// Copyright (c) 1991-1999 Matra Datavision // Copyright (c) 1999-2014 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 _gp_Elips_HeaderFile #define _gp_Elips_HeaderFile #include #include #include #include #include //! Describes an ellipse in 3D space. //! An ellipse is defined by its major and minor radii and //! positioned in space with a coordinate system (a gp_Ax2 object) as follows: //! - the origin of the coordinate system is the center of the ellipse, //! - its "X Direction" defines the major axis of the ellipse, and //! - its "Y Direction" defines the minor axis of the ellipse. //! Together, the origin, "X Direction" and "Y Direction" of //! this coordinate system define the plane of the ellipse. //! This coordinate system is the "local coordinate system" //! of the ellipse. In this coordinate system, the equation of //! the ellipse is: //! @code //! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0 //! @endcode //! The "main Direction" of the local coordinate system gives //! the normal vector to the plane of the ellipse. This vector //! gives an implicit orientation to the ellipse (definition of the //! trigonometric sense). We refer to the "main Axis" of the //! local coordinate system as the "Axis" of the ellipse. //! See Also //! gce_MakeElips which provides functions for more //! complex ellipse constructions //! Geom_Ellipse which provides additional functions for //! constructing ellipses and works, in particular, with the //! parametric equations of ellipses class gp_Elips { public: DEFINE_STANDARD_ALLOC //! Creates an indefinite ellipse. gp_Elips() : majorRadius (RealLast()), minorRadius (RealSmall()) {} //! The major radius of the ellipse is on the "XAxis" and the //! minor radius is on the "YAxis" of the ellipse. The "XAxis" //! is defined with the "XDirection" of theA2 and the "YAxis" is //! defined with the "YDirection" of theA2. //! Warnings : //! It is not forbidden to create an ellipse with theMajorRadius = //! theMinorRadius. //! Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0. gp_Elips (const gp_Ax2& theA2, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius) : pos (theA2), majorRadius (theMajorRadius), minorRadius (theMinorRadius) { Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < theMinorRadius, "gp_Elips() - invalid construction parameters"); } //! Changes the axis normal to the plane of the ellipse. //! It modifies the definition of this plane. //! The "XAxis" and the "YAxis" are recomputed. //! The local coordinate system is redefined so that: //! - its origin and "main Direction" become those of the //! axis theA1 (the "X Direction" and "Y Direction" are then //! recomputed in the same way as for any gp_Ax2), or //! Raises ConstructionError if the direction of theA1 //! is parallel to the direction of the "XAxis" of the ellipse. void SetAxis (const gp_Ax1& theA1) { pos.SetAxis (theA1); } //! Modifies this ellipse, by redefining its local coordinate //! so that its origin becomes theP. void SetLocation (const gp_Pnt& theP) { pos.SetLocation (theP); } //! The major radius of the ellipse is on the "XAxis" (major axis) //! of the ellipse. //! Raises ConstructionError if theMajorRadius < MinorRadius. void SetMajorRadius (const Standard_Real theMajorRadius) { Standard_ConstructionError_Raise_if (theMajorRadius < minorRadius, "gp_Elips::SetMajorRadius() - major radius should be greater or equal to minor radius"); majorRadius = theMajorRadius; } //! The minor radius of the ellipse is on the "YAxis" (minor axis) //! of the ellipse. //! Raises ConstructionError if theMinorRadius > MajorRadius or MinorRadius < 0. void SetMinorRadius (const Standard_Real theMinorRadius) { Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || majorRadius < theMinorRadius, "gp_Elips::SetMinorRadius() - minor radius should be a positive number lesser or equal to major radius"); minorRadius = theMinorRadius; } //! Modifies this ellipse, by redefining its local coordinate //! so that it becomes theA2. void SetPosition (const gp_Ax2& theA2) { pos = theA2; } //! Computes the area of the Ellipse. Standard_Real Area() const { return M_PI * majorRadius * minorRadius; } //! Computes the axis normal to the plane of the ellipse. const gp_Ax1& Axis() const { return pos.Axis(); } //! Computes the first or second directrix of this ellipse. //! These are the lines, in the plane of the ellipse, normal to //! the major axis, at a distance equal to //! MajorRadius/e from the center of the ellipse, where //! e is the eccentricity of the ellipse. //! The first directrix (Directrix1) is on the positive side of //! the major axis. The second directrix (Directrix2) is on //! the negative side. //! The directrix