void
NurbsTools::pca (const vector_vec2d &data, Eigen::Vector2d &mean, Eigen::Matrix2d &eigenvectors,
Eigen::Vector2d &eigenvalues)
{
if (data.empty ())
{
printf ("[NurbsTools::pca] Error, data is empty\n");
abort ();
}
mean = computeMean (data);
unsigned s = unsigned (data.size ());
Eigen::MatrixXd Q (2, s);
for (unsigned i = 0; i < s; i++)
Q.col (i) << (data[i] - mean);
Eigen::Matrix2d C = Q * Q.transpose ();
Eigen::SelfAdjointEigenSolver<Eigen::Matrix2d> eigensolver (C);
if (eigensolver.info () != Success)
{
printf ("[NurbsTools::pca] Can not find eigenvalues.\n");
abort ();
}
for (int i = 0; i < 2; ++i)
{
eigenvalues (i) = eigensolver.eigenvalues () (1 - i);
eigenvectors.col (i) = eigensolver.eigenvectors ().col (1 - i);
}
}
ON_NurbsCurve
FittingCurve2d::initCPsNurbsCurve2D (int order, const vector_vec2d &cps)
{
int cp_red = order - 2;
ON_NurbsCurve nurbs;
if (cps.size () < 3 || cps.size () < (2 * cp_red + 1))
{
printf ("[FittingCurve2d::initCPsNurbsCurve2D] Warning, number of control points too low.\n");
return nurbs;
}
int ncps = cps.size () + 2 * cp_red; // +2*cp_red for smoothness and +1 for closing
nurbs = ON_NurbsCurve (2, false, order, ncps);
nurbs.MakePeriodicUniformKnotVector (1.0 / (ncps - order + 1));
for (int j = 0; j < cps.size (); j++)
nurbs.SetCV (cp_red + j, ON_3dPoint (cps[j] (0), cps[j] (1), 0.0));
// close nurbs
nurbs.SetCV (cp_red + cps.size (), ON_3dPoint (cps[0] (0), cps[0] (1), 0.0));
// make smooth at closing point
for (int j = 0; j < cp_red; j++)
{
ON_3dPoint cp;
nurbs.GetCV (nurbs.CVCount () - 1 - cp_red + j, cp);
nurbs.SetCV (j, cp);
nurbs.GetCV (cp_red - j, cp);
nurbs.SetCV (nurbs.CVCount () - 1 - j, cp);
}
return nurbs;
}
ON_NurbsCurve
FittingCurve2d::initCPsNurbsCurve2D (int order, const vector_vec2d &cps)
{
ON_NurbsCurve nurbs;
if ((int)cps.size () < (2 * order))
{
printf ("[FittingCurve2d::initCPsNurbsCurve2D] Warning, number of control points too low.\n");
return nurbs;
}
int cp_red = order - 2;
int ncps = cps.size () + cp_red;
nurbs = ON_NurbsCurve (2, false, order, ncps);
nurbs.MakePeriodicUniformKnotVector (1.0 / (ncps - order + 1));
for (int j = 0; j < ncps; j++)
nurbs.SetCV (j, ON_3dPoint (cps[j] (0), cps[j] (1), 0.0));
for (int j = 0; j < cp_red; j++)
{
ON_3dPoint cp;
nurbs.GetCV (nurbs.m_cv_count - 1 - cp_red + j, cp);
nurbs.SetCV (j, cp);
nurbs.GetCV (cp_red - j, cp);
nurbs.SetCV (nurbs.m_cv_count - 1 - j, cp);
}
return nurbs;
}
void
ClosingBoundary::sampleFromBoundary (ON_NurbsSurface *nurbs, vector_vec3d &point_list, vector_vec2d ¶m_list,
unsigned samples)
{
double ds = 1.0 / (samples - 1);
double minU = nurbs->Knot (0, 0);
double maxU = nurbs->Knot (0, nurbs->KnotCount (0) - 1);
double minV = nurbs->Knot (1, 0);
double maxV = nurbs->Knot (1, nurbs->KnotCount (1) - 1);
Eigen::Vector2d params;
Eigen::Vector3d point;
double points[3];
// WEST
params (0) = minU;
for (unsigned i = 0; i < samples; i++)
{
params (1) = minV + (maxV - minV) * ds * i;
nurbs->Evaluate (params (0), params (1), 0, 3, points);
point_list.push_back (Eigen::Vector3d (points[0], points[1], points[2]));
param_list.push_back (params);
}
// EAST
params (0) = maxU;
for (unsigned i = 0; i < samples; i++)
{
params (1) = minV + (maxV - minV) * ds * i;
nurbs->Evaluate (params (0), params (1), 0, 3, points);
point_list.push_back (Eigen::Vector3d (points[0], points[1], points[2]));
param_list.push_back (params);
}
// SOUTH
params (1) = minV;
for (unsigned i = 0; i < samples; i++)
{
params (0) = minU + (maxU - minU) * ds * i;
nurbs->Evaluate (params (0), params (1), 0, 3, points);
point_list.push_back (Eigen::Vector3d (points[0], points[1], points[2]));
param_list.push_back (params);
}
// NORTH
params (1) = maxV;
for (unsigned i = 0; i < samples; i++)
