//===========================================================================
vector<shared_ptr<SplineSurface> >
SurfaceCreators::separateRationalParts(const SplineSurface& sf)
//===========================================================================
{
bool rat = sf.rational();
ASSERT(rat);
int dim= sf.dimension();
int rdim = dim + 1;
vector<shared_ptr<SplineSurface> > sep_sfs;
vector<double> coefs(sf.coefs_begin(), sf.coefs_end());
int nmb1 = sf.numCoefs_u();
int nmb2 = sf.numCoefs_v();
vector<double> rcoefs;
int num_coefs = nmb1*nmb2;
vector<double>::const_iterator rcoef_iter = sf.rcoefs_begin();
for (int ki = 0; ki < num_coefs; ++ki) {
rcoefs.push_back(rcoef_iter[ki*rdim+1]);
for (int kj = 0; kj < dim; ++kj) {
coefs[ki*dim+kj] /= (rcoefs.back());
}
}
sep_sfs.push_back(shared_ptr<SplineSurface>
(new SplineSurface(nmb1, nmb2, sf.order_u(), sf.order_v(),
sf.basis_u().begin(), sf.basis_v().begin(),
coefs.begin(), dim)));
sep_sfs.push_back(shared_ptr<SplineSurface>
(new SplineSurface(nmb1, nmb2, sf.order_u(), sf.order_v(),
sf.basis_u().begin(), sf.basis_v().begin(),
rcoefs.begin(), 1)));
return sep_sfs;
}
int main(int argc, char** argv)
{
if (argc < 3) {
cerr << "Usage: " << argv[0]
<< " inputfile outputfile [max_coefs_u max_coefs_v]" << endl;
return 1;
}
ifstream in(argv[1]);
ofstream out(argv[2]);
if (!in || !out) {
cout << "Bad file(s) or filename(s)." << endl;
return 1;
}
ObjectHeader oh;
SplineSurface sf;
in >> oh >> sf;
int m = sf.numCoefs_v() - sf.order_v() + 1;
int n = sf.numCoefs_u() - sf.order_u() + 1;
if (argc >= 5) {
// Note the weird order (v then u)
m = min(atoi(argv[4])-sf.numCoefs_v(), m);
n = min(atoi(argv[3])-sf.numCoefs_u(), n);
}
int i;
vector<double> newknots_v;
vector<double> newknots_u;
for (i = 0; i < m; ++i) {
vector<double>::const_iterator it = sf.basis_v().begin();
double newknot = 0.5*it[sf.order_v()+i-1] + 0.5*it[sf.order_v()+i];
newknots_v.push_back(newknot);
}
for (i = 0; i < n; ++i) {
vector<double>::const_iterator it = sf.basis_u().begin();
double newknot = 0.5*it[sf.order_u()+i-1] + 0.5*it[sf.order_u()+i];
newknots_u.push_back(newknot);
}
sf.insertKnot_v(newknots_v);
sf.insertKnot_u(newknots_u);
out << oh << sf;
return 0;
}
//==========================================================================
void GeometryTools::splitSurfaceIntoPatches(const SplineSurface& sf,
vector<SplineSurface>& pat)
//==========================================================================
{
SplineSurface orig = sf;
orig.makeBernsteinKnotsU();
orig.makeBernsteinKnotsV();
int num_u = orig.numCoefs_u();
int num_v = orig.numCoefs_v();
int order_u = orig.order_u();
int order_v = orig.order_v();
int numpat_u = num_u / order_u;
int numpat_v = num_v / order_v;
pat.resize(numpat_u * numpat_v);
typedef vector<double>::const_iterator const_iter;
const_iter itu = orig.basis_u().begin();
const_iter itv;
for (int i = 0; i < numpat_u; ++i) {
itv = orig.basis_v().begin();
for (int j = 0; j < numpat_v; ++j) {
shared_ptr<SplineSurface>
new_sf(orig.subSurface(*itu, *itv,
*(itu+order_u), *(itv+order_v)));
pat[numpat_u*j + i] = *new_sf;
itv += order_v;
}
itu += order_u;
}
return;
}
//==========================================================================
void cart_to_bary(const SplineSurface& sf, const BaryCoordSystem3D& bc,
SplineSurface& sf_bc)
//==========================================================================
{
ALWAYS_ERROR_IF(sf.dimension() != 3, "Dimension must be 3.");
int nu = sf.numCoefs_u();
int nv = sf.numCoefs_v();
Vector3D cart;
Vector4D bary;
vector<double> new_coefs;
if (!sf.rational()) {
new_coefs.resize(4 * nu * nv);
for (int iv = 0; iv < nv; ++iv) {
for (int iu = 0; iu < nu; ++iu) {
int offset = nu * iv + iu;
cart = Vector3D(sf.coefs_begin() + 3 * offset);
bary = bc.cartToBary(cart);
for (int j = 0; j < 4; ++j) {
new_coefs[4*offset + j] = bary[j];
}
}
}
} else {
new_coefs.resize(5 * nu * nv);
for (int iv = 0; iv < nv; ++iv) {
for (int iu = 0; iu < nu; ++iu) {
int offset = nu * iv + iu;
cart = Vector3D(sf.coefs_begin() + 3 * offset);
bary = bc.cartToBary(cart);
double w = sf.rcoefs_begin()[4*offset + 3];
for (int j = 0; j < 4; ++j) {
new_coefs[5*offset + j] = bary[j] * w;
}
new_coefs[5*offset + 4] = w;
}
}
}
sf_bc = SplineSurface(nu, nv, sf.order_u(), sf.order_v(),
sf.basis_u().begin(), sf.basis_v().begin(),
new_coefs.begin(), 4, sf.rational());
return;
}
//==========================================================================
void make_matrix(const SplineSurface& surf, int deg,
vector<vector<double> >& mat)
//==========================================================================
{
// Create BernsteinMulti. In the rational case the weights are
// included in an "extra" coordinate.
