0032995: Modeling algorithms - Interface for checking canonical geometry

GeomConvert_CurveToAnaCurve, GeomConvert_SurfToAnaSurf - geometrical algorithms for converting geometrical curve and surfaces in canonical geometry with given tolerance. ShapeAnalysis_CanonicalRecognition - interface for checking canonical geometry.
2025-08-09 13:22:24 +03:00 · 2022-05-15 08:04:58 +03:00
parent 7a52478f16
commit b47b075ac5
42 changed files with 4652 additions and 8 deletions
--- a/src/ShapeAnalysis/FILES
+++ b/src/ShapeAnalysis/FILES
@@ -44,3 +44,11 @@ ShapeAnalysis_WireOrder.cxx
 ShapeAnalysis_WireOrder.hxx
 ShapeAnalysis_WireVertex.cxx
 ShapeAnalysis_WireVertex.hxx
+ShapeAnalysis_CanonicalRecognition.cxx
+ShapeAnalysis_CanonicalRecognition.hxx
+ShapeAnalysis_FuncSphereLSDist.cxx
+ShapeAnalysis_FuncSphereLSDist.hxx
+ShapeAnalysis_FuncCylinderLSDist.cxx
+ShapeAnalysis_FuncCylinderLSDist.hxx
+ShapeAnalysis_FuncConeLSDist.cxx
+ShapeAnalysis_FuncConeLSDist.hxx
--- a/src/ShapeAnalysis/ShapeAnalysis_CanonicalRecognition.cxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_CanonicalRecognition.cxx
--- a/src/ShapeAnalysis/ShapeAnalysis_CanonicalRecognition.hxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_CanonicalRecognition.hxx
@@ -0,0 +1,169 @@
+// Copyright (c) 2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#ifndef _ShapeAnalysis_CanonicalRecognition_HeaderFile
+#define _ShapeAnalysis_CanonicalRecognition_HeaderFile
+
+#include <Standard.hxx>
+#include <Standard_DefineAlloc.hxx>
+#include <Standard_Handle.hxx>
+
+#include <Standard_Boolean.hxx>
+#include <Standard_Integer.hxx>
+#include <TopAbs_ShapeEnum.hxx>
+#include <TopoDS_Shape.hxx>
+#include <TopoDS_Shell.hxx>
+#include <TopoDS_Face.hxx>
+#include <TopoDS_Wire.hxx>
+#include <TopoDS_Edge.hxx>
+#include <GeomAbs_SurfaceType.hxx>
+#include <GeomAbs_CurveType.hxx>
+#include <GeomConvert_ConvType.hxx>
+#include <TColStd_Array1OfReal.hxx>
+
+class gp_Pln;
+class gp_Cone;
+class gp_Cylinder;
+class gp_Sphere;
+class gp_Lin;
+class gp_Circ;
+class gp_Elips;
+class Geom_Curve;
+class Geom_Surface;
+
+//! This class provides operators for analysis surfaces and curves of shapes
+//! in order to find out more simple geometry entities, which could replace
+//! existing complex (for exampe, BSpline) geometry objects with given tolerance.
+class ShapeAnalysis_CanonicalRecognition  
+{
+public:
+
+  DEFINE_STANDARD_ALLOC
+
+
+  //! Empty constructor
+  Standard_EXPORT ShapeAnalysis_CanonicalRecognition();
+  
+  //! constructor with shape initialisation
+  Standard_EXPORT ShapeAnalysis_CanonicalRecognition(const TopoDS_Shape& theShape);
+
+  //! Sets shape
+  Standard_EXPORT void SetShape(const TopoDS_Shape& theShape);
+  
+  //! Returns input shape
+  const TopoDS_Shape& GetShape() const
+  {
+    return myShape;
+  }
+
+  //! Returns deviation between input geometry entity and analytical entity
+  Standard_Real GetGap() const
+  {
+    return myGap;
+  }
+
+  //! Returns status of operation.
