C++ SplineSurface::order_v方法代码示例

//===========================================================================
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;
}