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 // Copyright (c) 2015 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 _BRepGProp_Gauss_HeaderFile
 #define _BRepGProp_Gauss_HeaderFile
 
 #include <NCollection_Handle.hxx>
 #include <NCollection_Array1.hxx>
 
 template <typename T>
 class math_VectorBase;
 using math_Vector = math_VectorBase<double>;
 
 //! Class performs computing of the global inertia properties
 //! of geometric object in 3D space by adaptive and non-adaptive
 //! 2D Gauss integration algorithms.
 class BRepGProp_Gauss
 {
   //! Auxiliary structure for storing of inertial moments.
   struct Inertia
   {
     //! Mass of the current system (without density).
     //! May correspond to: length, area, volume.
     Standard_Real Mass;
 
     //! Static moments of inertia.
     Standard_Real Ix;
     Standard_Real Iy;
     Standard_Real Iz;
 
     //! Quadratic moments of inertia.
     Standard_Real Ixx;
     Standard_Real Iyy;
     Standard_Real Izz;
     Standard_Real Ixy;
     Standard_Real Ixz;
     Standard_Real Iyz;
 
     //! Default constructor.
     Inertia();
 
     //! Zeroes all values.
     void Reset();
   };
 
   typedef NCollection_Handle<NCollection_Array1<Inertia>> InertiaArray;
   typedef Standard_Real (*BRepGProp_GaussFunc)(const Standard_Real, const Standard_Real);
 
 public: //! @name public API
   //! Describes types of geometric objects.
   //! - Vinert is 3D closed region of space delimited with:
   //! -- Surface;
   //! -- Point and Surface;
   //! -- Plane and Surface.
   //! - Sinert is face in 3D space.
   typedef enum
   {
     Vinert = 0,
     Sinert
   } BRepGProp_GaussType;
 
   //! Constructor
   Standard_EXPORT explicit BRepGProp_Gauss(const BRepGProp_GaussType theType);
 
   //! Computes the global properties of a solid region of 3D space which can be
   //! delimited by the surface and point or surface and plane. Surface can be closed.
   //! The method is quick and its precision is enough for many cases of analytical surfaces.
   //! Non-adaptive 2D Gauss integration with predefined numbers of Gauss points
   //! is used. Numbers of points depend on types of surfaces and curves.
   //! Error of the computation is not calculated.
   //! @param theSurface - bounding surface of the region;
   //! @param theLocation - location of the point or the plane;
   //! @param theCoeff - plane coefficients;
   //! @param theIsByPoint - flag of restricition (point/plane);
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   Standard_EXPORT void Compute(const BRepGProp_Face&  theSurface,
                                const gp_Pnt&          theLocation,
                                const Standard_Real    theCoeff[],
                                const Standard_Boolean theIsByPoint,
                                Standard_Real&         theOutMass,
                                gp_Pnt&                theOutGravityCenter,
                                gp_Mat&                theOutInertia);
 
   //! Computes the global properties of a surface. Surface can be closed.
   //! The method is quick and its precision is enough for many cases of analytical surfaces.
   //! Non-adaptive 2D Gauss integration with predefined numbers of Gauss points
   //! is used. Numbers of points depend on types of surfaces and curves.
   //! Error of the computation is not calculated.
   //! @param theSurface - bounding surface of the region;
   //! @param theLocation - surface location;
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   Standard_EXPORT void Compute(const BRepGProp_Face& theSurface,
                                const gp_Pnt&         theLocation,
                                Standard_Real&        theOutMass,
                                gp_Pnt&               theOutGravityCenter,
                                gp_Mat&               theOutInertia);
 
   //! Computes the global properties of a region of 3D space which can be
   //! delimited by the surface and point or surface and plane. Surface can be closed.
   //! The method is quick and its precision is enough for many cases of analytical surfaces.
   //! Non-adaptive 2D Gauss integration with predefined numbers of Gauss points is used.
   //! Numbers of points depend on types of surfaces and curves.
   //! Error of the computation is not calculated.
   //! @param theSurface - bounding surface of the region;
   //! @param theDomain - surface boundings;
   //! @param theLocation - location of the point or the plane;
   //! @param theCoeff - plane coefficients;
   //! @param theIsByPoint - flag of restricition (point/plane);
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   Standard_EXPORT void Compute(BRepGProp_Face&        theSurface,
                                BRepGProp_Domain&      theDomain,
                                const gp_Pnt&          theLocation,
                                const Standard_Real    theCoeff[],
                                const Standard_Boolean theIsByPoint,
                                Standard_Real&         theOutMass,
                                gp_Pnt&                theOutGravityCenter,
                                gp_Mat&                theOutInertia);
 
   //! Computes the global properties of a surface. Surface can be closed.
   //! The method is quick and its precision is enough for many cases of analytical surfaces.
   //! Non-adaptive 2D Gauss integration with predefined numbers of Gauss points
   //! is used. Numbers of points depend on types of surfaces and curves.
   //! Error of the computation is not calculated.
   //! @param theSurface - bounding surface of the region;
   //! @param theDomain - surface boundings;
   //! @param theLocation - surface location;
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   Standard_EXPORT void Compute(BRepGProp_Face&   theSurface,
                                BRepGProp_Domain& theDomain,
                                const gp_Pnt&     theLocation,
                                Standard_Real&    theOutMass,
                                gp_Pnt&           theOutGravityCenter,
                                gp_Mat&           theOutInertia);
 
