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/***************************************************************************
* Copyright (c) 2005 Imetric 3D GmbH *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#ifndef MESH_APPROXIMATION_H
#define MESH_APPROXIMATION_H
#include <Mod/Mesh/App/WildMagic4/Wm4QuadricSurface.h>
#ifndef MESH_GLOBAL_H
# include <Mod/Mesh/MeshGlobal.h>
#endif
#include <algorithm>
#include <limits>
#include <list>
#include <set>
#include <vector>
#include <Base/BoundBox.h>
#include <Base/Matrix.h>
#include <Base/Vector3D.h>
namespace Wm4
{
/**
* An implicit surface is defined by F(x,y,z) = 0.
* This polynomial surface is actually defined as z = f(x,y) = ax^2 + by^2 + cx + dy + exy + g.
* To use Wm3 routines for implicit surfaces we can write the surface also as F(x,y,z) = f(x,y) - z
* = 0.
* @author Werner Mayer
*/
template<class Real>
class PolynomialSurface: public ImplicitSurface<Real>
{
public:
explicit PolynomialSurface(const Real afCoeff[6])
{
for (int i = 0; i < 6; i++) {
m_afCoeff[i] = afCoeff[i];
}
}
// the function
Real F(const Vector3<Real>& rkP) const override
{
return (
m_afCoeff[0] * rkP.X() * rkP.X() + m_afCoeff[1] * rkP.Y() * rkP.Y()
+ m_afCoeff[2] * rkP.X() + m_afCoeff[3] * rkP.Y() + m_afCoeff[4] * rkP.X() * rkP.Y()
+ m_afCoeff[5] - rkP.Z()
);
}
// first-order partial derivatives
Real FX(const Vector3<Real>& rkP) const override
{
return (Real)(2.0 * m_afCoeff[0] * rkP.X() + m_afCoeff[2] + m_afCoeff[4] * rkP.Y());
}
Real FY(const Vector3<Real>& rkP) const override
{
return (Real)(2.0 * m_afCoeff[1] * rkP.Y() + m_afCoeff[3] + m_afCoeff[4] * rkP.X());
}
Real FZ(const Vector3<Real>& /*rkP*/) const override
{
return (Real)-1.0;
}
// second-order partial derivatives
Real FXX(const Vector3<Real>& /*rkP*/) const override
{
return (Real)(2.0 * m_afCoeff[0]);
}
Real FXY(const Vector3<Real>& /*rkP*/) const override
{
return (Real)(m_afCoeff[4]);
}
Real FXZ(const Vector3<Real>& /*rkP*/) const override
{
return (Real)0.0;
}
Real FYY(const Vector3<Real>& /*rkP*/) const override
{
return (Real)(2.0 * m_afCoeff[1]);
}
Real FYZ(const Vector3<Real>& /*rkP*/) const override
{
return (Real)0.0;
}
Real FZZ(const Vector3<Real>& /*rkP*/) const override
{
return (Real)0.0;
}
private:
Real m_afCoeff[6];
};
} // namespace Wm4
namespace MeshCore
{
class MeshPointArray;
/**
* Abstract base class for approximation of a geometry to a given set of points.
*/
class MeshExport Approximation
{
public:
/**
* Construction
*/
Approximation();
/**
* Destroys the object and frees any allocated resources.
*/
virtual ~Approximation();
/**
* Add point for the fit algorithm.
*/
void AddPoint(const Base::Vector3f& point);
/**
* Add points for the fit algorithm.
*/
void AddPoints(const std::vector<Base::Vector3f>& points);
/**
* Add points for the fit algorithm.
*/
void AddPoints(const std::set<Base::Vector3f>& points);
/**
* Add points for the fit algorithm.
*/
void AddPoints(const std::list<Base::Vector3f>& points);
/**
* Add points for the fit algorithm.
*/
void AddPoints(const MeshPointArray& points);
/**
* Get all added points.
*/
const std::list<Base::Vector3f>& GetPoints() const
{
return _vPoints;
}
/**
* Returns the center of gravity of the current added points.
* @return Base::Vector3f
*/
Base::Vector3f GetGravity() const;
/**
* Determines the number of the current added points.
