ON_NurbsSurface
FittingCylinder::initNurbsCylinderWithAxes (int order, NurbsDataSurface *data, Eigen::Matrix3d &axes)
{
Eigen::Vector3d mean;
unsigned s = unsigned (data->interior.size ());
mean = NurbsTools::computeMean (data->interior);
data->mean = mean;
Eigen::Vector3d v_max (0.0, 0.0, 0.0);
Eigen::Vector3d v_min (DBL_MAX, DBL_MAX, DBL_MAX);
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector3d p (axes.inverse () * (data->interior[i] - mean));
if (p (0) > v_max (0))
v_max (0) = p (0);
if (p (1) > v_max (1))
v_max (1) = p (1);
if (p (2) > v_max (2))
v_max (2) = p (2);
if (p (0) < v_min (0))
v_min (0) = p (0);
if (p (1) < v_min (1))
v_min (1) = p (1);
if (p (2) < v_min (2))
v_min (2) = p (2);
}
int ncpsU (order);
int ncpsV (2 * order + 4);
ON_NurbsSurface nurbs (3, false, order, order, ncpsU, ncpsV);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakePeriodicUniformKnotVector (1, 1.0 / (ncpsV - order + 1));
double dcu = (v_max (0) - v_min (0)) / (ncpsU - 1);
double dcv = (2.0 * M_PI) / (ncpsV - order + 1);
double ry = std::max<double> (std::fabs (v_min (1)), std::fabs (v_max (1)));
double rz = std::max<double> (std::fabs (v_min (2)), std::fabs (v_max (2)));
Eigen::Vector3d cv_t, cv;
for (int i = 0; i < ncpsU; i++)
{
for (int j = 0; j < ncpsV; j++)
{
cv (0) = v_min (0) + dcu * i;
cv (1) = ry * sin (dcv * j);
cv (2) = rz * cos (dcv * j);
cv_t = axes * cv + mean;
nurbs.SetCV (i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
}
return nurbs;
}
ON_NurbsSurface
FittingSurface::initNurbsPCA (int order, NurbsDataSurface *m_data, ON_3dVector z)
{
ON_3dVector mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = m_data->interior.size ();
NurbsTools::pca (m_data->interior, mean, eigenvectors, eigenvalues);
m_data->mean = mean;
//m_data->eigenvectors = (*eigenvectors);
bool flip (false);
Eigen::Vector3d ez(z[0],z[1],z[2]);
if (eigenvectors.col (2).dot (ez) < 0.0)
flip = true;
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
ON_3dVector sigma(sqrt(eigenvalues[0]), sqrt(eigenvalues[1]), sqrt(eigenvalues[2]));
ON_NurbsSurface nurbs (3, false, order, order, order, order);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakeClampedUniformKnotVector (1, 1.0);
// +- 2 sigma -> 95,45 % aller Messwerte
double dcu = (4.0 * sigma[0]) / (nurbs.Order (0) - 1);
double dcv = (4.0 * sigma[1]) / (nurbs.Order (1) - 1);
ON_3dVector cv_t, cv;
Eigen::Vector3d ecv_t, ecv;
Eigen::Vector3d emean(mean[0], mean[1], mean[2]);
for (int i = 0; i < nurbs.Order (0); i++)
{
for (int j = 0; j < nurbs.Order (1); j++)
{
cv[0] = -2.0 * sigma[0] + dcu * i;
cv[1] = -2.0 * sigma[1] + dcv * j;
cv[2] = 0.0;
ecv (0) = -2.0 * sigma[0] + dcu * i;
ecv (1) = -2.0 * sigma[1] + dcv * j;
ecv (2) = 0.0;
ecv_t = eigenvectors * ecv + emean;
cv_t[0] = ecv_t (0);
cv_t[1] = ecv_t (1);
cv_t[2] = ecv_t (2);
if (flip)
nurbs.SetCV (nurbs.Order (0) - 1 - i, j, ON_3dPoint (cv_t[0], cv_t[1], cv_t[2]));
else
nurbs.SetCV (i, j, ON_3dPoint (cv_t[0], cv_t[1], cv_t[2]));
}
}
return nurbs;
}
ON_NurbsSurface
FittingSurface::initNurbsPCA (int order, NurbsDataSurface *m_data, Eigen::Vector3d z)
{
Eigen::Vector3d mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = m_data->interior.size ();
NurbsTools::pca (m_data->interior, mean, eigenvectors, eigenvalues);
