5 added + 5 modified, total 10 files
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -N NewTrackTest.java
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ NewTrackTest.java 15 Jul 2006 09:12:45 -0000 1.1
@@ -0,0 +1,70 @@
+/**
+ * @version $Id: NewTrackTest.java,v 1.1 2006/07/15 09:12:45 jstrube Exp $
+ */
+package org.lcsim.contrib.JanStrube.tracking;
+
+import junit.framework.TestCase;
+
+/**
+ * @author jstrube
+ *
+ */
+public class NewTrackTest extends TestCase {
+
+ /* (non-Javadoc)
+ * @see junit.framework.TestCase#setUp()
+ */
+ protected void setUp() throws Exception {
+ super.setUp();
+ }
+
+ /* (non-Javadoc)
+ * @see junit.framework.TestCase#tearDown()
+ */
+ protected void tearDown() throws Exception {
+ super.tearDown();
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#NewTrack(org.lcsim.spacegeom.SpacePoint, org.lcsim.contrib.JanStrube.tracking.EMap, Jama.Matrix, int)}.
+ */
+ public void testNewTrack() {
+ fail("Not yet implemented");
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#getParameter(org.lcsim.contrib.JanStrube.tracking.Track.ParameterName)}.
+ */
+ public void testGetParameter() {
+ fail("Not yet implemented");
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#getPt()}.
+ */
+ public void testGetPt() {
+ fail("Not yet implemented");
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#getCharge()}.
+ */
+ public void testGetCharge() {
+ fail("Not yet implemented");
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#getReferencePoint()}.
+ */
+ public void testGetReferencePoint() {
+ fail("Not yet implemented");
+ }
+
+ /**
+ * Test method for {@link org.lcsim.contrib.JanStrube.tracking.NewTrack#getErrorMatrix()}.
+ */
+ public void testGetErrorMatrix() {
+ fail("Not yet implemented");
+ }
+
+}
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -N Constants.java
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ Constants.java 15 Jul 2006 09:12:45 -0000 1.1
@@ -0,0 +1,12 @@
+/**
+ * @version $Id: Constants.java,v 1.1 2006/07/15 09:12:45 jstrube Exp $
+ */
+package org.lcsim.contrib.JanStrube.tracking;
+
+/**
+ * @author jstrube
+ *
+ */
+public final class Constants {
+ public static final double fieldConversion = 3335.641;
+}
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -u -r1.1 -r1.2
--- NewTrack.java 13 Jul 2006 10:53:58 -0000 1.1
+++ NewTrack.java 15 Jul 2006 09:12:45 -0000 1.2
@@ -1,5 +1,5 @@
/**
- * @version $Id: NewTrack.java,v 1.1 2006/07/13 10:53:58 jstrube Exp $
+ * @version $Id: NewTrack.java,v 1.2 2006/07/15 09:12:45 jstrube Exp $
*/
package org.lcsim.contrib.JanStrube.tracking;
@@ -9,7 +9,9 @@
/**
* @author jstrube
- *
+ * The class to store the measurement information of the track of a charged particle in a magnetic field.
+ * This class represents the FastMC simulation.
+ * An invariant of this class is that the "origin" is the point of closest approach to the reference point.