* @return Number of points
*/
std::size_t CountPoints() const;
/**
* Deletes the inserted points and frees any allocated resources.
*/
void Clear();
/**
* Returns the result of the last fit.
* @return float Quality of the last fit.
*/
float GetLastResult() const;
/**
* Pure virtual function to fit the geometry to the given points. This function
* must be implemented by every subclass.
*/
virtual float Fit() = 0;
/**
* Returns true if Fit() has been called for the current set of points, false otherwise.
*/
bool Done() const;
protected:
/**
* Creates a vector of Wm4::Vector3 elements.
*/
void GetMgcVectorArray(std::vector<Wm4::Vector3<double>>& rcPts) const;
Approximation(const Approximation&) = default;
Approximation(Approximation&&) = default;
Approximation& operator=(const Approximation&) = default;
Approximation& operator=(Approximation&&) = default;
protected:
// NOLINTBEGIN
std::list<Base::Vector3f> _vPoints; /**< Holds the points for the fit algorithm. */
bool _bIsFitted {false}; /**< Flag, whether the fit has been called. */
float _fLastResult {std::numeric_limits<float>::max()}; /**< Stores the last result of the fit */
// NOLINTEND
};
// -------------------------------------------------------------------------------
/**
* Approximation of a plane into a given set of points.
*/
class MeshExport PlaneFit: public Approximation
{
public:
PlaneFit();
Base::Vector3f GetBase() const;
Base::Vector3f GetDirU() const;
Base::Vector3f GetDirV() const;
/**
* Returns the normal of the fitted plane. If Fit() has not been called the null vector is
* returned.
*/
Base::Vector3f GetNormal() const;
/**
* Fit a plane into the given points. We must have at least three non-collinear points
* to succeed. If the fit fails FLOAT_MAX is returned.
*/
float Fit() override;
/**
* Returns the distance from the point \a rcPoint to the fitted plane. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetDistanceToPlane(const Base::Vector3f& rcPoint) const;
/**
* Returns the standard deviation from the points to the fitted plane. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetStdDeviation() const;
/**
* Returns the standard deviation from the points to the fitted plane with respect to the
* orientation of the plane's normal. If Fit() has not been called FLOAT_MAX is returned.
*/
float GetSignedStdDeviation() const;
/**
* Projects the points onto the fitted plane.
*/
void ProjectToPlane();
/**
* Get the dimension of the fitted plane.
*/
void Dimension(float& length, float& width) const;
/**
* Returns an array of the transformed points relative to the coordinate system
* of the plane. If this method is called before the plane is computed an empty
* array is returned.
*/
std::vector<Base::Vector3f> GetLocalPoints() const;
/**
* Returns the local bounding box of the transformed points relative to the
* coordinate system of the plane. If this method is called before the plane is
* computed an invalid bounding box is returned.
*/
Base::BoundBox3f GetBoundings() const;
protected:
// NOLINTBEGIN
Base::Vector3f _vBase; /**< Base vector of the plane. */
Base::Vector3f _vDirU;
Base::Vector3f _vDirV;
Base::Vector3f _vDirW; /**< Normal of the plane. */
// NOLINTEND
};
// -------------------------------------------------------------------------------
/**
* Approximation of a quadratic surface into a given set of points. The implicit form of the surface
* is defined by F(x,y,z) = a * x^2 + b * y^2 + c * z^2 +
* 2d * x * y + 2e * x * z + 2f * y * z +
* g * x + h * y + * i * z + k
* = 0
* Depending on the parameters (a,..,k) this surface defines a sphere, ellipsoid, cylinder, cone
* and so on.
*/
class MeshExport QuadraticFit: public Approximation
{
public:
QuadraticFit() = default;
/**
* Get the quadric coefficients
* @param ulIndex Number of coefficient (0..9)
* @return double value of coefficient
*/
double GetCoeff(std::size_t ulIndex) const;
/**
* Get the quadric coefficients as reference to the
* internal array
* @return const double& Reference to the double array
*/
const double& GetCoeffArray() const;
/**
* Invocation of fitting algorithm
* @return float Quality of fit.
