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
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
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;
}