+  //! Current meaning of possible values of status:
+  //! -1 - algorithm is not initalazed by shape
+  //!  0 - no errors
+  //!  1 - error during any operation (usually - because of wrong input data)
+  //! Any operation (calling any methods like IsPlane(...), ...) can be performed 
+  //! when current staue is equal 0. 
+  //! If after any operation status != 0, it is necessary to set it 0 by method ClearStatus()
+  //! before calling other operation.
+  Standard_Integer GetStatus() const
+  {
+    return myStatus;
+  }
+
+  //! Returns status to be equal 0.
+  void ClearStatus() 
+  {
+    myStatus = 0;
+  }
+
+  //! Returns true if the underlined surface can be represent by plane with tolerance theTol
+  //! and sets in thePln the result plane.  
+  Standard_EXPORT Standard_Boolean IsPlane(const Standard_Real theTol, gp_Pln& thePln);
+
+  //! Returns true if the underlined surface can be represent by cylindrical one with tolerance theTol
+  //! and sets in theCyl the result cylinrical surface.  
+  Standard_EXPORT Standard_Boolean IsCylinder(const Standard_Real theTol, gp_Cylinder& theCyl);
+
+  //! Returns true if the underlined surface can be represent by conical one with tolerance theTol
+  //! and sets in theCone the result conical surface.  
+  Standard_EXPORT Standard_Boolean IsCone(const Standard_Real theTol, gp_Cone& theCone);
+
+  //! Returns true if the underlined surface can be represent by spherical one with tolerance theTol
+  //! and sets in theSphere the result spherical surface.  
+  Standard_EXPORT Standard_Boolean IsSphere(const Standard_Real theTol, gp_Sphere& theSphere);
+
+  //! Returns true if the underlined curve can be represent by line with tolerance theTol
+  //! and sets in theLin the result line.  
+  Standard_EXPORT Standard_Boolean IsLine(const Standard_Real theTol, gp_Lin& theLin);
+
+  //! Returns true if the underlined curve can be represent by circle with tolerance theTol
+  //! and sets in theCirc the result circle.  
+  Standard_EXPORT Standard_Boolean IsCircle(const Standard_Real theTol, gp_Circ& theCirc);
+
+  //! Returns true if the underlined curve can be represent by ellipse with tolerance theTol
+  //! and sets in theCirc the result ellipse.  
+  Standard_EXPORT Standard_Boolean IsEllipse(const Standard_Real theTol, gp_Elips& theElips);
+
+
+private:
+  Standard_Boolean IsElementarySurf(const GeomAbs_SurfaceType theTarget, const Standard_Real theTol,
+    gp_Ax3& thePos, TColStd_Array1OfReal& theParams);
+
+  Standard_Boolean IsConic(const GeomAbs_CurveType theTarget, const Standard_Real theTol,
+    gp_Ax2& thePos, TColStd_Array1OfReal& theParams);
+
+  static Handle(Geom_Surface) GetSurface(const TopoDS_Face& theFace, const Standard_Real theTol,
+    const GeomConvert_ConvType theType, const GeomAbs_SurfaceType theTarget,
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  static Handle(Geom_Surface) GetSurface(const TopoDS_Shell& theShell, const Standard_Real theTol,
+    const GeomConvert_ConvType theType, const GeomAbs_SurfaceType theTarget,
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  static Handle(Geom_Surface) GetSurface(const TopoDS_Edge& theEdge, const Standard_Real theTol,
+    const GeomConvert_ConvType theType, const GeomAbs_SurfaceType theTarget, 
+    gp_Ax3& thePos, TColStd_Array1OfReal& theParams, 
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  static Handle(Geom_Surface) GetSurface(const TopoDS_Wire& theWire, const Standard_Real theTol,
+    const GeomConvert_ConvType theType, const GeomAbs_SurfaceType theTarget,
+    gp_Ax3& thePos, TColStd_Array1OfReal& theParams,
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  static Handle(Geom_Curve) GetCurve(const TopoDS_Edge& theEdge, const Standard_Real theTol,