*/
float Fit() override;
void CalcZValues(double x, double y, double& dZ1, double& dZ2) const;
/**
* Calculate the curvatures of the quadric at a given point.
* @param x X-coordinate
* @param y Y-coordinate
* @param z Z-coordinate
* @param rfCurv0 1. principal curvature
* @param rfCurv1 2. principal curvature
* @param rkDir0 Direction of 1. principal curvature
* @param rkDir1 Direction of 2. principal curvature
* @param dDistance
* @return bool Success = true, otherwise false
*/
bool GetCurvatureInfo(
double x,
double y,
double z,
double& rfCurv0,
double& rfCurv1,
Base::Vector3f& rkDir0,
Base::Vector3f& rkDir1,
double& dDistance
);
bool GetCurvatureInfo(double x, double y, double z, double& rfCurv0, double& rfcurv1);
/**
* Compute form matrix A and calculate Eigenvalues.
* @param dLambda1 Eigenvalue 1
* @param dLambda2 Eigenvalue 2
* @param dLambda3 Eigenvalue 3
* @param clEV1 Eigenvector 1
* @param clEV2 Eigenvector 2
* @param clEV3 Eigenvector 3
*/
void CalcEigenValues(
double& dLambda1,
double& dLambda2,
double& dLambda3,
Base::Vector3f& clEV1,
Base::Vector3f& clEV2,
Base::Vector3f& clEV3
) const;
private:
double _fCoeff[10] {}; /**< Coefficients of the fit */
};
// -------------------------------------------------------------------------------
/**
* This is an 2.5D approach which first determines the bestfit plane of the point set (P_i =
* (x,y,z), i=1,...,n) to get a parametrisation of the points afterwards. The coordinates of the
* points with respect to the local coordinate system of the plane are determined and then a
* quadratic polynomial function of the form: w = f(u,v) = a*u^2 + b*v^2 + c*u*v + d*u + e*v + f is
* determined. This approach was developed as an alternative for the 3D approach with quadrics
* because the latter suffers from strange artifacts in planar areas.
*/
class MeshExport SurfaceFit: public PlaneFit
{
public:
SurfaceFit();
bool GetCurvatureInfo(
double x,
double y,
double z,
double& rfCurv0,
double& rfCurv1,
Base::Vector3f& rkDir0,
Base::Vector3f& rkDir1,
double& dDistance
);
bool GetCurvatureInfo(double x, double y, double z, double& rfCurv0, double& rfcurv1);
float Fit() override;
double Value(double x, double y) const;
void GetCoefficients(double& a, double& b, double& c, double& d, double& e, double& f) const;
/**
* @brief Transform
* Transforms points from the local coordinate system to the world coordinate system
*/
void Transform(std::vector<Base::Vector3f>&) const;
void Transform(std::vector<Base::Vector3d>&) const;
/**
* @brief toBezier
* @param umin Parameter range
* @param umax Parameter range
* @param vmin Parameter range
* @param vmax Parameter range
* @return control points of the Bezier surface
*/
std::vector<Base::Vector3d> toBezier(
double umin = 0.0,
double umax = 1.0,
double vmin = 0.0,
double vmax = 1.0
) const;
private:
double PolynomFit();
double _fCoeff[10]; /**< Ziel der Koeffizienten aus dem Fit */
};
// -------------------------------------------------------------------------------
/**
* Approximation of a cylinder into a given set of points.
*/
class MeshExport CylinderFit: public Approximation
{
public:
CylinderFit();
float GetRadius() const;
Base::Vector3f GetBase() const;
void SetInitialValues(const Base::Vector3f&, const Base::Vector3f&);
/**
* Returns the axis of the fitted cylinder. If Fit() has not been called the null vector is
* returned.
*/
Base::Vector3f GetAxis() const;
/**
* Returns an initial axis based on point normals.
*/
Base::Vector3f GetInitialAxisFromNormals(const std::vector<Base::Vector3f>& n) const;
/**
* Fit a cylinder into the given points. If the fit fails FLOAT_MAX is returned.
*/
float Fit() override;
/**
* Returns the distance from the point \a rcPoint to the fitted cylinder. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetDistanceToCylinder(const Base::Vector3f& rcPoint) const;
/**
* Returns the standard deviation from the points to the fitted cylinder. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetStdDeviation() const;
/**
* Projects the points onto the fitted cylinder.