*/
public class NewTrack implements Track {
private EMap _parameters;
@@ -38,7 +40,7 @@
* @see org.lcsim.contrib.JanStrube.tracking.Track#getPt()
*/
public double getPt() {
- return _parameters.get(ParameterName.pt);
+ return _parameters.pt;
}
/* (non-Javadoc)
* @see org.lcsim.contrib.JanStrube.tracking.Track#getCharge()
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -u -r1.1 -r1.2
--- EMap.java 13 Jul 2006 10:53:58 -0000 1.1
+++ EMap.java 15 Jul 2006 09:12:45 -0000 1.2
@@ -1,14 +1,20 @@
/**
- * @version $Id: EMap.java,v 1.1 2006/07/13 10:53:58 jstrube Exp $
+ * @version $Id: EMap.java,v 1.2 2006/07/15 09:12:45 jstrube Exp $
*/
package org.lcsim.contrib.JanStrube.tracking;
import org.lcsim.contrib.JanStrube.tracking.Track.ParameterName;
public class EMap {
- public double[] values;
+ double[] values;
+ double pt;
EMap() {
- values = new double[6];
+ values = new double[5];
+ pt = 0;
+ }
+ EMap(double[] vals, double p_t) {
+ values = vals;
+ pt = p_t;
}
double get(ParameterName name) {
return values[name.ordinal()];
@@ -16,4 +22,13 @@
void set(ParameterName name, double val) {
values[name.ordinal()] = val;
}
+ void setPt(double p_t) {
+ pt = p_t;
+ }
+ double[] getValues() {
+ return values;
+ }
+ double getPt() {
+ return pt;
+ }
}
\ No newline at end of file
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -u -r1.1 -r1.2
--- Track.java 13 Jul 2006 10:53:58 -0000 1.1
+++ Track.java 15 Jul 2006 09:12:45 -0000 1.2
@@ -1,5 +1,5 @@
/**
- * @version $Id: Track.java,v 1.1 2006/07/13 10:53:58 jstrube Exp $
+ * @version $Id: Track.java,v 1.2 2006/07/15 09:12:45 jstrube Exp $
*/
package org.lcsim.contrib.JanStrube.tracking;
@@ -14,7 +14,7 @@
public interface Track {
enum ParameterName {
- d0, phi0, omega, z0, tanLambda, pt
+ d0, phi0, omega, z0, tanLambda
}
/**
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -u -r1.1 -r1.2
--- HelixSwimmer.java 13 Jul 2006 10:53:58 -0000 1.1
+++ HelixSwimmer.java 15 Jul 2006 09:12:45 -0000 1.2
@@ -1,6 +1,5 @@
package org.lcsim.contrib.JanStrube.tracking;
-import org.lcsim.event.Track;
import org.lcsim.spacegeom.CartesianPoint;
import org.lcsim.spacegeom.SpacePoint;
import org.lcsim.util.swim.Helix;
@@ -12,13 +11,12 @@
import static java.lang.Math.cos;
import static java.lang.Math.sqrt;
import static java.lang.Math.signum;
-import static org.lcsim.constants.Constants.fieldConversion;
+import static org.lcsim.contrib.JanStrube.tracking.Constants.fieldConversion;
import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.d0;
import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.phi0;
import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.omega;
import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.z0;
import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.tanLambda;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.pt;
/**
* A simple helix smimmer for use in org.lcsim. Uses standard lcsim units
@@ -26,8 +24,8 @@
* <p>
* For more info on swimming see <a href="doc-files/transport.pdf">this paper</a>
* by Paul Avery.
- * @author tonyj
- * @version $Id: HelixSwimmer.java,v 1.1 2006/07/13 10:53:58 jstrube Exp $
+ * @author jstrube
+ * @version $Id: HelixSwimmer.java,v 1.2 2006/07/15 09:12:45 jstrube Exp $
*/
public class HelixSwimmer
{
@@ -66,16 +64,13 @@
*/
public void setTrack(SpacePoint p, SpacePoint r0, int iq)
{
- double temp = p.x()*p.x()+p.y()*p.y();
- double pmom = Math.sqrt(temp + p.z()*p.z());
- double sin_lambda = p.z()/pmom;
+ double tan_lambda = p.z()/p.rxy();
double phi = Math.atan2(p.y(),p.x());
- double lambda = Math.asin(sin_lambda);
+ double lambda = Math.atan(tan_lambda);
if (iq != 0 && field != 0)
{
- double p_t = Math.sqrt(temp);
- double radius = p_t/(iq*field);
+ double radius = p.rxy()/(iq*field);
trajectory = new Helix(r0,radius,phi,lambda);
}
else
@@ -85,27 +80,35 @@
spatialParms.isInvalid = true;
}