is returned as an axis (gp_Ax1 object), the //! origin of which is situated on the "X Axis" of the local //! coordinate system of this ellipse. //! Exceptions //! Standard_ConstructionError if the eccentricity is null //! (the ellipse has degenerated into a circle). gp_Ax1 Directrix1() const; //! This line is obtained by the symmetrical transformation //! of "Directrix1" with respect to the "YAxis" of the ellipse. //! Exceptions //! Standard_ConstructionError if the eccentricity is null //! (the ellipse has degenerated into a circle). gp_Ax1 Directrix2() const; //! Returns the eccentricity of the ellipse between 0.0 and 1.0 //! If f is the distance between the center of the ellipse and //! the Focus1 then the eccentricity e = f / MajorRadius. //! Raises ConstructionError if MajorRadius = 0.0 Standard_Real Eccentricity() const; //! Computes the focal distance. It is the distance between the //! two focus focus1 and focus2 of the ellipse. Standard_Real Focal() const { return 2.0 * sqrt (majorRadius * majorRadius - minorRadius * minorRadius); } //! Returns the first focus of the ellipse. This focus is on the //! positive side of the "XAxis" of the ellipse. gp_Pnt Focus1() const; //! Returns the second focus of the ellipse. This focus is on the //! negative side of the "XAxis" of the ellipse. gp_Pnt Focus2() const; //! Returns the center of the ellipse. It is the "Location" //! point of the coordinate system of the ellipse. const gp_Pnt& Location() const { return pos.Location(); } //! Returns the major radius of the ellipse. Standard_Real MajorRadius() const { return majorRadius; } //! Returns the minor radius of the ellipse. Standard_Real MinorRadius() const { return minorRadius; } //! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity //! of the ellipse. //! Returns 0 if MajorRadius = 0 Standard_Real Parameter() const; //! Returns the coordinate system of the ellipse. const gp_Ax2& Position() const { return pos; } //! Returns the "XAxis" of the ellipse whose origin //! is the center of this ellipse. It is the major axis of the //! ellipse. gp_Ax1 XAxis() const { return gp_Ax1 (pos.Location(), pos.XDirection()); } //! Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction" //! of the local coordinate system of this ellipse. //! This is the minor axis of the ellipse. gp_Ax1 YAxis() const { return gp_Ax1 (pos.Location(), pos.YDirection()); } Standard_EXPORT void Mirror (const gp_Pnt& theP); //! Performs the symmetrical transformation of an ellipse with //! respect to the point theP which is the center of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Pnt& theP) const; Standard_EXPORT void Mirror (const gp_Ax1& theA1); //! Performs the symmetrical transformation of an ellipse with //! respect to an axis placement which is the axis of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax1& theA1) const; Standard_EXPORT void Mirror (const gp_Ax2& theA2); //! Performs the symmetrical transformation of an ellipse with //! respect to a plane. The axis placement theA2 locates the plane //! of the symmetry (Location, XDirection, YDirection). Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax2& theA2) const; void Rotate (const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate (theA1, theAng); } //! Rotates an ellipse. theA1 is the axis of the rotation. //! theAng is the angular value of the rotation in radians. Standard_NODISCARD gp_Elips Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const { gp_Elips anE = *this; anE.pos.Rotate (theA1, theAng); return anE; } void Scale (const gp_Pnt& theP, const Standard_Real theS); //! Scales an ellipse. theS is the scaling value. Standard_NODISCARD gp_Elips Scaled (const gp_Pnt& theP, const Standard_Real theS) const; void Transform (const gp_Trsf& theT); //! Transforms an ellipse with the transformation theT from class Trsf. Standard_NODISCARD gp_Elips Transformed (const gp_Trsf& theT) const; void Translate (const gp_Vec& theV) { pos.Translate (theV); } //! Translates an ellipse in the direction of the vector theV. //! The magnitude of the translation is the vector's magnitude. Standard_NODISCARD gp_Elips Translated (const gp_Vec& theV) const { gp_Elips anE = *this; anE.pos.Translate (theV); return anE; } void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { pos.Translate (theP1, theP2); } //! Translates an ellipse from the point theP1 to the point theP2. Standard_NODISCARD gp_Elips Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const { gp_Elips anE = *this; anE.pos.Translate (theP1, theP2); return anE; } private: gp_Ax2 pos; Standard_Real majorRadius; Standard_Real minorRadius; }; // ======================================================================= // function : Directrix1 // purpose : // ======================================================================= inline gp_Ax1 gp_Elips::Directrix1() const { Standard_Real anE = Eccentricity(); Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix1() - zero eccentricity"); gp_XYZ anOrig = pos.XDirection().XYZ(); anOrig.Multiply (majorRadius / anE); anOrig.Add (pos.Location().XYZ()); return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection()); } // ======================================================================= // function : Directrix2 // purpose : // ======================================================================= inline gp_Ax1 gp_Elips::Directrix2() const { Standard_Real anE = Eccentricity(); Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix2() - zero eccentricity"); gp_XYZ anOrig = pos.XDirection().XYZ(); anOrig.Multiply (-majorRadius / anE); anOrig.Add (pos.Location().XYZ()); return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection()); } // ======================================================================= // function : Eccentricity // purpose : // ======================================================================= inline Standard_Real gp_Elips::Eccentricity() const { if (majorRadius == 0.0) { return 0.0; } else { return sqrt (majorRadius * majorRadius - minorRadius * minorRadius) / majorRadius; } } // ======================================================================= // function : Focus1 // purpose : // ======================================================================= inline gp_Pnt gp_Elips::Focus1() const { Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius); const gp_Pnt& aPP = pos.Location(); const gp_Dir& aDD = pos.XDirection(); return gp_Pnt (aPP.X() + aC * aDD.X(), aPP.Y() + aC * aDD.Y(), aPP.Z() + aC * aDD.Z()); } // ======================================================================= // function : Focus2 // purpose : // ======================================================================= inline gp_Pnt gp_Elips::Focus2() const { Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius); const gp_Pnt& aPP = pos.Location(); const gp_Dir& aDD = pos.XDirection(); return gp_Pnt (aPP.X() - aC * aDD.X(), aPP.Y() - aC * aDD.Y(), aPP.Z() - aC * aDD.Z()); } // ======================================================================= // function : Parameter // purpose : // ======================================================================= inline Standard_Real gp_Elips::Parameter() const { if (majorRadius == 0.0) { return 0.0; } else { return (minorRadius * minorRadius) / majorRadius; } } // ======================================================================= // function : Scale // purpose : // ======================================================================= inline void gp_Elips::Scale (const gp_Pnt& theP, const Standard_Real theS) // Modified by skv - Fri Apr 8 10:28:10 2005 OCC8559 Begin // { pos.Scale(P, S); } { majorRadius *= theS; if (majorRadius < 0) { majorRadius = -majorRadius; } minorRadius *= theS; if (minorRadius < 0) { minorRadius = -minorRadius; } pos.Scale (theP, theS); } // Modified by skv - Fri Apr 8 10:28:10 2005 OCC8559 End // ======================================================================= // function : Scaled // purpose : // ======================================================================= inline gp_Elips gp_Elips::Scaled (const gp_Pnt& theP, const Standard_Real theS) const { gp_Elips anE = *this; anE.majorRadius *= theS; if (anE.majorRadius < 0) { anE.majorRadius = -anE.majorRadius; } anE.minorRadius *= theS; if (anE.minorRadius < 0) { anE.minorRadius = -anE.minorRadius; } anE.pos.Scale (theP, theS); return anE; } // ======================================================================= // function : Transform // purpose : // ======================================================================= inline void gp_Elips::Transform (const gp_Trsf& theT) { majorRadius *= theT.ScaleFactor(); if (majorRadius < 0) { majorRadius = -majorRadius; } minorRadius *= theT.ScaleFactor(); if (minorRadius < 0) { minorRadius = -minorRadius; } pos.Transform (theT); } // ======================================================================= // function : Transformed // purpose : // ======================================================================= inline gp_Elips gp_Elips::Transformed (const gp_Trsf& theT) const { gp_Elips anE = *this; anE.majorRadius *= theT.ScaleFactor(); if (anE.majorRadius < 0) { anE.majorRadius = -anE.majorRadius; } anE.minorRadius *= theT.ScaleFactor(); if (anE.minorRadius < 0) { anE.minorRadius = -anE.minorRadius; } anE.pos.Transform (theT); return anE; } #endif // _gp_Elips_HeaderFile