*/
void ProjectToCylinder();
/**
* Get the bottom and top points of the cylinder. The distance of these
* points gives the height of the cylinder.
*/
void GetBounding(Base::Vector3f& bottom, Base::Vector3f& top) const;
private:
Base::Vector3f _vBase; /**< Base vector of the cylinder. */
Base::Vector3f _vAxis; /**< Axis of the cylinder. */
float _fRadius {0}; /**< Radius of the cylinder. */
bool _initialGuess {false};
};
// -------------------------------------------------------------------------------
/**
* Approximation of a sphere into a given set of points.
*/
class MeshExport SphereFit: public Approximation
{
public:
SphereFit();
float GetRadius() const;
Base::Vector3f GetCenter() const;
/**
* Fit a sphere into the given points. If the fit fails FLOAT_MAX is returned.
*/
float Fit() override;
/**
* Returns the distance from the point \a rcPoint to the fitted sphere. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetDistanceToSphere(const Base::Vector3f& rcPoint) const;
/**
* Returns the standard deviation from the points to the fitted sphere. If Fit() has not been
* called FLOAT_MAX is returned.
*/
float GetStdDeviation() const;
/**
* Projects the points onto the fitted sphere.
*/
void ProjectToSphere();
private:
Base::Vector3f _vCenter; /**< Center of the sphere. */
float _fRadius {0}; /**< Radius of the cylinder. */
};
// -------------------------------------------------------------------------------
/**
* Helper class for the quadric fit. Includes the
* partial derivates of the quadric and serves for
* calculation of the quadric properties.
*/
class FunctionContainer
{
public:
/**
* WildMagic library uses function with this interface
*/
using Function = double (*)(double, double, double);
/**
* The constructor expects an array of quadric coefficients.
* @param pKoef Pointer to the quadric coefficients
* (double [10])
*/
// NOLINTBEGIN
explicit FunctionContainer(const double* pKoef)
{
Assign(pKoef);
pImplSurf = new Wm4::QuadricSurface<double>(dKoeff);
}
// NOLINTEND
FunctionContainer(const FunctionContainer&) = delete;
FunctionContainer(FunctionContainer&&) = delete;
FunctionContainer& operator=(const FunctionContainer&) = delete;
FunctionContainer& operator=(FunctionContainer&&) = delete;
/**
* Apply quadric coefficients
* @param pKoef Pointer to the quadric coefficients
* (double [10])
*/
void Assign(const double* pKoef)
{
for (long ct = 0; ct < 10; ct++) {
dKoeff[ct] = pKoef[ct];
}
}
/**
* Destructor. Deletes the ImpicitSurface instance
* of the WildMagic library
*/
~FunctionContainer()
{
delete pImplSurf;
}
/**
* Access to the quadric coefficients
* @param idx Index to coefficient
* @return double& coefficient
*/
double& operator[](int idx)
{
return dKoeff[idx];
}
/**
* Redirector to a method of the WildMagic library. Determines
* the principal curvatures and their directions at the given point.
* @param x X-coordinate
* @param y Y-coordinate
* @param z Z-coordinate
* @param rfCurv0 1. principal curvature
* @param rfCurv1 2. principal curvature
* @param rkDir0 direction of 1. principal curvature
* @param rkDir1 direction of 2. principal curvature
* @param dDistance Gives distances from the point to the quadric.