- public void setTrack(org.lcsim.contrib.JanStrube.tracking.Track t)
+ public void setTrack(Track t)
{
double o = t.getParameter(omega);
double p = t.getParameter(phi0);
double lambda = Math.atan(t.getParameter(tanLambda));
-
- // origin of the circle that is the x-y projection of the helix
- trajectory = new Helix(origin,1/o,p,lambda);
+
+ SpacePoint ref = t.getReferencePoint();
+ double x = ref.x() - t.getParameter(d0)*sin(t.getParameter(phi0));
+ double y = ref.y() + t.getParameter(d0)*cos(t.getParameter(phi0));
+ double z = ref.z() + t.getParameter(z0);
+ SpacePoint origin = new CartesianPoint(x, y, z);
+ trajectory = new Helix(origin, 1/o, p, lambda);
spatialParms.isInvalid = true;
track=t;
}
+
public SpacePoint getPointAtDistance(double alpha)
{
- if (trajectory == null) throw new RuntimeException("Trajectory not set");
+ if (trajectory == null)
+ throw new RuntimeException("Trajectory not set");
return trajectory.getPointAtDistance(alpha);
}
+
public double getDistanceToRadius(double r)
{
if (trajectory == null) throw new RuntimeException("Trajectory not set");
return trajectory.getDistanceToInfiniteCylinder(r);
}
+
public double getDistanceToZ(double z)
{
if (trajectory == null) throw new RuntimeException("Trajectory not set");
@@ -113,6 +116,7 @@
if (result<0) result = trajectory.getDistanceToZPlane(-z);
return result;
}
+
public double getDistanceToCylinder(double r,double z)
{
double x1 = getDistanceToRadius(r);
@@ -145,6 +149,7 @@
double pz = p_t*t;
return new CartesianPoint(px, py, pz);
}
+
public Trajectory getTrajectory() {
return trajectory;
}
lcsim/src/org/lcsim/contrib/JanStrube/tracking
diff -u -r1.1 -r1.2
--- NewFastMCTrackFactory.java 13 Jul 2006 10:53:58 -0000 1.1
+++ NewFastMCTrackFactory.java 15 Jul 2006 09:12:45 -0000 1.2
@@ -1,43 +1,58 @@
/**
- * @version $Id: NewFastMCTrackFactory.java,v 1.1 2006/07/13 10:53:58 jstrube Exp $
+ * @version $Id: NewFastMCTrackFactory.java,v 1.2 2006/07/15 09:12:45 jstrube Exp $
*/
package org.lcsim.contrib.JanStrube.tracking;
+import static java.lang.Math.PI;
+import static java.lang.Math.abs;
+import static java.lang.Math.atan2;
+import static java.lang.Math.cos;
+import static java.lang.Math.sin;
+import static java.lang.Math.sqrt;
+import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.d0;
+import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.omega;
+import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.phi0;
+import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.tanLambda;
+import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.z0;
+import static org.lcsim.contrib.JanStrube.tracking.Constants.fieldConversion;
+
import java.io.IOException;
import java.util.Random;
import org.lcsim.conditions.ConditionsManager;
import org.lcsim.conditions.ConditionsSet;
+import org.lcsim.event.EventHeader;
import org.lcsim.geometry.Detector;
import org.lcsim.mc.fast.tracking.ResolutionTable;
import org.lcsim.mc.fast.tracking.SimpleTables;
import org.lcsim.mc.fast.tracking.TrackResolutionTables;
import org.lcsim.spacegeom.SpacePoint;
+import Jama.EigenvalueDecomposition;
import Jama.Matrix;
-import static java.lang.Math.abs;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.d0;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.phi0;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.omega;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.z0;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.tanLambda;
-import static org.lcsim.contrib.JanStrube.tracking.Track.ParameterName.pt;
/**
* @author jstrube
+ * This class creates a new FastMC Track. It is used as the interface between the track measurement and the detector.
+ * Since Track doesn't know anything about the magnetic field, and the material, it cannot transport its own parameters.
+ * Changing the reference point of a track requires swimming; it is therefore done in this class.