+    const GeomConvert_ConvType theType, const GeomAbs_CurveType theTarget,
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  static Standard_Boolean GetSurfaceByLS(const TopoDS_Wire& theWire, const Standard_Real theTol,
+    const GeomAbs_SurfaceType theTarget,
+    gp_Ax3& thePos, TColStd_Array1OfReal& theParams,
+    Standard_Real& theGap, Standard_Integer& theStatus);
+
+  void Init(const TopoDS_Shape& theShape);
+
+private:
+
+  TopoDS_Shape myShape;
+  TopAbs_ShapeEnum mySType;
+  Standard_Real myGap;
+  Standard_Integer myStatus;
+
+};
+
+#endif // _ShapeAnalysis_CanonicalRecognition_HeaderFile
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncConeLSDist.cxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncConeLSDist.cxx
@@ -0,0 +1,68 @@
+// Copyright (c) 1995-1999 Matra Datavision
+// Copyright (c) 1999-2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+
+#include <ShapeAnalysis_FuncConeLSDist.hxx>
+#include <gp_Pnt.hxx>
+#include <gp_Vec.hxx>
+#include <gp_Ax3.hxx>
+#include <math_Vector.hxx>
+#include <ElSLib.hxx>
+
+//=======================================================================
+//function : ShapeAnalysis_FuncConeLSDist
+//purpose  : 
+//=======================================================================
+ShapeAnalysis_FuncConeLSDist::ShapeAnalysis_FuncConeLSDist(
+                                  const Handle(TColgp_HArray1OfXYZ)& thePoints,
+                                  const gp_Dir& theDir):
+  myPoints(thePoints), myDir(theDir)
+{
+}
+
+//=======================================================================
+//function : NbVariables
+//purpose  : 
+//=======================================================================
+Standard_Integer ShapeAnalysis_FuncConeLSDist::NbVariables () const
+{
+  return 5;
+}
+
+//=======================================================================
+//function : Value
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncConeLSDist::Value(const math_Vector& X, Standard_Real& F)
+{
+  gp_Pnt aLoc(X(1), X(2), X(3));
+  Standard_Real aSemiAngle = X(4), anR = X(5);
+  gp_Ax3 aPos(aLoc, myDir);
+
+  F = 0.;
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    Standard_Real u, v;
+    gp_Pnt aPi(myPoints->Value(i));
+    ElSLib::ConeParameters(aPos, anR, aSemiAngle, aPi, u, v);
+    gp_Pnt aPp;
+    ElSLib::ConeD0(u, v, aPos, anR, aSemiAngle, aPp);
+    F += aPi.SquareDistance(aPp);
+  }
+
+  return Standard_True;
+}
+
+
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncConeLSDist.hxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncConeLSDist.hxx
@@ -0,0 +1,66 @@
+// Copyright (c) 1991-1999 Matra Datavision
+// Copyright (c) 1999-2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#ifndef _ShapeAnalysis_FuncConeLSDist_HeaderFile
+#define _ShapeAnalysis_FuncConeLSDist_HeaderFile
+
+#include <Standard.hxx>
+#include <Standard_DefineAlloc.hxx>
+
+#include <math_MultipleVarFunction.hxx>
+#include <TColgp_HArray1OfXYZ.hxx>
+#include <math_Vector.hxx>
+#include <gp_Dir.hxx>
+
+//! Function for search of Cone canonic parameters: coordinates of center local coordinate system, 
+//! direction of axis, radius and semi-angle from set of points
+//! by least square method.
+//! 
+//!
+class ShapeAnalysis_FuncConeLSDist : public math_MultipleVarFunction
+{
+public:
+
+  DEFINE_STANDARD_ALLOC
+
+  //! Constructor.
+  Standard_EXPORT ShapeAnalysis_FuncConeLSDist() {};
+  
+  Standard_EXPORT ShapeAnalysis_FuncConeLSDist(const Handle(TColgp_HArray1OfXYZ)& thePoints,
+                                                   const gp_Dir& theDir);
+
+  void SetPoints(const Handle(TColgp_HArray1OfXYZ)& thePoints)
+  {
+    myPoints = thePoints;
+  }
+
+  void SetDir(const gp_Dir& theDir)
+  {
+    myDir = theDir;
+  }
+
+  //! Number of variables.
