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SimplePointingConstraint Class Reference

#include <SimplePointingConstraint.h>

Inheritance diagram for SimplePointingConstraint:
KinematicConstraint

Public Member Functions

virtual SimplePointingConstraintclone () const
 
virtual std::pair
< AlgebraicMatrix,
AlgebraicVector
derivative (const AlgebraicVector &exPoint) const
 
virtual std::pair
< AlgebraicMatrix,
AlgebraicVector
derivative (const std::vector< RefCountedKinematicParticle > &par) const
 
virtual AlgebraicVector deviations (int nStates) const
 
virtual int numberOfEquations () const
 
 SimplePointingConstraint (const GlobalPoint &ref)
 
virtual std::pair
< AlgebraicVector,
AlgebraicVector
value (const AlgebraicVector &exPoint) const
 
virtual std::pair
< AlgebraicVector,
AlgebraicVector
value (const std::vector< RefCountedKinematicParticle > &par) const
 
- Public Member Functions inherited from KinematicConstraint
 KinematicConstraint ()
 
virtual ~KinematicConstraint ()
 

Private Member Functions

std::pair< AlgebraicMatrix,
AlgebraicVector
makeDerivative (const AlgebraicVector &exPoint) const
 
std::pair< AlgebraicVector,
AlgebraicVector
makeValue (const AlgebraicVector &exPoint) const
 

Private Attributes

GlobalPoint refPoint
 

Detailed Description

Topological constraint making a momentum vector to point to the given location in space. Example: if b-meson momentum is reconstructed at b-meson decay position (secondary vertex), making reconstructed momentum pointing the the primary vertex

Multiple track refit is not supported in current version

Kirill Prokofiev, March 2004 MultiState version: July 2004

Definition at line 21 of file SimplePointingConstraint.h.

Constructor & Destructor Documentation

SimplePointingConstraint::SimplePointingConstraint ( const GlobalPoint ref)
inline

Definition at line 25 of file SimplePointingConstraint.h.

Referenced by clone().

25  :refPoint(ref)
26  {}

Member Function Documentation

virtual SimplePointingConstraint* SimplePointingConstraint::clone ( ) const
inlinevirtual

Clone method

Implements KinematicConstraint.

Definition at line 53 of file SimplePointingConstraint.h.

References SimplePointingConstraint().

54  {return new SimplePointingConstraint(*this);}
SimplePointingConstraint(const GlobalPoint &ref)
std::pair< AlgebraicMatrix, AlgebraicVector > SimplePointingConstraint::derivative ( const AlgebraicVector exPoint) const
virtual

Implements KinematicConstraint.

Definition at line 25 of file SimplePointingConstraint.cc.

References makeDerivative().

26 {
27  if(exPoint.num_row() ==0 ) throw VertexException("PointingKinematicConstraint::value requested for zero Linearization point");
28 
29 //security check for extended cartesian parametrization
30  int inSize = exPoint.num_row();
31  if((inSize%7) !=0) throw VertexException("PointingKinematicConstraint::linearization point has a wrong dimension");
32  int nStates = inSize/7;
33  if(nStates != 1) throw VertexException("PointingKinematicConstraint::Current version does not support the multistate refit");
34  AlgebraicVector lPar = exPoint;
35 
36 //2x7 derivative matrix for given particle
37  AlgebraicMatrix lDeriv = makeDerivative(lPar).first;
38  AlgebraicMatrix dr(2,7,0);
39  dr.sub(1,1,lDeriv);
40  return std::pair<AlgebraicMatrix,AlgebraicVector>(dr,lPar);
41 }
Common base class.
CLHEP::HepMatrix AlgebraicMatrix
CLHEP::HepVector AlgebraicVector
std::pair< AlgebraicMatrix, AlgebraicVector > makeDerivative(const AlgebraicVector &exPoint) const
std::pair< AlgebraicMatrix, AlgebraicVector > SimplePointingConstraint::derivative ( const std::vector< RefCountedKinematicParticle > &  par) const
virtual

Vector of values and matrix of derivatives calculated using current state parameters as expansion point

Implements KinematicConstraint.

Definition at line 43 of file SimplePointingConstraint.cc.

References makeDerivative().