int dim = surf.dimension();
bool rational = surf.rational();
vector<BernsteinMulti> beta;
spline_to_bernstein(surf, beta);
// Make vector of basis functions (with the surface plugged in) by
// using recursion
int num = (deg+1) * (deg+2) * (deg+3) / 6;
vector<BernsteinMulti> basis(num);
vector<BernsteinMulti> tmp(num);
basis[0] = BernsteinMulti(1.0);
BernsteinMulti zero_multi = BernsteinMulti(0.0);
for (int r = 1; r <= deg; ++r) {
int m = -1;
int tmp_num = (r + 1) * (r + 2) * (r + 3) / 6;
fill(tmp.begin(), tmp.begin() + tmp_num, zero_multi);
for (int i = 0; i < r; ++i) {
int k = (i + 1) * (i + 2) / 2;
for (int j = 0; j <= i; ++j) {
for (int l = 0; l <= j; ++l) {
++m;
tmp[m] += beta[0] * basis[m];
tmp[m + k] += beta[1] * basis[m];
tmp[m + 1 + j + k] += beta[2] * basis[m];
tmp[m + 2 + j + k] += beta[3] * basis[m];
}
}
}
basis.swap(tmp);
}
// Fill up the matrix mat
int deg_u = surf.order_u() - 1;
int deg_v = surf.order_v() - 1;
int numbas = (deg * deg_u + 1) * (deg * deg_v + 1);
mat.resize(numbas);
for (int row = 0; row < numbas; ++row) {
mat[row].resize(num);
for (int col = 0; col < num; ++col) {
mat[row][col] = basis[col][row];
}
}
// If rational, include diagonal scaling matrix. Dividing the
// D-matrix by the weights has the same effect as multiplying the
// basis with the same weights. (Included for numerical reasons only -
// it makes the basis a partition of unity.)
if (rational) {
BernsteinMulti weights = BernsteinMulti(1.0);
for (int i = 1; i <= deg; ++i)
weights *= beta[dim];
for (int row = 0; row < numbas; ++row) {
double scaling = 1.0 / weights[row];
for (int col = 0; col < num; ++col) {
mat[row][col] *= scaling;
}
}
}
// // Check Frobenius norm
// double norm = 0.0;
// for (int irow = 0; irow < numbas; ++irow) {
// for (int icol = 0; icol < num; ++icol) {
// norm += mat[irow][icol] * mat[irow][icol];
// }
// }
// norm = sqrt(norm);
// cout << "Frobenius norm = " << norm << endl;
return;
}
//===========================================================================
shared_ptr<SplineSurface>
SurfaceCreators::mult1DBezierPatches(const SplineSurface& patch1,
const SplineSurface& patch2)
//===========================================================================
{
// @@sbr This should be fixed shortly. Nothing more than separating the
// spatial and rational components.
ASSERT(!patch1.rational() && !patch2.rational());
// We should of course also check the actual knots, but why bother (trusting the user).
// ASSERT(basis1_u.numCoefs() == basis2_u.numCoefs() &&
// basis1_v.numCoefs() == basis2_v.numCoefs() &&
// basis1_u.order() == basis2_u.order() &&
// basis1_v.order() == basis2_v.order());
ASSERT((patch1.dimension() == 1) && (patch2.dimension() == 1));
// @@sbr Suppose we could allow for differing orders (but equal parameter domain).