+  Standard_EXPORT Standard_Integer NbVariables() const Standard_OVERRIDE;
+
+  //! Value.
+  Standard_EXPORT Standard_Boolean Value(const math_Vector& X,Standard_Real& F) Standard_OVERRIDE;
+
+
+private:
+
+  Handle(TColgp_HArray1OfXYZ) myPoints;
+  gp_Dir myDir;
+  
+};
+#endif // _ShapeAnalysis_FuncConeLSDist_HeaderFile
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncCylinderLSDist.cxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncCylinderLSDist.cxx
@@ -0,0 +1,140 @@
+// Copyright (c) 1995-1999 Matra Datavision
+// Copyright (c) 1999-2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+
+#include <ShapeAnalysis_FuncCylinderLSDist.hxx>
+#include <gp_Pnt.hxx>
+#include <gp_Vec.hxx>
+#include <math_Vector.hxx>
+
+//=======================================================================
+//function : ShapeAnalysis_FuncCylinderLSDist
+//purpose  : 
+//=======================================================================
+ShapeAnalysis_FuncCylinderLSDist::ShapeAnalysis_FuncCylinderLSDist(
+                                  const Handle(TColgp_HArray1OfXYZ)& thePoints,
+                                  const gp_Dir& theDir):
+  myPoints(thePoints), myDir(theDir)
+{
+}
+
+//=======================================================================
+//function : NbVariables
+//purpose  : 
+//=======================================================================
+Standard_Integer ShapeAnalysis_FuncCylinderLSDist::NbVariables () const
+{
+  return 4;
+}
+
+//=======================================================================
+//function : Value
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncCylinderLSDist::Value(const math_Vector& X,Standard_Real& F)
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR2 = X(4)*X(4);
+
+  F = 0.;
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    gp_Vec aV(myPoints->Value(i) - aLoc);
+    Standard_Real aD2 = aV.CrossSquareMagnitude(myDir);
+    Standard_Real d = aD2 - anR2;
+    F += d * d;
+  }
+
+  return Standard_True;
+}
+
+//=======================================================================
+//function : Gradient
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncCylinderLSDist::Gradient(const math_Vector& X,math_Vector& G)
+
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR = X(4), anR2 = anR * anR;
+  Standard_Real x = myDir.X(), y = myDir.Y(), z = myDir.Z();
+  G.Init(0.);
+
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    gp_Vec aV(myPoints->Value(i) - aLoc);
+    Standard_Real aD2 = aV.CrossSquareMagnitude(myDir);
+    Standard_Real d = aD2 - anR2;
+    Standard_Real Dx0 =  2.*(aV.Z()*x - aV.X()*z)*z
+                        -2.*(aV.X()*y - aV.Y()*x)*y;
+    Standard_Real Dy0 = -2.*(aV.Y()*z - aV.Z()*y)*z
+                        +2.*(aV.X()*y - aV.Y()*x)*x;
+    Standard_Real Dz0 =  2.*(aV.Y()*z - aV.Z()*y)*y
+                        -2.*(aV.Z()*x - aV.X()*z)*x;
+
+    G(1) += d * Dx0;
+    G(2) += d * Dy0;
+    G(3) += d * Dz0;
+    //
+    G(4) += d;
+  }
+
+  G *= 2;
+  G(6) *= -2.*anR;
+
+  return Standard_True;
+}
+
+//=======================================================================
+//function : Values