* @return bool Success = true, otherwise false
*/
bool CurvatureInfo(
double x,
double y,
double z,
double& rfCurv0,
double& rfCurv1,
Wm4::Vector3<double>& rkDir0,
Wm4::Vector3<double>& rkDir1,
double& dDistance
)
{
(void)dDistance;
return pImplSurf->ComputePrincipalCurvatureInfo(
Wm4::Vector3<double>(x, y, z),
rfCurv0,
rfCurv1,
rkDir0,
rkDir1
);
}
Base::Vector3f GetGradient(double x, double y, double z) const
{
Wm4::Vector3<double> grad = pImplSurf->GetGradient(Wm4::Vector3<double>(x, y, z));
return Base::Vector3f(
static_cast<float>(grad.X()),
static_cast<float>(grad.Y()),
static_cast<float>(grad.Z())
);
}
Base::Matrix4D GetHessian(double x, double y, double z) const
{
Wm4::Matrix3<double> hess = pImplSurf->GetHessian(Wm4::Vector3<double>(x, y, z));
Base::Matrix4D cMat;
cMat.setToUnity();
cMat[0][0] = hess[0][0];
cMat[0][1] = hess[0][1];
cMat[0][2] = hess[0][2];
cMat[1][0] = hess[1][0];
cMat[1][1] = hess[1][1];
cMat[1][2] = hess[1][2];
cMat[2][0] = hess[2][0];
cMat[2][1] = hess[2][1];
cMat[2][2] = hess[2][2];
return cMat;
}
bool CurvatureInfo(double x, double y, double z, double& rfCurv0, double& rfCurv1)
{
double dQuot = Fz(x, y, z);
double zx = -(Fx(x, y, z) / dQuot);
double zy = -(Fy(x, y, z) / dQuot);
double zxx = -(2.0 * (dKoeff[5] + dKoeff[6] * zx * zx + dKoeff[8] * zx)) / dQuot;
double zyy = -(2.0 * (dKoeff[5] + dKoeff[6] * zy * zy + dKoeff[9] * zy)) / dQuot;
double zxy = -(dKoeff[6] * zx * zy + dKoeff[7] + dKoeff[8] * zy + dKoeff[9] * zx) / dQuot;
double dNen = 1 + zx * zx + zy * zy;
double dNenSqrt = sqrt(dNen);
double K = (zxx * zyy - zxy * zxy) / (dNen * dNen);
double H = 0.5
* ((1.0 + zx * zx - 2 * zx * zy * zxy + (1.0 + zy * zy) * zxx)
/ (dNenSqrt * dNenSqrt * dNenSqrt));
double dDiscr = sqrt(fabs(H * H - K));
rfCurv0 = H - dDiscr;
rfCurv1 = H + dDiscr;
return true;
}
//+++++++++ Quadric +++++++++++++++++++++++++++++++++++++++
double F(double x, double y, double z)
{
return (
dKoeff[0] + dKoeff[1] * x + dKoeff[2] * y + dKoeff[3] * z + dKoeff[4] * x * x
+ dKoeff[5] * y * y + dKoeff[6] * z * z + dKoeff[7] * x * y + dKoeff[8] * x * z
+ dKoeff[9] * y * z
);
}
//+++++++++ 1. derivations ++++++++++++++++++++++++++++++++
double Fx(double x, double y, double z)
{
return (dKoeff[1] + 2.0 * dKoeff[4] * x + dKoeff[7] * y + dKoeff[8] * z);
}
double Fy(double x, double y, double z)
{
return (dKoeff[2] + 2.0 * dKoeff[5] * y + dKoeff[7] * x + dKoeff[9] * z);
}
double Fz(double x, double y, double z)
{
return (dKoeff[3] + 2.0 * dKoeff[6] * z + dKoeff[8] * x + dKoeff[9] * y);
}
//+++++++++ 2. derivations ++++++++++++++++++++++++++++++++
double Fxx(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (2.0 * dKoeff[4]);
}
double Fxy(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (dKoeff[7]);
}
double Fxz(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (dKoeff[8]);
}
double Fyy(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (2.0 * dKoeff[5]);
}
double Fyz(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (dKoeff[9]);
}
double Fzz(double x, double y, double z)
{
(void)x;
(void)y;
(void)z;
return (2.0 * dKoeff[6]);
}
private:
double dKoeff[10]; /**< Coefficients of quadric */
Wm4::ImplicitSurface<double>* pImplSurf; /**< Access to the WildMagic library */
private:
/**
* Private construction.
*/
FunctionContainer() = default;
};
class MeshExport PolynomialFit: public Approximation
{
public:
PolynomialFit();
float Fit() override;
float Value(float x, float y) const;
private:
float _fCoeff[9];
};
} // namespace MeshCore
#endif // MESH_APPROXIMATION_H
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