// Insert knots and compute knot insertion matrix (to update control points)
SparseMatrix BSplineBasis1D::insertKnots(double tau, unsigned int multiplicity)
{
if (!insideSupport(tau))
throw Exception("BSplineBasis1D::insertKnots: Cannot insert knot outside domain!");
if (knotMultiplicity(tau) + multiplicity > degree + 1)
throw Exception("BSplineBasis1D::insertKnots: Knot multiplicity is too high!");
// New knot vector
int index = indexHalfopenInterval(tau);
std::vector<double> extKnots = knots;
for (unsigned int i = 0; i < multiplicity; i++)
extKnots.insert(extKnots.begin()+index+1, tau);
if (!isKnotVectorRegular(extKnots))
throw Exception("BSplineBasis1D::insertKnots: New knot vector is not regular!");
// Return knot insertion matrix
SparseMatrix A = buildKnotInsertionMatrix(extKnots);
// Update knots
knots = extKnots;
return A;
}
SparseMatrix BSplineBasis1D::refineKnotsLocally(double x)
{
if (!insideSupport(x))
throw Exception("BSplineBasis1D::refineKnotsLocally: Cannot refine outside support!");
if (getNumBasisFunctions() >= getNumBasisFunctionsTarget()
|| assertNear(knots.front(), knots.back()))
{
unsigned int n = getNumBasisFunctions();
DenseMatrix A = DenseMatrix::Identity(n,n);
return A.sparseView();
}
// Refined knot vector
std::vector<double> refinedKnots = knots;
auto upper = std::lower_bound(refinedKnots.begin(), refinedKnots.end(), x);
// Check left boundary
if (upper == refinedKnots.begin())
std::advance(upper, degree+1);
// Get previous iterator
auto lower = std::prev(upper);
// Do not insert if upper and lower bounding knot are close
if (assertNear(*upper, *lower))
{
unsigned int n = getNumBasisFunctions();
DenseMatrix A = DenseMatrix::Identity(n,n);
return A.sparseView();
}
// Insert knot at x
double insertVal = x;
// Adjust x if it is on or close to a knot
if (knotMultiplicity(x) > 0
|| assertNear(*upper, x, 1e-6, 1e-6)
|| assertNear(*lower, x, 1e-6, 1e-6))
{
insertVal = (*upper + *lower)/2.0;
}
// Insert new knot
refinedKnots.insert(upper, insertVal);
if (!isKnotVectorRegular(refinedKnots) || !isRefinement(refinedKnots))
throw Exception("BSplineBasis1D::refineKnotsLocally: New knot vector is not a proper refinement!");
// Build knot insertion matrix
SparseMatrix A = buildKnotInsertionMatrix(refinedKnots);
// Update knots
knots = refinedKnots;
return A;
}
// Return indices of supporting basis functions at x
std::vector<int> BSplineBasis1D::indexSupportedBasisfunctions(double x) const
{
std::vector<int> ret;
if(insideSupport(x))
{
int last = indexHalfopenInterval(x);
if(last < 0)
{
last = knots.size() - 1 - (degree + 1);
}
int first = std::max((int)(last - degree), 0);
for(int i = first; i <= last; i++)
{
ret.push_back(i);
}
}
return ret;
}
// Insert knots and compute knot insertion matrix (to update control points)
bool BSplineBasis1D::insertKnots(SparseMatrix &A, double tau, unsigned int multiplicity)
{
if(!insideSupport(tau) || knotMultiplicity(tau) + multiplicity > degree + 1)
return false;
// New knot vector
int index = indexHalfopenInterval(tau);
std::vector<double> extKnots = knots;
for(unsigned int i = 0; i < multiplicity; i++)
extKnots.insert(extKnots.begin()+index+1, tau);
assert(isKnotVectorRegular(extKnots));
// Return knot insertion matrix
if(!buildKnotInsertionMatrix(A, extKnots))
return false;
// Update knots
knots = extKnots;
return true;
}