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncCylinderLSDist::Values(const math_Vector& X,Standard_Real& F,math_Vector& G)
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR = X(4), anR2 = anR * anR;
+  Standard_Real x = myDir.X(), y = myDir.Y(), z = myDir.Z();
+
+  F = 0.;
+  G.Init(0.);
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    gp_Vec aV(myPoints->Value(i) - aLoc);
+    Standard_Real aD2 = aV.CrossSquareMagnitude(myDir);
+    Standard_Real d = aD2 - anR2;
+    Standard_Real Dx0 = 2.*(aV.Z()*x - aV.X()*z)*z
+      - 2.*(aV.X()*y - aV.Y()*x)*y;
+    Standard_Real Dy0 = -2.*(aV.Y()*z - aV.Z()*y)*z
+      + 2.*(aV.X()*y - aV.Y()*x)*x;
+    Standard_Real Dz0 = 2.*(aV.Y()*z - aV.Z()*y)*y
+      - 2.*(aV.Z()*x - aV.X()*z)*x;
+
+    G(1) += d * Dx0;
+    G(2) += d * Dy0;
+    G(3) += d * Dz0;
+    //
+    G(4) += d;
+    //
+    F += d * d;
+  }
+
+  G *= 2;
+  G(4) *= -2.*anR;
+
+  return true;
+}
+
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncCylinderLSDist.hxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncCylinderLSDist.hxx
@@ -0,0 +1,100 @@
+// Copyright (c) 1991-1999 Matra Datavision
+// Copyright (c) 1999-2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#ifndef _ShapeAnalysis_FuncCylinderLSDist_HeaderFile
+#define _ShapeAnalysis_FuncCylinderLSDist_HeaderFile
+
+#include <Standard.hxx>
+#include <Standard_DefineAlloc.hxx>
+
+#include <math_MultipleVarFunctionWithGradient.hxx>
+#include <TColgp_HArray1OfXYZ.hxx>
+#include <math_Vector.hxx>
+#include <gp_Dir.hxx>
+
+//! Function for search of cylinder canonic parameters: coordinates of center local coordinate system, 
+//! direction of axis and radius from set of points
+//! by least square method.
+//! 
+//! The class inherits math_MultipleVarFunctionWithGradient and thus is intended
+//! for use in math_BFGS algorithm.
+//!
+//! Parametrisation:
+//! Cylinder is defined by its axis and radius. Axis is defined by 3 cartesian coordinats it location x0, y0, z0 
+//! and direction, which is constant and set by user: 
+//! dir.x, dir.y, dir.z
+//! The criteria is:
+//! F(x0, y0, z0, theta, phi, R) = Sum[|(P(i) - Loc)^dir|^2 - R^2]^2 => min
+//! P(i) is i-th sample point, Loc, dir - axis location and direction, R - radius
+//!
+//! The square vector product |(P(i) - Loc)^dir|^2 is:
+//!
+//! [(y - y0)*dir.z - (z - z0)*dir.y]^2 +
+//! [(z - z0)*dir.x - (x - x0)*dir.z]^2 +
+//! [(x - x0)*dir.y - (y - y0)*dir.x]^2
+//!
+//! First derivative of square vector product are:
+//! Dx0 =  2*[(z - z0)*dir.x - (x - x0)*dir.z]*dir.z 
+//!       -2*[(x - x0)*dir.y - (y - y0)*dir.x]*dir.y
+//! Dy0 = -2*[(y - y0)*dir.z - (z - z0)*dir.y]*dir.z
+//!       +2*[(x - x0)*dir.y - (y - y0)*dir.x]*dir.x
+//! Dz0 =  2*[(y - y0)*dir.z - (z - z0)*dir.y]*dir.y
+//!       -2*[(z - z0)*dir.x - (x - x0)*dir.z]*dir.x
+//!
+//! dF/dx0 : G1(...) = 2*Sum{[...]*Dx0}
+//! dF/dy0 : G2(...) = 2*Sum{[...]*Dy0}
+//! dF/dz0 : G3(...) = 2*Sum{[...]*Dz0}
+//! dF/dR : G4(...) = -4*R*Sum[...]
+//! [...] = [|(P(i) - Loc)^dir|^2 - R^2]
+class ShapeAnalysis_FuncCylinderLSDist : public math_MultipleVarFunctionWithGradient
+{
+public:
+
+  DEFINE_STANDARD_ALLOC
+
+  //! Constructor.
