| Geant4 Cross Reference |
1 // -*- C++ -*-
2 // ---------------------------------------------------------------------------
3 //
4 // This file is a part of the CLHEP - a Class Library for High Energy Physics.
5 //
6 // This is the implementation of those parts of the HepLorentzRotation class
7 // which involve decomposition into Boost*Rotation.
8
9 #include "CLHEP/Vector/LorentzRotation.h"
10
11 #include <cmath>
12 #include <iostream>
13
14 namespace CLHEP {
15
16 // ---------- Decomposition:
17
18 void HepLorentzRotation::decompose
19 (HepBoost & bboost, HepRotation & rotation) const {
20
21 // The boost will be the pure boost based on column 4 of the transformation
22 // matrix. Since the constructor takes the beta vector, and not beta*gamma,
23 // we first divide through by gamma = the tt element. This of course can
24 // never be zero since the last row has t**2 - v**2 = +1.
25
26 Hep3Vector betaVec ( xt(), yt(), zt() );
27 betaVec *= 1.0 / tt();
28 bboost.set( betaVec );
29
30 // The rotation will be inverse of B times T.
31
32 HepBoost B( -betaVec );
33 HepLorentzRotation R( B * *this );
34
35 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
36 R.yx(), R.yy(), R.yz(),
37 R.zx(), R.zy(), R.zz() );
38 rotation.set( m1 );
39 rotation.rectify();
40
41 return;
42
43 }
44
45 void HepLorentzRotation::decompose
46 (Hep3Vector & bboost, HepAxisAngle & rotation) const {
47 HepRotation r;
48 HepBoost b;
49 decompose(b,r);
50 bboost = b.boostVector();
51 rotation = r.axisAngle();
52 return;
53 }
54
55 void HepLorentzRotation::decompose
56 (HepRotation & rotation, HepBoost & bboost) const {
57
58 // In this case the pure boost is based on row 4 of the matrix.
59
60 Hep3Vector betaVec( tx(), ty(), tz() );
61 betaVec *= 1.0 / tt();
62 bboost.set( betaVec );
63
64 // The rotation will be T times the inverse of B.
65
66 HepBoost B( -betaVec );
67 HepLorentzRotation R( *this * B );
68
69 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
70 R.yx(), R.yy(), R.yz(),
71 R.zx(), R.zy(), R.zz() );
72 rotation.set( m1 );
73 rotation.rectify();
74 return;
75
76 }
77
78 void HepLorentzRotation::decompose
79 (HepAxisAngle & rotation, Hep3Vector & bboost) const {
80 HepRotation r;
81 HepBoost b;
82 decompose(r,b);
83 rotation = r.axisAngle();
84 bboost = b.boostVector();
85 return;
86 }
87
88 double HepLorentzRotation::distance2( const HepBoost & b ) const {
89 HepBoost b1;
90 HepRotation r1;
91 decompose( b1, r1 );
92 double db2 = b1.distance2( b );
93 double dr2 = r1.norm2();
94 return ( db2 + dr2 );
95 }
96
97 double HepLorentzRotation::distance2( const HepRotation & r ) const {
98 HepBoost b1;
99 HepRotation r1;
100 decompose( b1, r1 );
101 double db2 = b1.norm2( );
102 double dr2 = r1.distance2( r );
103 return ( db2 + dr2 );
104 }
105
106 double HepLorentzRotation::distance2(
107 const HepLorentzRotation & lt ) const {
108 HepBoost b1;
109 HepRotation r1;
110 decompose( b1, r1 );
111 HepBoost b2;
112 HepRotation r2;
113 lt.decompose (b2, r2);
114 double db2 = b1.distance2( b2 );
115 double dr2 = r1.distance2( r2 );
116 return ( db2 + dr2 );
117 }
118
119 double HepLorentzRotation::howNear( const HepBoost & b ) const {
120 return std::sqrt( distance2( b ) );
121 }
122 double HepLorentzRotation::howNear( const HepRotation & r ) const {
123 return std::sqrt( distance2( r ) );
124 }
125 double HepLorentzRotation::howNear( const HepLorentzRotation & lt )const {
126 return std::sqrt( distance2( lt ) );
127 }
128
129 bool HepLorentzRotation::isNear(
130 const HepBoost & b, double epsilon ) const {
131 HepBoost b1;
132 HepRotation r1;
133 decompose( b1, r1 );
134 double db2 = b1.distance2(b);
135 if ( db2 > epsilon*epsilon ) {
136 return false; // Saves the time-consuming Rotation::norm2
137 }
138 double dr2 = r1.norm2();
139 return ( (db2 + dr2) <= epsilon*epsilon );
140 }
141
142 bool HepLorentzRotation::isNear(
143 const HepRotation & r, double epsilon ) const {
144 HepBoost b1;
145 HepRotation r1;
146 decompose( b1, r1 );
147 double db2 = b1.norm2();
148 if ( db2 > epsilon*epsilon ) {
149 return false; // Saves the time-consuming Rotation::distance2
150 }
151 double dr2 = r1.distance2(r);
152 return ( (db2 + dr2) <= epsilon*epsilon );
153 }
154
155 bool HepLorentzRotation::isNear(
156 const HepLorentzRotation & lt, double epsilon ) const {
157 HepBoost b1;
158 HepRotation r1;
159 decompose( b1, r1 );
160 HepBoost b2;
161 HepRotation r2;
162 lt.decompose (b2, r2);
163 double db2 = b1.distance2(b2);
164 if ( db2 > epsilon*epsilon ) {
165 return false; // Saves the time-consuming Rotation::distance2
166 }
167 double dr2 = r1.distance2(r2);
168 return ( (db2 + dr2) <= epsilon*epsilon );
169 }
170
171 double HepLorentzRotation::norm2() const {
172 HepBoost b;
173 HepRotation r;
174 decompose( b, r );
175 return b.norm2() + r.norm2();
176 }
177
178 void HepLorentzRotation::rectify() {
179
180 // Assuming the representation of this is close to a true LT,
181 // but may have drifted due to round-off error from many operations,
182 // this forms an "exact" orthosymplectic matrix for the LT again.
183
184 // There are several ways to do this, all equivalent to lowest order in
185 // the corrected error. We choose to form an LT based on the inverse boost
186 // extracted from row 4, and left-multiply by LT to form what would be
187 // a rotation if the LT were kosher. We drop the possibly non-zero t
188 // components of that, rectify that rotation and multiply back by the boost.
189
190 Hep3Vector beta (tx(), ty(), tz());
191 double gam = tt(); // NaN-proofing
192 if ( gam <= 0 ) {
193 std::cerr << "HepLorentzRotation::rectify() - "
194 << "rectify() on a transformation with tt() <= 0 - will not help!"
195 << std::endl;
196 gam = 1;
197 }
198 beta *= 1.0/gam;
199 HepLorentzRotation R = (*this) * HepBoost(-beta);
200
201 HepRep3x3 m1 ( R.xx(), R.xy(), R.xz(),
202 R.yx(), R.yy(), R.yz(),
203 R.zx(), R.zy(), R.zz() );
204
205 HepRotation Rgood (m1);
206 Rgood.rectify();
207
208 set ( Rgood, HepBoost(beta) );
209 }
210
211 } // namespace CLHEP
212