*
*/
public class NewFastMCTrackFactory {
private TrackResolutionTables _tables;
private SimpleTables _simpleTables;
private ConditionsManager _manager;
- private final static double Bz = 5.;
+ private double _Bz;
private HelixSwimmer _swimmer;
- public NewFastMCTrackFactory(String detector, boolean beamConstraint) {
+ public NewFastMCTrackFactory(EventHeader event, boolean beamConstraint) {
+ String detectorName = event.getDetectorName();
+ Detector detector = event.getDetector();
+ // We want always the z component of the field at 0, 0, 0
+ _Bz = detector.getFieldMap().getField(new double[3])[2];
_manager = ConditionsManager.defaultInstance();
try {
- _manager.setDetector(detector, 0);
+ _manager.setDetector(detectorName, 0);
} catch (ConditionsManager.ConditionsNotFoundException e) {
}
ConditionsSet trackParameters = _manager.getConditions("TrackParameters");
@@ -47,31 +62,31 @@
_simpleTables = new SimpleTables(simpleTrack);
} catch (IOException e) {
}
- _swimmer = new HelixSwimmer(Bz);
+ _swimmer = new HelixSwimmer(_Bz);
}
- public Track getTrack(
- SpacePoint momentum
- , SpacePoint location
- , SpacePoint referencePoint
- , int charge
- , Random random) {
+ public Track getTrack(SpacePoint momentum, SpacePoint location, SpacePoint referencePoint, int charge, Random random) {
_swimmer.setTrack(momentum, location, charge);
double alpha = _swimmer.getDistanceToPoint(referencePoint);
SpacePoint poca = _swimmer.getPointAtDistance(alpha);
SpacePoint momentumAtPoca = _swimmer.getMomentumAtDistance(alpha);
EMap parameters = new EMap();
- parameters.set(d0, 0);
- parameters.set(phi0, 0);
- parameters.set(omega, 0);
- parameters.set(tanLambda, 0);
- parameters.set(z0, 0);
- parameters.set(pt, 0);
+ parameters.pt = momentumAtPoca.rxy();
+ parameters.set(phi0, atan2(momentumAtPoca.y(), momentumAtPoca.x()));
+ parameters.set(d0, - (poca.x() - referencePoint.x())
+ * sin(parameters.get(phi0))
+ + (poca.y() - referencePoint.y())
+ * cos(parameters.get(phi0)));
+ parameters.set(omega, charge * _Bz * fieldConversion / parameters.pt);
+ parameters.set(tanLambda, momentumAtPoca.z()/parameters.pt);
+ parameters.set(z0, poca.z()-referencePoint.z());
Matrix errorMatrix = new Matrix(5, 5);
// this sets the measurement error
double cosTheta = abs(momentumAtPoca.cosTheta());
double p_mag = momentumAtPoca.magnitude();
- ResolutionTable table = cosTheta < _tables.getPolarInner() ? _tables.getBarrelTable() : _tables.getEndcapTable();
+ ResolutionTable table = cosTheta < _tables.getPolarInner()
+ ? _tables.getBarrelTable()
+ : _tables.getEndcapTable();
errorMatrix = new Matrix(5, 5);
for (int i = 0; i < 5; i++ ) {
for (int j = 0; j <= i; j++ ) {
@@ -82,29 +97,51 @@
}
}
}
+ smearParameters(parameters, errorMatrix, random);
return new NewTrack(referencePoint, parameters, errorMatrix, charge);
}
- Track getTrack(
- SpacePoint momentum
- , SpacePoint location
- , SpacePoint referencePoint
- , int charge) {
+ private EMap smearParameters(EMap oldParams, Matrix errorMatrix, Random random) {
+ EigenvalueDecomposition eigen = errorMatrix.eig();
+ double[] realEigen = eigen.getRealEigenvalues();
+ double[] imaginaryEigen = eigen.getImagEigenvalues();
+ Matrix eigenValues = eigen.getV();
+ if (eigenValues.det() == 0) {
+ throw new RuntimeException("ErrorMatrix does not have orthogonal basis");
+ }
+ for (int i = 0; i < imaginaryEigen.length; i++ ) {
+ if (imaginaryEigen[i] != 0)
+ throw new RuntimeException("ErrorMatrix has imaginary eigenvalues");
+ }
+ Matrix x = new Matrix(5, 1);
+ for (int i = 0; i < 5; i++ ) {
+ if (realEigen[i] <= 0)
+ throw new RuntimeException("non-positive eigenvalue encountered");
+ x.set(i, 0, sqrt(realEigen[i]) * random.nextGaussian());
+ }
+ Matrix shift = eigenValues.times(x);
+ Matrix params = new Matrix(oldParams.values, 5);
+ // calculate the new parameters
+ double[] parameters = params.plus(shift).getColumnPackedCopy();
+ double pt = oldParams.pt * oldParams.get(omega) / parameters[omega.ordinal()];
+ // adjust the new parameters if necessary
+ if (parameters[phi0.ordinal()] > PI) {
+ parameters[phi0.ordinal()] -= 2 * PI;
+ } else if (parameters[phi0.ordinal()] < -PI) {
+ parameters[phi0.ordinal()] += 2 * PI;
+ }
+ return new EMap(parameters, pt);
+ }
+
+ Track getTrack(SpacePoint momentum, SpacePoint location, SpacePoint referencePoint, int charge) {