   //! Computes the global properties of the region of 3D space which can be
   //! delimited by the surface and point or surface and plane.
   //! Adaptive 2D Gauss integration is used.
   //! If Epsilon more than 0.001 then algorithm performs non-adaptive integration.
   //! @param theSurface - bounding surface of the region;
   //! @param theDomain - surface boundings;
   //! @param theLocation - location of the point or the plane;
   //! @param theEps - maximal relative error of computed mass (volume) for face;
   //! @param theCoeff - plane coefficients;
   //! @param theIsByPoint - flag of restricition (point/plane);
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   //! @return value of error which is calculated as
   //! Abs((M(i+1)-M(i))/M(i+1)), M(i+1) and M(i) are values
   //! for two successive steps of adaptive integration.
   Standard_EXPORT Standard_Real Compute(BRepGProp_Face&        theSurface,
                                         BRepGProp_Domain&      theDomain,
                                         const gp_Pnt&          theLocation,
                                         const Standard_Real    theEps,
                                         const Standard_Real    theCoeff[],
                                         const Standard_Boolean theByPoint,
                                         Standard_Real&         theOutMass,
                                         gp_Pnt&                theOutGravityCenter,
                                         gp_Mat&                theOutInertia);
 
   //! Computes the global properties of the face. Adaptive 2D Gauss integration is used.
   //! If Epsilon more than 0.001 then algorithm performs non-adaptive integration.
   //! @param theSurface - bounding surface of the region;
   //! @param theDomain - surface boundings;
   //! @param theLocation - surface location;
   //! @param theEps - maximal relative error of computed mass (square) for face;
   //! @param[out] theOutMass - mass (volume) of region;
   //! @param[out] theOutGravityCenter - garvity center of region;
   //! @param[out] theOutInertia - matrix of inertia;
   //! @return value of error which is calculated as
   //! Abs((M(i+1)-M(i))/M(i+1)), M(i+1) and M(i) are values
   //! for two successive steps of adaptive integration.
   Standard_EXPORT Standard_Real Compute(BRepGProp_Face&     theSurface,
                                         BRepGProp_Domain&   theDomain,
                                         const gp_Pnt&       theLocation,
                                         const Standard_Real theEps,
                                         Standard_Real&      theOutMass,
                                         gp_Pnt&             theOutGravityCenter,
                                         gp_Mat&             theOutInertia);
 
 private: //! @name private methods
   BRepGProp_Gauss(BRepGProp_Gauss const&);
   BRepGProp_Gauss& operator=(BRepGProp_Gauss const&);
 
   void computeVInertiaOfElementaryPart(const gp_Pnt&             thePoint,
                                        const gp_Vec&             theNormal,
                                        const gp_Pnt&             theLocation,
                                        const Standard_Real       theWeight,
                                        const Standard_Real       theCoeff[],
                                        const Standard_Boolean    theIsByPoint,
                                        BRepGProp_Gauss::Inertia& theOutInertia);
 
   void computeSInertiaOfElementaryPart(const gp_Pnt&             thePoint,
                                        const gp_Vec&             theNormal,
                                        const gp_Pnt&             theLocation,
                                        const Standard_Real       theWeight,
                                        BRepGProp_Gauss::Inertia& theOutInertia);
 
   void checkBounds(const Standard_Real theU1,
                    const Standard_Real theU2,
                    const Standard_Real theV1,
                    const Standard_Real theV2);
 
   void addAndRestoreInertia(const BRepGProp_Gauss::Inertia& theInInertia,
                             BRepGProp_Gauss::Inertia&       theOutInertia);
 
   void multAndRestoreInertia(const Standard_Real theValue, BRepGProp_Gauss::Inertia& theInertia);
 
   void convert(const BRepGProp_Gauss::Inertia& theInertia,
                gp_Pnt&                         theOutGravityCenter,
                gp_Mat&                         theOutMatrixOfInertia,
                Standard_Real&                  theOutMass);
 
   void convert(const BRepGProp_Gauss::Inertia& theInertia,
                const Standard_Real             theCoeff[],
                const Standard_Boolean          theIsByPoint,
                gp_Pnt&                         theOutGravityCenter,
                gp_Mat&                         theOutMatrixOfInertia,
                Standard_Real&                  theOutMass);
 
   static Standard_Integer MaxSubs(const Standard_Integer theN,
                                   const Standard_Integer theCoeff = 32);
 
   static void Init(NCollection_Handle<math_Vector>& theOutVec,
                    const Standard_Real              theValue,
                    const Standard_Integer           theFirst = 0,
                    const Standard_Integer           theLast  = 0);
 
   static void InitMass(const Standard_Real    theValue,
                        const Standard_Integer theFirst,
                        const Standard_Integer theLast,
                        InertiaArray&          theArray);
 
   static Standard_Integer FillIntervalBounds(const Standard_Real              theA,
                                              const Standard_Real              theB,
                                              const TColStd_Array1OfReal&      theKnots,
                                              const Standard_Integer           theNumSubs,
                                              InertiaArray&                    theInerts,
                                              NCollection_Handle<math_Vector>& theParam1,
                                              NCollection_Handle<math_Vector>& theParam2,
                                              NCollection_Handle<math_Vector>& theError,
                                              NCollection_Handle<math_Vector>& theCommonError);
 
 private:                      //! @name private fields
   BRepGProp_GaussType myType; //!< Type of geometric object
   BRepGProp_GaussFunc add;    //!< Pointer on the add function
   BRepGProp_GaussFunc mult;   //!< Pointer on the mult function
 };
 
 #endif

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