+  Standard_EXPORT ShapeAnalysis_FuncCylinderLSDist() {};
+  
+  Standard_EXPORT ShapeAnalysis_FuncCylinderLSDist(const Handle(TColgp_HArray1OfXYZ)& thePoints,
+                                                   const gp_Dir& theDir);
+
+  void SetPoints(const Handle(TColgp_HArray1OfXYZ)& thePoints)
+  {
+    myPoints = thePoints;
+  }
+
+  void SetDir(const gp_Dir& theDir)
+  {
+    myDir = theDir;
+  }
+
+  //! Number of variables.
+  Standard_EXPORT Standard_Integer NbVariables() const Standard_OVERRIDE;
+
+  //! Value.
+  Standard_EXPORT Standard_Boolean Value(const math_Vector& X,Standard_Real& F) Standard_OVERRIDE;
+
+  //! Gradient.
+  Standard_EXPORT Standard_Boolean Gradient(const math_Vector& X,math_Vector& G) Standard_OVERRIDE;
+
+  //! Value and gradient.
+  Standard_EXPORT Standard_Boolean Values(const math_Vector& X,Standard_Real& F,math_Vector& G) Standard_OVERRIDE;
+
+private:
+
+  Handle(TColgp_HArray1OfXYZ) myPoints;
+  gp_Dir myDir;
+  
+};
+#endif // _ShapeAnalysis_FuncCylinderLSDist_HeaderFile
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncSphereLSDist.cxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncSphereLSDist.cxx
@@ -0,0 +1,115 @@
+// Created on: 2016-05-10
+// Created by: Alexander MALYSHEV
+// Copyright (c) 1995-1999 Matra Datavision
+// Copyright (c) 1999-2016 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+
+#include <ShapeAnalysis_FuncSphereLSDist.hxx>
+#include <gp_Pnt.hxx>
+#include <gp_Vec.hxx>
+#include <math_Vector.hxx>
+
+//=======================================================================
+//function : ShapeAnalysis_FuncSphereLSDist
+//purpose  : 
+//=======================================================================
+ShapeAnalysis_FuncSphereLSDist::ShapeAnalysis_FuncSphereLSDist(const Handle(TColgp_HArray1OfXYZ)& thePoints):
+  myPoints(thePoints)
+{
+}
+
+//=======================================================================
+//function : NbVariables
+//purpose  : 
+//=======================================================================
+Standard_Integer ShapeAnalysis_FuncSphereLSDist::NbVariables () const
+{
+  return 4;
+}
+
+//=======================================================================
+//function : Value
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncSphereLSDist::Value(const math_Vector& X,Standard_Real& F)
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR2 = X(4)*X(4);
+
+  F = 0.;
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    Standard_Real d = (myPoints->Value(i) - aLoc).SquareModulus() - anR2;
+    F += d * d;
+  }
+
+  return Standard_True;
+}
+
+//=======================================================================
+//function : Gradient
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncSphereLSDist::Gradient(const math_Vector& X,math_Vector& G)
+
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR = X(4), anR2 = anR * anR;
+
+  G.Init(0.);
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    gp_XYZ dLoc = myPoints->Value(i) - aLoc;
+    Standard_Real d = dLoc.SquareModulus() - anR2;
+    G(1) += d * dLoc.X();
+    G(2) += d * dLoc.Y();
+    G(3) += d * dLoc.Z();
+    G(4) += d;
+  }
+  G *= -4;
+  G(4) *= anR;
+