44 {
45  int nStates = par.size();
46  if(nStates == 0) throw VertexException("PointingKinematicConstraint::Empty vector of particles passed");
47  if(nStates != 1) throw VertexException("PointingKinematicConstraint::Current version does not support the multistate refit");
48 
49  AlgebraicMatrix dr(2,7,0);
50  AlgebraicVector lPoint = asHepVector<7>(par.front()->currentState().kinematicParameters().vector());
51 
52 //2x7 derivative matrix for given state
53  AlgebraicMatrix lDeriv = makeDerivative(lPoint).first;
54  dr.sub(1,1,lDeriv);
55 // cout<<"Derivative returned: "<<dr<<endl;
56 // cout<<"For the value: "<<lPoint<<endl;
57  return std::pair<AlgebraicMatrix,AlgebraicVector>(dr,lPoint);
58 }
Common base class.
CLHEP::HepMatrix AlgebraicMatrix
CLHEP::HepVector AlgebraicVector
std::pair< AlgebraicMatrix, AlgebraicVector > makeDerivative(const AlgebraicVector &exPoint) const
AlgebraicVector SimplePointingConstraint::deviations ( int  nStates) const
virtual

Returns vector of sigma squared associated to the KinematicParameters of refitted particles Initial deviations are given by user for the constraining parameters (mass, momentum components etc). In case of multiple states exactly the same values are added to every particle parameters

Implements KinematicConstraint.

Definition at line 75 of file SimplePointingConstraint.cc.

76 {return AlgebraicVector(7*nStates,0);}
CLHEP::HepVector AlgebraicVector
std::pair< AlgebraicMatrix, AlgebraicVector > SimplePointingConstraint::makeDerivative ( const AlgebraicVector exPoint) const
private

Definition at line 120 of file SimplePointingConstraint.cc.

References point, funct::pow(), refPoint, mathSSE::sqrt(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by derivative().

