ROOT   6.08/07 Reference Guide
Plane3D.cxx
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1 // @(#)root/mathcore:$Id$
2 // Authors: W. Brown, M. Fischler, L. Moneta 2005
3
4 /**********************************************************************
5  * *
6  * Copyright (c) 2005 , LCG ROOT MathLib Team *
7  * *
8  * *
9  **********************************************************************/
10
11 // implementation file for class Plane3D
12 //
13 // Created by: Lorenzo Moneta December 2 2005
14 //
15 //
16
17 #include "Math/GenVector/Plane3D.h"
18
19 #include <cmath>
20
21
22
23
24 namespace ROOT {
25
26 namespace Math {
27
28
30 typedef Plane3D::Point XYZPoint;
32
33 // ========== Constructors and Assignment =====================
34
35
36 // constructor from 4 scalars numbers (a,b,c,d)
37 Plane3D::Plane3D(const Scalar & a, const Scalar & b, const Scalar & c, const Scalar & d) :
38  fA(a), fB(b), fC(c), fD(d)
39 {
40  //renormalize a,b,c to unit
41  Normalize();
42 }
43
44 // internal method to construct from a normal vector and a point
45 void Plane3D::BuildFromVecAndPoint(const XYZVector & n, const XYZPoint & p )
46 {
47  // build from a normal vector and a point
48  fA = n.X();
49  fB = n.Y();
50  fC = n.Z();
51  fD = - n.Dot(p);
52  Normalize();
53 }
54
55 // internl method to construct from three points
56 void Plane3D::BuildFrom3Points( const XYZPoint & p1, const XYZPoint & p2, const XYZPoint & p3 ) {
57
58  // plane from thre points
59  // normal is (x3-x1) cross (x2 -x1)
60  XYZVector n = (p2-p1).Cross(p3-p1);
61  fA = n.X();
62  fB = n.Y();
63  fC = n.Z();
64  fD = - n.Dot(p1);
65  Normalize();
66 }
67
68 // distance plane- point
69 Scalar Plane3D::Distance(const XYZPoint & p) const {
70  return fA*p.X() + fB*p.Y() + fC*p.Z() + fD;
71 }
72
74  // normalize the plane
75  Scalar s = std::sqrt( fA*fA + fB*fB + fC*fC );
76  // what to do if s = 0 ??
77  if ( s == 0) { fD = 0; return; }
78  Scalar w = 1./s;
79  fA *= w;
80  fB *= w;
81  fC *= w;
82  fD *= w;
83 }
84
85
86 // projection of a point onto the plane
87 XYZPoint Plane3D::ProjectOntoPlane(const XYZPoint & p) const {
88  Scalar d = Distance(p);
89  return XYZPoint( p.X() - fA*d, p.Y() - fB*d, p.Z() - fC*d);
90 }
91
92
93 // output
94 std::ostream & operator<< (std::ostream & os, const Plane3D & p) {
95  os << "\n" << p.Normal().X()
96  << " " << p.Normal().Y()
97  << " " << p.Normal().Z()
98  << " " << p.HesseDistance()
99  << "\n";
100  return os;
101 }
102
103
104
105
106
107 } // end namespace Math
108 } // end namespace ROOT
109
Class describing a geometrical plane in 3 dimensions.
Definition: Plane3D.h:47
static double p3(double t, double a, double b, double c, double d)
This namespace contains pre-defined functions to be used in conjuction with TExecutor::Map and TExecu...
Definition: StringConv.hxx:21
Plane3D()
default constructor create plane z = 0
Definition: Plane3D.h:63
return c
Scalar Distance(const Point &p) const
Return the signed distance to a Point.
Definition: Plane3D.cxx:69
PositionVector3D< Cartesian3D< double >, DefaultCoordinateSystemTag > XYZPoint
3D Point based on the cartesian coordinates x,y,z in double precision
Definition: Point3Dfwd.h:33
Class describing a generic position vector (point) in 3 dimensions.
TArc * a
Definition: textangle.C:12
std::ostream & operator<<(std::ostream &os, const AxisAngle &a)
Stream Output and Input.
Definition: AxisAngle.cxx:91
Scalar X() const
Cartesian X, converting if necessary from internal coordinate system.
double sqrt(double)
Scalar Z() const
Cartesian Z, converting if necessary from internal coordinate system.
Scalar Y() const
Cartesian Y, converting if necessary from internal coordinate system.
static double p2(double t, double a, double b, double c)
Vector Normal() const
Return normal vector to the plane as Cartesian DisplacementVector.
Definition: Plane3D.h:166
Scalar Z() const
Cartesian Z, converting if necessary from internal coordinate system.
Scalar X() const
Cartesian X, converting if necessary from internal coordinate system.
Scalar HesseDistance() const
Return the Hesse Distance (distance from the origin) of the plane or the d coefficient expressed in n...
Definition: Plane3D.h:174
static double p1(double t, double a, double b)
SVector< T, 3 > Cross(const SVector< T, 3 > &lhs, const SVector< T, 3 > &rhs)
Vector Cross Product (only for 3-dim vectors) .
Definition: Functions.h:324
void BuildFromVecAndPoint(const Vector &n, const Point &p)
Definition: Plane3D.cxx:45
void Normalize()
Normalize the normal (a,b,c) plane components.
Definition: Plane3D.cxx:73
DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTag > XYZVector
3D Vector based on the cartesian coordinates x,y,z in double precision
Definition: Vector3Dfwd.h:34
Namespace for new Math classes and functions.
void BuildFrom3Points(const Point &p1, const Point &p2, const Point &p3)
Definition: Plane3D.cxx:56
Scalar Y() const
Cartesian Y, converting if necessary from internal coordinate system.
you should not use this method at all Int_t Int_t Double_t Double_t Double_t Int_t Double_t Double_t Double_t Double_t b
Definition: TRolke.cxx:630
Plane3D::Scalar Scalar
Definition: Plane3D.cxx:29
const Int_t n
Definition: legend1.C:16
Point ProjectOntoPlane(const Point &p) const
Return the projection of a Cartesian point to a plane.
Definition: Plane3D.cxx:87
Scalar Dot(const DisplacementVector3D< OtherCoords, Tag > &v) const
Return the scalar (dot) product of two displacement vectors.