+  return Standard_True;
+}
+
+//=======================================================================
+//function : Values
+//purpose  : 
+//=======================================================================
+Standard_Boolean ShapeAnalysis_FuncSphereLSDist::Values(const math_Vector& X,Standard_Real& F,math_Vector& G)
+{
+  gp_XYZ aLoc(X(1), X(2), X(3));
+  Standard_Real anR = X(4), anR2 = anR * anR;
+
+  G.Init(0.);
+  F = 0.;
+  Standard_Integer i;
+  for (i = myPoints->Lower(); i <= myPoints->Upper(); ++i)
+  {
+    gp_XYZ dLoc = myPoints->Value(i) - aLoc;
+    Standard_Real d = dLoc.SquareModulus() - anR2;
+    G(1) += d * dLoc.X();
+    G(2) += d * dLoc.Y();
+    G(3) += d * dLoc.Z();
+    G(4) += d;
+    F += d * d;
+  }
+  G *= -4;
+  G(4) *= anR;
+
+  return true;
+}
+
--- a/src/ShapeAnalysis/ShapeAnalysis_FuncSphereLSDist.hxx
+++ b/src/ShapeAnalysis/ShapeAnalysis_FuncSphereLSDist.hxx
@@ -0,0 +1,77 @@
+
+// Copyright (c) 1991-1999 Matra Datavision
+// Copyright (c) 1999-2022 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#ifndef _ShapeAnalysis_FuncSphereLSDist_HeaderFile
+#define _ShapeAnalysis_FuncSphereLSDist_HeaderFile
+
+#include <Standard.hxx>
+#include <Standard_DefineAlloc.hxx>
+
+#include <math_MultipleVarFunctionWithGradient.hxx>
+#include <TColgp_HArray1OfXYZ.hxx>
+#include <math_Vector.hxx>
+
+//! Function for search of sphere canonic parameters: coordinates of center and radius from set of moints
+//! by least square method.
+//! //!
+//! The class inherits math_MultipleVarFunctionWithGradient and thus is intended
+//! for use in math_BFGS algorithm.
+//!
+//! The criteria is:
+//! F(x0, y0, z0, R) = Sum[(x(i) - x0)^2 + (y(i) - y0)^2 + (z(i) - z0)^2 - R^2]^2 => min,
+//! x(i), y(i), z(i) - coordinates of sample points, x0, y0, z0, R - coordinates of center and radius of sphere,
+//! which must be defined
+//!
+//! The first derivative are:
+//! dF/dx0 : G1(x0, y0, z0, R) = -4*Sum{[...]*(x(i) - x0)} 
+//! dF/dy0 : G2(x0, y0, z0, R) = -4*Sum{[...]*(y(i) - y0)}
+//! dF/dz0 : G3(x0, y0, z0, R) = -4*Sum{[...]*(z(i) - z0)}
+//! dF/dR : G4(x0, y0, z0, R) = -4*R*Sum[...]
+//! [...] = [(x(i) - x0)^2 + (y(i) - y0)^2 + (z(i) - z0)^2 - R^2]
+//!
+class ShapeAnalysis_FuncSphereLSDist : public math_MultipleVarFunctionWithGradient
+{
+public:
+
+  DEFINE_STANDARD_ALLOC
+
+  //! Constructor.
+  Standard_EXPORT ShapeAnalysis_FuncSphereLSDist() {};
+  
+  Standard_EXPORT ShapeAnalysis_FuncSphereLSDist(const Handle(TColgp_HArray1OfXYZ)& thePoints);
+
+  void SetPoints(const Handle(TColgp_HArray1OfXYZ)& thePoints)
+  {
+    myPoints = thePoints;
+  }
+
+  //! Number of variables.
+  Standard_EXPORT Standard_Integer NbVariables() const Standard_OVERRIDE;
+
+  //! Value.
+  Standard_EXPORT Standard_Boolean Value(const math_Vector& X,Standard_Real& F) Standard_OVERRIDE;
+
+  //! Gradient.
+  Standard_EXPORT Standard_Boolean Gradient(const math_Vector& X,math_Vector& G) Standard_OVERRIDE;
+
+  //! Value and gradient.
+  Standard_EXPORT Standard_Boolean Values(const math_Vector& X,Standard_Real& F,math_Vector& G) Standard_OVERRIDE;
+
+private:
+
+  Handle(TColgp_HArray1OfXYZ) myPoints;
+  
+};
+#endif // _ShapeAnalysis_FuncSphereLSDist_HeaderFile