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class ROOT::Math::Plane3D


      Class describing a geometrical plane in 3 dimensions.
      A Plane3D is a 2 dimensional surface spanned by two linearly independent vectors.
      The plane is described by the equation
      \f$ a*x + b*y + c*z + d = 0 \f$ where (a,b,c) are the components of the
      normal vector to the plane \f$ n = (a,b,c)  \f$ and \f$ d = - n \dot x \f$, where x is any point
      belonging to plane.
      More information on the mathematics describing a plane in 3D is available on
      <A HREF=http://mathworld.wolfram.com/Plane.html>MathWord</A>.
      The Plane3D class contains the 4 scalar values in double which represent the
      four coefficients, fA, fB, fC, fD. fA, fB, fC are the normal components normalized to 1,
      i.e. fA**2 + fB**2 + fC**2 = 1

      @ingroup GenVector

Function Members (Methods)

protected:
voidNormalize()
private:
voidBuildFrom3Points(const ROOT::Math::Plane3D::Point& p1, const ROOT::Math::Plane3D::Point& p2, const ROOT::Math::Plane3D::Point& p3)
voidBuildFromVecAndPoint(const ROOT::Math::Plane3D::Vector& n, const ROOT::Math::Plane3D::Point& p)

Data Members

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

Function documentation

D()
         default constructor create plane z = 0
{ }
Plane3D(const ROOT::Math::Plane3D::Scalar& a, const ROOT::Math::Plane3D::Scalar& b, const ROOT::Math::Plane3D::Scalar& c, const ROOT::Math::Plane3D::Scalar& d)
         generic constructors from the four scalar values describing the plane
	 according to the equation ax + by + cz + d = 0
         \param a scalar value
         \param b scalar value
         \param c scalar value
         \param d sxcalar value
Plane3D(const ROOT::Math::Plane3D::Vector& n, const ROOT::Math::Plane3D::Point& p)
         constructor a Plane3D from a normal vector and a point coplanar to the plane
	 \param n normal expressed as a ROOT::Math::DisplacementVector3D<Cartesian3D<double> >
	 \param p point  expressed as a  ROOT::Math::PositionVector3D<Cartesian3D<double> >
BuildFromVecAndPoint(const ROOT::Math::Plane3D::Vector& n, const ROOT::Math::Plane3D::Point& p)
Plane3D(const ROOT::Math::Plane3D::Vector& n, const ROOT::Math::Plane3D::Point& p)
         Construct from a generic DisplacementVector3D (normal vector) and PositionVector3D (point coplanar to
         the plane)
	 \param n normal expressed as a generic ROOT::Math::DisplacementVector3D
	 \param p point  expressed as a generic ROOT::Math::PositionVector3D
Plane3D(const ROOT::Math::Plane3D::Point& p1, const ROOT::Math::Plane3D::Point& p2, const ROOT::Math::Plane3D::Point& p3)
         constructor from three Cartesian point belonging to the plane
	 \param p1 point1  expressed as a generic ROOT::Math::PositionVector3D
	 \param p2 point2  expressed as a generic ROOT::Math::PositionVector3D
	 \param p3 point3  expressed as a generic ROOT::Math::PositionVector3D
BuildFrom3Points(const ROOT::Math::Plane3D::Point& p1, const ROOT::Math::Plane3D::Point& p2, const ROOT::Math::Plane3D::Point& p3)
Plane3D(const ROOT::Math::Plane3D::Point& p1, const ROOT::Math::Plane3D::Point& p2, const ROOT::Math::Plane3D::Point& p3)
         constructor from three generic point belonging to the plane
	 \param p1 point1 expressed as  ROOT::Math::DisplacementVector3D<Cartesian3D<double> >
	 \param p2 point2 expressed as  ROOT::Math::DisplacementVector3D<Cartesian3D<double> >
	 \param p3 point3 expressed as  ROOT::Math::DisplacementVector3D<Cartesian3D<double> >
Plane3D & operator=(const ROOT::Math::Plane3D& plane)
 compiler-generated copy ctor and dtor are fine.
 ------ assignment ------

         Assignment operator from other Plane3D class
Scalar A()
         Return the a coefficient of the plane equation \f$ a*x + b*y + c*z + d = 0 \f$. It is also the
         x-component of the vector perpendicular to the plane.
{ return fA; }
Scalar B()
         Return the b coefficient of the plane equation \f$ a*x + b*y + c*z + d = 0 \f$. It is also the
         y-component of the vector perpendicular to the plane
{ return fB; }
Scalar C()
         Return the c coefficient of the plane equation \f$ a*x + b*y + c*z + d = 0 \f$. It is also the
         z-component of the vector perpendicular to the plane
{ return fC; }
Vector Normal() const
         Return normal vector to the plane as Cartesian DisplacementVector
Scalar HesseDistance() const
	  Return the Hesse Distance (distance from the origin) of the plane or
          the d coefficient expressed in normalize form
Scalar Distance(const ROOT::Math::Plane3D::Point& p) const
	 Return the signed distance to a Point.
	 The distance is signed positive if the Point is in the same side of the
	 normal vector to the plane.
	 \param p Point expressed in Cartesian Coordinates
Point ProjectOntoPlane(const ROOT::Math::Plane3D::Point& p) const
	 Return the projection of a Cartesian point to a plane
	 \param p Point expressed as PositionVector3D<Cartesian3D<double> >
bool operator==(const ROOT::Math::Plane3D& rhs) const
 ------------------- Equality -----------------

         Exact equality
bool operator!=(const ROOT::Math::Plane3D& rhs) const
void Normalize()
         Normalize the normal (a,b,c) plane components