m_data->mean = mean;
m_data->eigenvectors = eigenvectors;
bool flip (false);
if (eigenvectors.col (2).dot (z) < 0.0)
flip = true;
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
Eigen::Vector3d sigma (sqrt (eigenvalues (0)), sqrt (eigenvalues (1)), sqrt (eigenvalues (2)));
ON_NurbsSurface nurbs (3, false, order, order, order, order);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakeClampedUniformKnotVector (1, 1.0);
// +- 2 sigma -> 95,45 % aller Messwerte
double dcu = (4.0 * sigma (0)) / (nurbs.Order (0) - 1);
double dcv = (4.0 * sigma (1)) / (nurbs.Order (1) - 1);
Eigen::Vector3d cv_t, cv;
for (int i = 0; i < nurbs.Order (0); i++)
{
for (int j = 0; j < nurbs.Order (1); j++)
{
cv (0) = -2.0 * sigma (0) + dcu * i;
cv (1) = -2.0 * sigma (1) + dcv * j;
cv (2) = 0.0;
cv_t = eigenvectors * cv + mean;
if (flip)
nurbs.SetCV (nurbs.Order (0) - 1 - i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
else
nurbs.SetCV (i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
}
return nurbs;
}
ON_NurbsSurface
FittingSurface::initNurbs4Corners (int order, ON_3dPoint ll, ON_3dPoint lr, ON_3dPoint ur, ON_3dPoint ul)
{
std::map<int, std::map<int, ON_3dPoint> > cv_map;
double dc = 1.0 / (order - 1);
for (int i = 0; i < order; i++)
{
double di = dc * i;
cv_map[i][0] = ll + (lr - ll) * di;
cv_map[0][i] = ll + (ul - ll) * di;
cv_map[i][order - 1] = ul + (ur - ul) * di;
cv_map[order - 1][i] = lr + (ur - lr) * di;
}
for (int i = 1; i < order - 1; i++)
{
for (int j = 1; j < order - 1; j++)
{
ON_3dPoint du = cv_map[0][j] + (cv_map[order - 1][j] - cv_map[0][j]) * dc * i;
ON_3dPoint dv = cv_map[i][0] + (cv_map[i][order - 1] - cv_map[i][0]) * dc * j;
cv_map[i][j] = du * 0.5 + dv * 0.5;
}
}
ON_NurbsSurface nurbs (3, false, order, order, order, order);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakeClampedUniformKnotVector (1, 1.0);
for (int i = 0; i < order; i++)
{
for (int j = 0; j < order; j++)
{
nurbs.SetCV (i, j, cv_map[i][j]);
}
}
return nurbs;
}
ON_NurbsSurface
FittingCylinder::initNurbsPCACylinder (int order, NurbsDataSurface *data)
{
Eigen::Vector3d mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = unsigned (data->interior.size ());
NurbsTools::pca (data->interior, mean, eigenvectors, eigenvalues);
data->mean = mean;
data->eigenvectors = eigenvectors;
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
Eigen::Vector3d v_max (0.0, 0.0, 0.0);
Eigen::Vector3d v_min (DBL_MAX, DBL_MAX, DBL_MAX);
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector3d p (eigenvectors.inverse () * (data->interior[i] - mean));
if (p (0) > v_max (0))
v_max (0) = p (0);
if (p (1) > v_max (1))
v_max (1) = p (1);
if (p (2) > v_max (2))
v_max (2) = p (2);
if (p (0) < v_min (0))
v_min (0) = p (0);
if (p (1) < v_min (1))
v_min (1) = p (1);
if (p (2) < v_min (2))
v_min (2) = p (2);
}
int ncpsU (order);
int ncpsV (2 * order + 4);
ON_NurbsSurface nurbs (3, false, order, order, ncpsU, ncpsV);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakePeriodicUniformKnotVector (1, 1.0 / (ncpsV - order + 1));
double dcu = (v_max (0) - v_min (0)) / (ncpsU - 1);
double dcv = (2.0 * M_PI) / (ncpsV - order + 1);
double ry = std::max<double> (std::fabs (v_min (1)), std::fabs (v_max (1)));
