Array1D_Real NURBSCurve<Real>::insertKnot(Real u, int k, int s, int r, Array1D_Vector3 & Qw, int * uq)
{
Array1D_Real UP = GetKnotVector();
Array1D_Vector3 Pw = mCtrlPoint;
Array1D_Real UQ;
Array1D_Vector3 Rw;
Scalar alpha;
int L = 0;
int order = this->GetDegree() + 1;
int p = order - 1;
int np = Pw.size() - 1;
int mp = np+p+1;
int nq = np+r;
// Define array
UQ.resize(mp+r+1);
Qw.resize(nq+1);
Rw.resize(p+1);
// Load new knot vector
for (int i=0; i<=k; i++) UQ[i] = UP[i];
for (int i=1; i<=r; i++) UQ[k+i] = u;
for (int i=k+1; i<=mp; i++) UQ[i+r] = UP[i];
// Save unaltered control points
for (int i=0; i<=k-p; i++) Qw[i] = Pw[i];
for (int i=k-s; i<=np; i++) Qw[i+r] = Pw[i];
for (int i=0; i<=p-s; i++) Rw[i] = Pw[k-p+i];
// Insert the knot r times
for (int j=1; j<=r; j++)
{
L = k-p+j;
for (int i=0; i<=p-j-s; i++)
{
alpha = (u-UP[L+i])/(UP[i+k+1]-UP[L+i]);
Rw[i] = alpha*Rw[i+1] + (1.0 - alpha) * Rw[i];
}
Qw[L] = Rw[0];
Qw[k+r-j-s] = Rw[p-j-s];
}
// Load remaining control points
for (int i=L+1; i<k-s; i++)
Qw[i] = Rw[i-L];
if(uq) *uq = k-p+1;
return UQ;
}
Array1D_Vector3 NURBSCurve<Real>::removeKnots(int iterations)
{
NURBSCurve<Real> curCurve = *this;
for(int itr = 0; itr < iterations; itr++)
{
Array1D_Real U = curCurve.GetKnotVector();
Array1D_Vector3 P = curCurve.mCtrlPoint;
int p = curCurve.GetDegree();
QMap<Real, int> errors;
for(int i = p + 1; i < (int)U.size() - 1; i++)
{
if(U[i] < U[i+1])
errors[ curCurve.KnotRemovalError(i, 1) ] = i;
}
int r = errors.values().at(itr); // Knot to remove
int num = 1;
int s = 1;
int deg_ = curCurve.GetDegree();
int m = U.size() ;
int ord = deg_+1 ;
int fout = (2*r-s-deg_)/2 ;
int last = r-s ;
int first = r-deg_ ;
Real alfi, alfj ;
int i,j,k,ii,jj,off ;
Real u ;
Array1D_Vector3 temp( 2*deg_+1, Vector3(0,0,0) ) ;
u = U[r] ;
int t;
for(t=0; t<num; ++t)
{
off = first-1 ;
temp[0] = P[off] ;
temp[last+1-off] = P[last+1] ;
i = first;
j = last ;
ii = 1 ;
jj = last-off ;
while(j-i > t) {
alfi = (u-U[i])/(U[i+ord+t]-U[i]) ;
alfj = (u-U[j-t])/(U[j+ord]-U[j-t]) ;
temp[ii] = (P[i]-(1.0-alfi)*temp[ii-1])/alfi ;
temp[jj] = (P[j]-alfj*temp[jj+1])/(1.0-alfj) ;
++i ;
++ii ;
--j ;
--jj ;
}
i = first ;
j = last ;
while(j-i>t) {
P[i] = temp[i-off] ;
P[j] = temp[j-off] ;
++i;
--j ;
}
--first ;
++last ;
}
if(t == 0)
return P;
for(k=r+1; k<m ; ++k)
U[k-t] = U[k] ;
j = fout ;
i=j ; // Pj thru Pi will be overwritten
for(k=1; k<t; k++)
if( (k%2) == 1)
++i ;
else
--j ;
for(k=i+1; k<(int)P.size() ; k++) {// Shift
P[j++] = P[k] ;
}
P.resize(P.size() - t);
curCurve = createCurveFromPoints(P);
}
return curCurve.mCtrlPoint;
}
void NURBSCurve<Real>::refine(Array1D_Real & insknts, Array1D_Vector3 & Qw, Array1D_Real & Ubar )
{
// Input
Array1D_Real X = insknts;
Array1D_Vector3 Pw = this->mCtrlPoint;
Array1D_Real U = GetKnotVector();
int s = insknts.size();
int order = this->GetDegree() + 1;
int p = order - 1;
int n = Pw.size() - 1;
int r = X.size() - 1;
int m = n+p+1;
// Output
Qw.resize ( n+s+1, Vector3(0,0,0) );
Ubar.resize ( m+s+1, 0 );
int a = findSpan(n,p,X[0],U);
int b = findSpan(n,p,X[r],U) + 1;
int j = 0;
for(j=0 ; j<=a-p; j++) Qw[j] = Pw[j];
for(j=b-1; j<=n ; j++) Qw[j+r+1] = Pw[j];
for(j=0 ; j<=a ; j++) Ubar[j] = U[j];
for(j=b+p; j<=m ; j++) Ubar[j+r+1] = U[j];
int i = b+p-1;
int k = b+p+r;
Real alfa = 0;
for (int j=r; j>=0; j--)
{
while (X[j] <= U[i] && i > a) {
Qw[k-p-1] = Pw[i-p-1];
Ubar[k] = U[i];
k = k - 1;
i = i - 1;
}
Qw[k-p-1] = Qw[k-p];
for (int l=1; l<=p; l++)
{
int ind = k-p+l;
alfa = Ubar[k+l] - X[j];
if (fabs(alfa) == 0.0)
{
Qw[ind-1] = Qw[ind];
}
else
{
alfa = alfa / (Ubar[k+l] - U[i-p+l]);
Qw[ind-1] = alfa * Qw[ind-1] + (1.0 - alfa) * Qw[ind];
}
}
Ubar[k] = X[j];
k = k - 1;
}
}