121 {
122  AlgebraicMatrix dr(2,7,0);
123  AlgebraicVector point = exPoint;
124  double dx = point(1) - refPoint.x();
125  double dy = point(2) - refPoint.y();
126  double dz = point(3) - refPoint.z();
127  double px = point(4);
128  double py = point(5);
129  double pz = point(6);
130 
131 
132 //half angle solution
133 //d/dx_i
134  dr(1,1) = (sqrt((1 + dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 - px/sqrt(pow(px,2) + pow(py,2)))) -
135  sqrt((1 - dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 + px/sqrt(pow(px,2) + pow(py,2)))))/2.;
136 
137  dr(1,2) = (((-(pow(dx,2)/pow(pow(dx,2) + pow(dy,2),1.5)) + 1/sqrt(pow(dx,2) + pow(dy,2)))*
138  (1 - px/sqrt(pow(px,2) + pow(py,2))))/
139  (2.*sqrt((1 + dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 - px/sqrt(pow(px,2) + pow(py,2))))) -
140  ((pow(dx,2)/pow(pow(dx,2) + pow(dy,2),1.5) - 1/sqrt(pow(dx,2) + pow(dy,2)))*
141  (1 + px/sqrt(pow(px,2) + pow(py,2))))/
142  (2.*sqrt((1 - dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 + px/sqrt(pow(px,2) + pow(py,2))))))/2.;
143 
144 
145  dr(1,3) = 0;
146 
147 //d/dp_i
148 //debug: x->p index xhange in denominator
149  dr(1,4) = (-(dx*dy*(1 - px/sqrt(pow(px,2) + pow(py,2))))/
150  (2.*pow(pow(dx,2) + pow(dy,2),1.5)*
151  sqrt((1 + dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 - px/sqrt(pow(px,2) + pow(py,2))))) -
152  (dx*dy*(1 + px/sqrt(pow(px,2) + pow(py,2))))/
153  (2.*pow(pow(dx,2) + pow(dy,2),1.5)*
154  sqrt((1 - dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 + px/sqrt(pow(px,2) + pow(py,2))))))/2.;
155 
156 
157  dr(1,5) = (((1 + dx/sqrt(pow(dx,2) + pow(dy,2)))*px*py)/
158  (2.*pow(pow(px,2) + pow(py,2),1.5)*
159  sqrt((1 + dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 - px/sqrt(pow(px,2) + pow(py,2))))) +
160  ((1 - dx/sqrt(pow(dx,2) + pow(dy,2)))*px*py)/
161  (2.*pow(pow(px,2) + pow(py,2),1.5)*
162  sqrt((1 - dx/sqrt(pow(dx,2) + pow(dy,2)))*(1 + px/sqrt(pow(px,2) + pow(py,2))))))/2.;
163 
164 
165 
166  dr(1,6) = 0;
167  dr(1,7) = 0;
168 
169 //2nd equation
170 //d/dx_i
171 
172  dr(2,1) =(((-((dx*sqrt(pow(dx,2) + pow(dy,2)))/pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5)) +
173  dx/(sqrt(pow(dx,2) + pow(dy,2))*sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2))))*
174  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
175  (2.*sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
176  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) -
177  (((dx*sqrt(pow(dx,2) + pow(dy,2)))/pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5) -
178  dx/(sqrt(pow(dx,2) + pow(dy,2))*sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2))))*
179  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
180  (2.*sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
181  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
182 
183 
184  dr(2,2) = (((-((dy*sqrt(pow(dx,2) + pow(dy,2)))/pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5)) +
185  dy/(sqrt(pow(dx,2) + pow(dy,2))*sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2))))*
186  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
187  (2.*sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
188  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) -
189  (((dy*sqrt(pow(dx,2) + pow(dy,2)))/pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5) -
190  dy/(sqrt(pow(dx,2) + pow(dy,2))*sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2))))*
191  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
192  (2.*sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
193  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
194 
195 
196  dr(2,3) = (-(sqrt(pow(dx,2) + pow(dy,2))*dz*(1 - sqrt(pow(px,2) + pow(py,2))/
197  sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
198  (2.*pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5)*
199  sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
200  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) -
201  (sqrt(pow(dx,2) + pow(dy,2))*dz*(1 +
202  sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))/
203  (2.*pow(pow(dx,2) + pow(dy,2) + pow(dz,2),1.5)*
204  sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
205  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
206 
207 
208 
209 //d/dp_i
210 //debug: x->p index xhange in denominator
211 
212  dr(2,4) = (((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
213  ((px*sqrt(pow(px,2) + pow(py,2)))/pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5) -
214  px/(sqrt(pow(px,2) + pow(py,2))*sqrt(pow(px,2) + pow(py,2) + pow(pz,2)))))/
215  (2.*sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
216  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) -
217  ((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
218  (-((px*sqrt(pow(px,2) + pow(py,2)))/pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5)) +
219  px/(sqrt(pow(px,2) + pow(py,2))*sqrt(pow(px,2) + pow(py,2) + pow(pz,2)))))/
220  (2.*sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
221  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
222 
223 
224  dr(2,5) = (((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
225  ((py*sqrt(pow(px,2) + pow(py,2)))/pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5) -
226  py/(sqrt(pow(px,2) + pow(py,2))*sqrt(pow(px,2) + pow(py,2) + pow(pz,2)))))/
227  (2.*sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
228  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) -
229  ((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
230  (-((py*sqrt(pow(px,2) + pow(py,2)))/pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5)) +
231  py/(sqrt(pow(px,2) + pow(py,2))*sqrt(pow(px,2) + pow(py,2) + pow(pz,2)))))/
232  (2.*sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
233  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
234 
235 
236  dr(2,6) = (((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
237  sqrt(pow(px,2) + pow(py,2))*pz)/
238  (2.*pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5)*
239  sqrt((1 + sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
240  (1 - sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))) +
241  ((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
242  sqrt(pow(px,2) + pow(py,2))*pz)/
243  (2.*pow(pow(px,2) + pow(py,2) + pow(pz,2),1.5)*
244  sqrt((1 - sqrt(pow(dx,2) + pow(dy,2))/sqrt(pow(dx,2) + pow(dy,2) + pow(dz,2)))*
245  (1 + sqrt(pow(px,2) + pow(py,2))/sqrt(pow(px,2) + pow(py,2) + pow(pz,2))))))/2.;
246 
247 
248  dr(2,7) = 0;
249 
250 // cout<<"derivative matrix "<<dr<<endl;
251  return std::pair<AlgebraicMatrix,AlgebraicVector>(dr,point);
252 }
T y() const
Definition: PV3DBase.h:63
CLHEP::HepMatrix AlgebraicMatrix
T sqrt(T t)
Definition: SSEVec.h:18
T z() const
Definition: PV3DBase.h:64
CLHEP::HepVector AlgebraicVector
T x() const
Definition: PV3DBase.h:62
Power< A, B >::type pow(const A &a, const B &b)
Definition: Power.h:40
*vegas h *****************************************************used in the default bin number in original ***version of VEGAS is ***a higher bin number might help to derive a more precise ***grade subtle point
Definition: invegas.h:5
std::pair< AlgebraicVector, AlgebraicVector > SimplePointingConstraint::makeValue ( const AlgebraicVector exPoint) const
private

Definition at line 81 of file SimplePointingConstraint.cc.

References point, refPoint, mathSSE::sqrt(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by value().