// Ported from SISL routine s6multsfs().
int order = max(2*(patch1.order_u() - 1) + 1, 2*(patch1.order_v() - 1) + 1);;
vector<double> pascal((order+1)*(order+2)/2, 0.0); // Binomial coefficients (Pascal's triangle)
int ki, kj;
vector<double>::iterator psl1; /* Pointer used in Pascals triangle */
vector<double>::iterator psl2; /* Pointer used in Pascals triangle */
for(ki = 0, psl2 = pascal.begin(); ki <= order ; ki++, psl1 = psl2, psl2 += ki) {
psl2[0] = 1.0;
for(kj = 1; kj < ki; kj++)
psl2[kj] = psl1[kj-1] + psl1[kj];
psl2[ki] = 1.0;
}
int order11 = patch1.order_u();
int order12 = patch1.order_v();
int order21 = patch2.order_u();
int order22 = patch2.order_v();
vector<double>::const_iterator c1 = patch1.coefs_begin();
vector<double>::const_iterator c2 = patch2.coefs_begin();
// vector<double> mult_coefs(patch1.numCoefs_u()*patch1.numCoefs_v()*patch1.dimension(), 0.0);
int p1,p2,r1,r2;
int kgrad11 = order11-1;
int kgrad12 = order12-1;
int kgrad21 = order21-1;
int kgrad22 = order22-1;
int kgrad1 = kgrad11 + kgrad21; // Degree of mult basis functions in 1st dir.
int kgrad2 = kgrad12 + kgrad22;
int kstop2 = order12+order22-1;
int kstop1 = order11+order21-1;
vector<double> mult_coefs(kstop1*kstop2, 0.0);
vector<double>::const_iterator psl_kgrad11 = pascal.begin()+kgrad11*(kgrad11+1)/2;
vector<double>::const_iterator psl_kgrad12 = pascal.begin()+kgrad12*(kgrad12+1)/2;
vector<double>::const_iterator psl_kgrad21 = pascal.begin()+kgrad21*(kgrad21+1)/2;
vector<double>::const_iterator psl_kgrad22 = pascal.begin()+kgrad22*(kgrad22+1)/2;
vector<double>::const_iterator psl_kgrad1 = pascal.begin()+kgrad1 *(kgrad1 +1)/2;
vector<double>::const_iterator psl_kgrad2 = pascal.begin()+kgrad2 *(kgrad2 +1)/2;
vector<double>::const_iterator qsc1, qsc2;
double tsum, sumi;
vector<double>::iterator temp = mult_coefs.begin();
double tdiv, t2;
int kstop3, kstop4;
for (p2 = 0; p2 < kstop2; ++p2)
for (p1 = 0; p1 <kstop1; p1++, temp++) {
tdiv = psl_kgrad1[p1]*psl_kgrad2[p2];
kstop4 = min(p2,kgrad12);
for (r2 = max(0,p2-kgrad22),tsum = 0.0; r2 <= kstop4; r2++) {
t2 = psl_kgrad12[r2]*psl_kgrad22[p2-r2];
kstop3 = min(p1,kgrad11);
for (r1 = max(0,p1-kgrad21),sumi = 0.0,
qsc1 = c1+r2*order11,qsc2 = c2+(p2-r2)*order21;
r1 <= kstop3; r1++)
sumi += psl_kgrad11[r1]*psl_kgrad21[p1-r1]*qsc1[r1]*qsc2[p1-r1];
tsum += t2*sumi;
}
tsum /= tdiv;
*temp = tsum;
}
// *order_newsurf1 = kstop1;
// *order_newsurf2 = kstop2;
// We must add knots to input basises according to new order.
vector<double> new_knots_u, new_knots_v;
new_knots_u.insert(new_knots_u.begin(), kstop1, patch1.startparam_u());
new_knots_u.insert(new_knots_u.end(), kstop1, patch1.endparam_u());
new_knots_v.insert(new_knots_v.begin(), kstop2, patch1.startparam_v());
new_knots_v.insert(new_knots_v.end(), kstop2, patch1.endparam_v());
// Finally we create the spline sf with the multiplied coefs.
shared_ptr<SplineSurface> mult_sf(new SplineSurface(kstop1, kstop2, kstop1, kstop2,
new_knots_u.begin(), new_knots_v.begin(),
mult_coefs.begin(), patch1.dimension(),
patch1.rational()));
// SplineSurface* mult_sf = new SplineSurface(patch1.numCoefs_u(), patch1.numCoefs_v(),
// patch1.order_u(), patch1.order_v(),
// patch1.basis_u().begin(), patch1.basis_v().begin(),
// mult_coefs.begin(), patch1.dimension(),
// patch1.rational());
return mult_sf;
}