std::vector<double>
FittingSurface::getElementVector (const ON_NurbsSurface &nurbs, int dim) // !
{
std::vector<double> result;
int idx_min = 0;
int idx_max = nurbs.KnotCount (dim) - 1;
if (nurbs.IsClosed (dim))
{
idx_min = nurbs.Order (dim) - 2;
idx_max = nurbs.KnotCount (dim) - nurbs.Order (dim) + 1;
}
const double* knots = nurbs.Knot (dim);
result.push_back (knots[idx_min]);
//for(int E=(m_nurbs.Order(0)-2); E<(m_nurbs.KnotCount(0)-m_nurbs.Order(0)+2); E++) {
for (int E = idx_min + 1; E <= idx_max; E++)
{
if (!NEAR_EQUAL(knots[E], knots[E - 1], SMALL_FASTF)) // do not count double knots
result.push_back (knots[E]);
}
return result;
}
std::vector<double>
FittingCylinder::getElementVector (const ON_NurbsSurface &nurbs, int dim) // !
{
std::vector<double> result;
if (dim == 0)
{
int idx_min = 0;
int idx_max = nurbs.KnotCount (0) - 1;
if (nurbs.IsClosed (0))
{
idx_min = nurbs.Order (0) - 2;
idx_max = nurbs.KnotCount (0) - nurbs.Order (0) + 1;
}
const double* knotsU = nurbs.Knot (0);
result.push_back (knotsU[idx_min]);
//for(int E=(m_nurbs.m_order[0]-2); E<(m_nurbs.m_knot_capacity[0]-m_nurbs.m_order[0]+2); E++) {
for (int E = idx_min + 1; E <= idx_max; E++)
{
if (knotsU[E] != knotsU[E - 1]) // do not count double knots
result.push_back (knotsU[E]);
}
}
else if (dim == 1)
{
int idx_min = 0;
int idx_max = nurbs.KnotCount (1) - 1;
if (nurbs.IsClosed (1))
{
idx_min = nurbs.Order (1) - 2;
idx_max = nurbs.KnotCount (1) - nurbs.Order (1) + 1;
}
const double* knotsV = nurbs.Knot (1);
result.push_back (knotsV[idx_min]);
//for(int F=(m_nurbs.m_order[1]-2); F<(m_nurbs.m_knot_capacity[1]-m_nurbs.m_order[1]+2); F++) {
for (int F = idx_min + 1; F <= idx_max; F++)
{
if (knotsV[F] != knotsV[F - 1])
result.push_back (knotsV[F]);
}
}
else
printf ("[FittingCylinder::getElementVector] Error, index exceeds problem dimensions!\n");
return result;
}
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;
}
void ON_GL( const ON_NurbsSurface& s,
GLUnurbsObj* nobj, // created with gluNewNurbsRenderer )
GLenum type, // = 0 (and type is automatically set)
int bPermitKnotScaling,
double* knot_scale0,
double* knot_scale1
)
{
int i, j, k;
// The "bPermitScaling" parameters to the ON_GL() call that
// fills in the knot vectors is set to false because any
// rescaling that is applied to a surface domain must also
// be applied to parameter space trimming curve geometry.
// GL "s" knots
GLint sknot_count = s.KnotCount(0) + 2;
GLfloat* sknot = (GLfloat*)onmalloc( sknot_count*sizeof(*sknot) );
ON_GL( s.Order(0), s.CVCount(0), s.Knot(0), sknot,
bPermitKnotScaling, knot_scale0 );
// GL "t" knots
GLint tknot_count = s.KnotCount(1) + 2;
GLfloat* tknot = (GLfloat*)onmalloc( tknot_count*sizeof(*tknot) );
ON_GL( s.Order(1), s.CVCount(1), s.Knot(1), tknot,
bPermitKnotScaling, knot_scale1 );
// control vertices
const int cv_size= s.CVSize();
const int cv_count[2] = {s.CVCount(0), s.CVCount(1)};
GLint s_stride = cv_size*cv_count[1];
GLint t_stride = cv_size;
GLfloat* ctlarray = (GLfloat*)onmalloc( s_stride*cv_count[0]*sizeof(*ctlarray) );
for ( i = 0; i < cv_count[0]; i++ ) {
for ( j = 0; j < cv_count[1]; j++ ) {
const double* cv = s.CV(i,j);
GLfloat* gl_cv = ctlarray + s_stride*i + t_stride*j;
for ( k = 0; k < cv_size; k++ ) {
gl_cv[k] = (GLfloat)cv[k];
}
}
}
GLint sorder = s.Order(0);
GLint torder = s.Order(1);
if ( type == 0 ) {
// set GL surface type for 3d CVs in homogeneous/euclidean form.
type = ( s.IsRational() ) ? GL_MAP2_VERTEX_4 : GL_MAP2_VERTEX_3;
}
gluNurbsSurface (
nobj,
sknot_count,
sknot,
tknot_count,
tknot,
s_stride,
t_stride,
ctlarray,
sorder,
torder,
type
);
onfree( ctlarray );
onfree( tknot );
onfree( sknot );
}
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;
}