{
params (0) = minU + (maxU - minU) * ds * i;
nurbs->Evaluate (params (0), params (1), 0, 3, points);
point_list.push_back (Eigen::Vector3d (points[0], points[1], points[2]));
param_list.push_back (params);
}
}
unsigned
NurbsTools::getClosestPoint (const Eigen::Vector2d &p, const vector_vec2d &data)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
size_t idx = 0;
double dist2 (DBL_MAX);
for (size_t i = 0; i < data.size (); i++)
{
double d2 = (data[i] - p).squaredNorm ();
if (d2 < dist2)
{
idx = i;
dist2 = d2;
}
}
return idx;
}
unsigned
NurbsTools::getClosestPoint (const ON_2dPoint &p, const vector_vec2d &data)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
unsigned idx (0);
double dist2 (DBL_MAX);
for (unsigned i = 0; i < data.size (); i++)
{
ON_2dVector v = (data[i] - p);
double d2 = ON_DotProduct(v, v); // Was the squaredNorm in Eigen
if (d2 < dist2)
{
idx = i;
dist2 = d2;
}
}
return idx;
}
ON_2dVector
NurbsTools::computeMean (const vector_vec2d &data)
{
ON_2dVector u (0.0, 0.0);
unsigned s = data.size ();
double ds = 1.0 / s;
for (unsigned i = 0; i < s; i++)
u += (data[i] * ds);
return u;
}
Eigen::Vector2d
NurbsTools::computeMean (const vector_vec2d &data)
{
Eigen::Vector2d u (0.0, 0.0);
size_t s = data.size ();
double ds = 1.0 / double (s);
for (size_t i = 0; i < s; i++)
u += (data[i] * ds);
return u;
}
ON_NurbsCurve
FittingCurve2d::initNurbsCurve2D (int order, const vector_vec2d &data, int ncps, double radiusF)
{
if (data.empty ())
printf ("[FittingCurve2d::initNurbsCurve2D] Warning, no boundary parameters available\n");
Eigen::Vector2d mean = NurbsTools::computeMean (data);
unsigned s = data.size ();
double r (0.0);
for (unsigned i = 0; i < s; i++)
{
Eigen::Vector2d d = data[i] - mean;
double sn = d.squaredNorm ();
if (sn > r)
r = sn;
}
r = radiusF * sqrt (r);
if (ncps < 2 * order)
ncps = 2 * order;
ON_NurbsCurve nurbs = ON_NurbsCurve (2, false, order, ncps);
nurbs.MakePeriodicUniformKnotVector (1.0 / (ncps - order + 1));
double dcv = (2.0 * M_PI) / (ncps - order + 1);
Eigen::Vector2d cv;
for (int j = 0; j < ncps; j++)
{
cv (0) = r * sin (dcv * j);
cv (1) = r * cos (dcv * j);
cv = cv + mean;
nurbs.SetCV (j, ON_3dPoint (cv (0), cv (1), 0.0));
}
return nurbs;
}
unsigned
NurbsTools::getClosestPoint (const ON_2dPoint &p, const ON_2dVector &dir, const vector_vec2d &data,
unsigned &idxcp)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
unsigned idx (0);
idxcp = 0;
double dist2 (0.0);
double dist2cp (DBL_MAX);
for (unsigned i = 0; i < data.size (); i++)
{
ON_2dVector v = (data[i] - p);
double d2 = ON_DotProduct(v, v);
if (d2 < dist2cp)
{
idxcp = i;
dist2cp = d2;
}
if (NEAR_ZERO(d2, SMALL_FASTF))
return i;
v.Unitize();
double d1 = ON_DotProduct(dir, v);
if (d1 / d2 > dist2)
{
idx = i;
dist2 = d1 / d2;
}
}
return idx;
}
unsigned
NurbsTools::getClosestPoint (const Eigen::Vector2d &p, const Eigen::Vector2d &dir, const vector_vec2d &data,
unsigned &idxcp)
{
if (data.empty ())
throw std::runtime_error ("[NurbsTools::getClosestPoint(2d)] Data empty.\n");
size_t idx = 0;
idxcp = 0;
double dist2 (0.0);
double dist2cp (DBL_MAX);
for (size_t i = 0; i < data.size (); i++)
{
Eigen::Vector2d v = (data[i] - p);
double d2 = v.squaredNorm ();
if (d2 < dist2cp)
{
idxcp = i;
dist2cp = d2;
}
if (d2 == 0.0)
return i;
v.normalize ();
double d1 = dir.dot (v);
if (d1 / d2 > dist2)
{
idx = i;
dist2 = d1 / d2;
}
}
return idx;
}
Eigen::Vector2d
NurbsTools::computeVariance (const Eigen::Vector2d &mean, const vector_vec2d &data)
{
Eigen::Vector2d var (0.0, 0.0);
size_t s = data.size ();
double ds = 1.0 / double (s);
for (size_t i = 0; i < s; i++)
{
Eigen::Vector2d v = data[i] - mean;
var += Eigen::Vector2d (v (0) * v (0) * ds, v (1) * v (1) * ds);
}
return var;
}