double rz = std::max<double> (std::fabs (v_min (2)), std::fabs (v_max (2)));
Eigen::Vector3d cv_t, cv;
for (int i = 0; i < ncpsU; i++)
{
for (int j = 0; j < ncpsV; j++)
{
cv (0) = v_min (0) + dcu * i;
cv (1) = ry * sin (dcv * j);
cv (2) = rz * cos (dcv * j);
cv_t = eigenvectors * cv + mean;
nurbs.SetCV (i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
}
return nurbs;
}
ON_NurbsSurface
FittingSurface::initNurbsPCABoundingBox (int order, NurbsDataSurface *m_data, ON_3dVector z)
{
ON_3dVector mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = m_data->interior.size ();
m_data->interior_param.clear ();
NurbsTools::pca (m_data->interior, mean, eigenvectors, eigenvalues);
m_data->mean = mean;
//m_data->eigenvectors = (*eigenvectors);
bool flip (false);
Eigen::Vector3d ez(z[0],z[1],z[2]);
if (eigenvectors.col (2).dot (ez) < 0.0)
flip = true;
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
Eigen::Matrix3d eigenvectors_inv = eigenvectors.inverse ();
ON_3dVector v_max(0.0, 0.0, 0.0);
ON_3dVector v_min(DBL_MAX, DBL_MAX, DBL_MAX);
Eigen::Vector3d emean(mean[0], mean[1], mean[2]);
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector3d eint(m_data->interior[i][0], m_data->interior[i][1], m_data->interior[i][2]);
Eigen::Vector3d ep = eigenvectors_inv * (eint - emean);
ON_3dPoint p(ep (0), ep (1), ep(2));
m_data->interior_param.push_back (ON_2dPoint(p[0], p[1]));
if (p[0] > v_max[0])
v_max[0] = p[0];
if (p[1] > v_max[1])
v_max[1] = p[1];
if (p[2] > v_max[2])
v_max[2] = p[2];
if (p[0] < v_min[0])
v_min[0] = p[0];
if (p[1] < v_min[1])
v_min[1] = p[1];
if (p[2] < v_min[2])
v_min[2] = p[2];
}
for (unsigned i = 0; i < s; i++)
{
ON_2dVector &p = m_data->interior_param[i];
if (v_max[0] > v_min[0] && v_max[0] > v_min[0])
{
p[0] = (p[0] - v_min[0]) / (v_max[0] - v_min[0]);
p[1] = (p[1] - v_min[1]) / (v_max[1] - v_min[1]);
}
else
{
throw std::runtime_error ("[NurbsTools::initNurbsPCABoundingBox] Error: v_max <= v_min");
}
}
ON_NurbsSurface nurbs (3, false, order, order, order, order);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakeClampedUniformKnotVector (1, 1.0);
double dcu = (v_max[0] - v_min[0]) / (nurbs.Order (0) - 1);
double dcv = (v_max[1] - v_min[1]) / (nurbs.Order (1) - 1);
ON_3dPoint cv_t, cv;
Eigen::Vector3d ecv_t2, ecv2;
Eigen::Vector3d emean2(mean[0],mean[1],mean[2]);
for (int i = 0; i < nurbs.Order (0); i++)
{
for (int j = 0; j < nurbs.Order (1); j++)
{
cv[0] = v_min[0] + dcu * i;
cv[1] = v_min[1] + dcv * j;
cv[2] = 0.0;
ecv2 (0) = cv[0];
ecv2 (1) = cv[1];
ecv2 (2) = cv[2];
ecv_t2 = eigenvectors * ecv2 + emean2;
if (flip)
nurbs.SetCV (nurbs.Order (0) - 1 - i, j, cv_t);
else
nurbs.SetCV (i, j, cv_t);
}
}
return nurbs;
}
ON_NurbsSurface
FittingSurface::initNurbsPCABoundingBox (int order, NurbsDataSurface *m_data, Eigen::Vector3d z)
{
Eigen::Vector3d mean;
Eigen::Matrix3d eigenvectors;
Eigen::Vector3d eigenvalues;
unsigned s = m_data->interior.size ();
m_data->interior_param.clear ();
NurbsTools::pca (m_data->interior, mean, eigenvectors, eigenvalues);
m_data->mean = mean;
m_data->eigenvectors = eigenvectors;
bool flip (false);
if (eigenvectors.col (2).dot (z) < 0.0)
flip = true;
eigenvalues = eigenvalues / s; // seems that the eigenvalues are dependent on the number of points (???)
