp2 - ridge).begin());
Rational det_basis = det(basis_matrix);
int calibrate(sign(det_basis));
new_col[new_index] = calibrate * det_basis;
// the orientation of simp1 is the calibration according to a point with
// infinite height:
calibrate = -calibrate;
// build the matrices with the point not in simp1 and the facets of simp1:
basis_type basis(simp1);
for (Simplex::const_iterator simp_iter = simp1.begin();
simp_iter != simp1.end();
++simp_iter) {
const size_type idx(*simp_iter);
basis -= idx;
StairCaseMatrix basis_matrix;
basis_matrix.append((*_pointsptr)[new_index]);
for (basis_type::const_iterator basis_iter = basis.begin();
basis_iter != basis.end();
++basis_iter) {
basis_matrix.augment((*_pointsptr)[*basis_iter]);
}
new_col[idx] = calibrate * det(basis_matrix);
calibrate = -calibrate;
basis += idx;
}
// finally, append the new column; it corresponds to
// local regularity at ridge (we take a column for efficiency reasons,
// in cdd it will be a row, of course:
_coeffs.append(new_col);
}
}
if (CommandlineOptions::debug()) {
std::cerr << "The coefficient matrix for regularity check:" << std::endl;
if (_coeffs.coldim() == 0) {
std::cerr << "no constraints." << std::endl;
}
else {
transpose(_coeffs).pretty_print(std::cout);
}
}
}
// eof RegularityCheck.cc
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