82 {
83 // cout<<"Make value called"<<endl;
84  AlgebraicVector vl(2,0);
85  AlgebraicVector point = exPoint;
86  double dx = point(1) - refPoint.x();
87  double dy = point(2) - refPoint.y();
88  double dz = point(3) - refPoint.z();
89  double px = point(4);
90  double py = point(5);
91  double pz = point(6);
92 
93 
94 //half angle solution: sin((alpha - betha)/2)
95  double cos_phi_p = px/sqrt(px*px + py*py);
96  double cos_phi_x = dx/sqrt(dx*dx + dy*dy);
97 // cout<<"mom cos phi"<<cos_phi_p<<endl;
98 // cout<<"x cos phi"<<cos_phi_x<<endl;
99 
100 
101  double cos_theta_p = sqrt(px*px + py*py)/sqrt(px*px + py*py + pz*pz);
102  double cos_theta_x = sqrt(dx*dx + dy*dy)/sqrt(dx*dx + dy*dy + dz*dz);
103 
104  float feq = sqrt((1-cos_phi_p)*(1+cos_phi_x)) - sqrt((1+cos_phi_p)*(1-cos_phi_x));
105  float seq = sqrt((1-cos_theta_p)*(1+cos_theta_x)) - sqrt((1+cos_theta_p)*(1-cos_theta_x));
106 
107 // cout<<"First factor: "<<feq/2<<endl;
108 // cout<<"Second factor: "<<seq/2<<endl;
109 
110  vl(1) = feq/2;
111  vl(2) = seq/2;
112 
113 // cout<<"Value "<<vl<<endl;
114 //half angle corrected
115 // vl(1) = (sin_x/(1+cos_x)) - (sin_p/(1+cos_p));
116 // vl(2) = (sin_xt/(1+cos_xt)) - (sin_pt/(1+cos_pt));
117  return std::pair<AlgebraicVector,AlgebraicVector>(vl,point);
118 }
T y() const
Definition: PV3DBase.h:63
T sqrt(T t)
Definition: SSEVec.h:18
T z() const
Definition: PV3DBase.h:64
CLHEP::HepVector AlgebraicVector
T x() const
Definition: PV3DBase.h:62
*vegas h *****************************************************used in the default bin number in original ***version of VEGAS is ***a higher bin number might help to derive a more precise ***grade subtle point
Definition: invegas.h:5
int SimplePointingConstraint::numberOfEquations ( ) const
virtual

Returns number of constraint equations used for fitting. Method is relevant for proper NDF calculations.

Implements KinematicConstraint.

Definition at line 78 of file SimplePointingConstraint.cc.

79 {return 2;}
std::pair< AlgebraicVector, AlgebraicVector > SimplePointingConstraint::value ( const AlgebraicVector exPoint) const
virtual

Vector of values and matrix of derivatives calculated at given expansion 7xNumberOfStates point

Implements KinematicConstraint.

Definition at line 5 of file SimplePointingConstraint.cc.

References makeValue().

6 {
7  if(exPoint.num_row() ==0 ) throw VertexException("PointingKinematicConstraint::value requested for zero Linearization point");
8 
9 //security check for extended cartesian parametrization
10  int inSize = exPoint.num_row();
11  if((inSize%7) !=0) throw VertexException("PointingKinematicConstraint::linearization point has a wrong dimension");
12  int nStates = inSize/7;
13  if(nStates != 1) throw VertexException("PointingKinematicConstraint::Current version does not support the multistate refit");
14 
15  AlgebraicVector lPar = exPoint;
16  AlgebraicVector vl(2,0);
17 
18 //vector of values 1x2 for given particle
19  AlgebraicVector lValue = makeValue(lPar).first;
20  vl(1) =lValue(1);
21  vl(2) =lValue(2);
22  return std::pair<AlgebraicVector,AlgebraicVector>(vl,lPar);
23 }
Common base class.
std::pair< AlgebraicVector, AlgebraicVector > makeValue(const AlgebraicVector &exPoint) const
CLHEP::HepVector AlgebraicVector
std::pair< AlgebraicVector, AlgebraicVector > SimplePointingConstraint::value ( const std::vector< RefCountedKinematicParticle > &  par) const
virtual

Methods making value and derivative matrix using current state parameters as expansion 7-point. Constraint can be made equaly for single and multiple states

Implements KinematicConstraint.

Definition at line 60 of file SimplePointingConstraint.cc.

References makeValue().

61 {
62  int nStates = par.size();
63  if(nStates == 0) throw VertexException("PointingKinematicConstraint::Empty vector of particles passed");
64  if(nStates != 1) throw VertexException("PointingKinematicConstraint::Current version does not support the multistate refit");
65  AlgebraicVector vl(2,0);
66  AlgebraicVector lPoint = asHepVector<7>(par.front()->currentState().kinematicParameters().vector());
67  vl(1) = makeValue(lPoint).first(1);
68  vl(2) = makeValue(lPoint).first(2);
69 // cout<<"Value returned: "<<vl<<endl;
70 // cout<<"For the point: "<<lPoint<<endl;
71 
72  return std::pair<AlgebraicVector,AlgebraicVector>(vl,lPoint);
73 }
Common base class.
std::pair< AlgebraicVector, AlgebraicVector > makeValue(const AlgebraicVector &exPoint) const
CLHEP::HepVector AlgebraicVector

Member Data Documentation

GlobalPoint SimplePointingConstraint::refPoint
private

Definition at line 61 of file SimplePointingConstraint.h.

Referenced by makeDerivative(), and makeValue().