Eigen::Matrix3d eigenvectors_inv = eigenvectors.inverse ();
Eigen::Vector3d v_max (0.0, 0.0, 0.0);
Eigen::Vector3d v_min (DBL_MAX, DBL_MAX, DBL_MAX);
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector3d p = eigenvectors_inv * (m_data->interior[i] - mean);
m_data->interior_param.push_back (Eigen::Vector2d (p (0), p (1)));
if (p (0) > v_max (0))
v_max (0) = p (0);
if (p (1) > v_max (1))
v_max (1) = p (1);
if (p (2) > v_max (2))
v_max (2) = p (2);
if (p (0) < v_min (0))
v_min (0) = p (0);
if (p (1) < v_min (1))
v_min (1) = p (1);
if (p (2) < v_min (2))
v_min (2) = p (2);
}
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector2d &p = m_data->interior_param[i];
if (v_max (0) > v_min (0) && v_max (0) > v_min (0))
{
p (0) = (p (0) - v_min (0)) / (v_max (0) - v_min (0));
p (1) = (p (1) - v_min (1)) / (v_max (1) - v_min (1));
}
else
{
throw std::runtime_error ("[NurbsTools::initNurbsPCABoundingBox] Error: v_max <= v_min");
}
}
ON_NurbsSurface nurbs (3, false, order, order, order, order);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakeClampedUniformKnotVector (1, 1.0);
double dcu = (v_max (0) - v_min (0)) / (nurbs.Order (0) - 1);
double dcv = (v_max (1) - v_min (1)) / (nurbs.Order (1) - 1);
Eigen::Vector3d cv_t, cv;
for (int i = 0; i < nurbs.Order (0); i++)
{
for (int j = 0; j < nurbs.Order (1); j++)
{
cv (0) = v_min (0) + dcu * i;
cv (1) = v_min (1) + dcv * j;
cv (2) = 0.0;
cv_t = eigenvectors * cv + mean;
if (flip)
nurbs.SetCV (nurbs.Order (0) - 1 - i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
else
nurbs.SetCV (i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
}
return nurbs;
}
ON_NurbsSurface
FittingSphere::initNurbsSphere (int order, NurbsDataSurface *data, Eigen::Vector3d)
{
Eigen::Vector3d mean = NurbsTools::computeMean (data->interior);
Eigen::Vector3d _min (DBL_MAX, DBL_MAX, DBL_MAX);
Eigen::Vector3d _max (-DBL_MAX, -DBL_MAX, -DBL_MAX);
for (const auto &i : data->interior)
{
Eigen::Vector3d p = i - mean;
if (p (0) < _min (0))
_min (0) = p (0);
if (p (1) < _min (1))
_min (1) = p (1);
if (p (2) < _min (2))
_min (2) = p (2);
if (p (0) > _max (0))
_max (0) = p (0);
if (p (1) > _max (1))
_max (1) = p (1);
if (p (2) > _max (2))
_max (2) = p (2);
}
int ncpsU (order + 2);
int ncpsV (2 * order + 4);
ON_NurbsSurface nurbs (3, false, order, order, ncpsU, ncpsV);
nurbs.MakeClampedUniformKnotVector (0, 1.0);
nurbs.MakePeriodicUniformKnotVector (1, 1.0 / (ncpsV - order + 1));
double dcu = (_max (2) - _min (2)) / (ncpsU - 3);
double dcv = (2.0 * M_PI) / (ncpsV - order + 1);
double rx = std::max<double> (std::fabs (_min (0)), std::fabs (_max (0)));
double ry = std::max<double> (std::fabs (_min (1)), std::fabs (_max (1)));
Eigen::Vector3d cv_t, cv;
for (int i = 1; i < ncpsU - 1; i++)
// for (int i = 0; i < ncpsU; i++)
{
for (int j = 0; j < ncpsV; j++)
{
cv (0) = rx * sin (dcv * j);
cv (1) = ry * cos (dcv * j);
cv (2) = _min (2) + dcu * (i - 1);
cv_t = cv + mean;
nurbs.SetCV (i, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
}
for (int j = 0; j < ncpsV; j++)
{
// cv (0) = 0.0;
// cv (1) = 0.0;
cv (0) = 0.01 * rx * sin (dcv * j);
cv (1) = 0.01 * ry * cos (dcv * j);
cv (2) = _min (2);
cv_t = cv + mean;
nurbs.SetCV (0, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
for (int j = 0; j < ncpsV; j++)
{
// cv (0) = 0.0;
// cv (1) = 0.0;
cv (0) = 0.01 * rx * sin (dcv * j);
cv (1) = 0.01 * ry * cos (dcv * j);
cv (2) = _max (2);
cv_t = cv + mean;
nurbs.SetCV (ncpsU - 1, j, ON_3dPoint (cv_t (0), cv_t (1), cv_t (2)));
}
return nurbs;
}