return getTrack(momentum, location, referencePoint, charge, new Random());
}
- Track getTrack(
- SpacePoint momentum
- , SpacePoint location
- , int charge
- , Random random) {
+ Track getTrack(SpacePoint momentum, SpacePoint location, int charge, Random random) {
return getTrack(momentum, location, new SpacePoint(), charge, random);
}
- Track getTrack(
- SpacePoint momentum
- , SpacePoint location
- , int charge) {
+ Track getTrack(SpacePoint momentum, SpacePoint location, int charge) {
return getTrack(momentum, location, new SpacePoint(), charge, new Random());
}
lcsim/src/org/lcsim/contrib/JanStrube/vtxFitter
diff -N vertexing.lyx
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ vertexing.lyx 15 Jul 2006 09:12:47 -0000 1.1
@@ -0,0 +1,268 @@
+#LyX 1.4.1 created this file. For more info see http://www.lyx.org/
+\lyxformat 245
+\begin_document
+\begin_header
+\textclass article
+\language english
+\inputencoding auto
+\fontscheme default
+\graphics default
+\paperfontsize default
+\spacing single
+\papersize default
+\use_geometry false
+\use_amsmath 2
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 2
+\paperpagestyle default
+\tracking_changes false
+\output_changes true
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Vertexing in org.lcsim
+\end_layout
+
+\begin_layout Section
+Track Parametrization at the point of closest approach to a reference point
+\end_layout
+
+\begin_layout Standard
+The track of a charged particle in a magnetic field is uniquely identified
+ by a five-component measurement vector.
+ However, since the track is supposed to represent a charged physical unity,
+ the physical properties of which cannot be restored from only these five
+ parameters, the class that represents the track in the org.lcsim was awarded
+ a parameter
+\begin_inset Formula $p_{t}$
+\end_inset
+
+ for computational convenience.
+ It should be noted that this parameter is not part of the measurement vector
+ and the covariance matrix is a
+\begin_inset Formula $5\times5$
+\end_inset
+
+ element symmetric table.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename helixDef.png
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+From physical quantities to track parameters
+\end_layout
+
+\begin_layout Standard
+Given an abitrary reference point with respect to which the parameters are
+ defined, and a point in space and a momentum, the track of the particle
+ that has the given momentum at this point can be parameterized by a helix,
+ which is then swum to the point of closest approach to the reference point,
+ and the momentum at this point
+\begin_inset Formula $P^{0}$
+\end_inset
+
+is then calculated.
+ The track parameters are computed by the following equations:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+pt & =\sqrt{p_{x}^{2}+p_{y}^{2}}\\
+\omega & =aq\frac{B_{z}}{p_{t}}\\
+\phi_{0} & =\text{atan2}(py,px)\\
+\tan(\lambda) & =\frac{p_{z}}{p_{t}}\\
+z_{0} & =P_{z}^{0}-P_{z}^{\text{r}}\\
+d_{0} & =-(P_{x}^{0}-P_{x}^{\text{r}})\sin(\phi_{0})+(P_{y}^{0}-P_{y}^{\text{r}})\cos(\phi_{0})\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+with the unit conversion constant
+\begin_inset Formula $a=p_{t}/(qB_{z}r)$
+\end_inset
+
+ and therefore
+\begin_inset Formula $[a]=1$
+\end_inset
+
+, specifically
+\begin_inset Formula $a=\text{GeV}/(ce\text{ T mm})=3335.641$
+\end_inset
+
+, where
+\begin_inset Formula $c$
+\end_inset
+
+ is the speed of light, and
+\begin_inset Formula $e$
+\end_inset
+
+ is the charge of the proton.
+\end_layout
+
+\begin_layout Subsection
+From track parameters to physical quantities
+\end_layout
+
+\begin_layout Standard
+Conversely, the physical quantities position and momentum at the point of
+ closest approach can also be computed given the track parameters:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+p_{t} & =\left|\frac{qaB_{z}}{\omega}\right|\\
+p_{x} & =p_{t}\cos(\phi_{0})\\
+p_{y} & =p_{t}\sin(\phi_{0})\\
+p_{z} & =p_{t}\tan(\lambda)\\
+x & =P_{x}^{\text{r}}-d_{0}\sin(\phi_{0})\\
+y & =P_{y}^{\text{r}}+d_{0}\cos(\phi_{0})\\
+z & =P_{z}^{\text{r}}+z_{0}\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+General parameterization
+\end_layout
+
+\begin_layout Subsection
+From track parameters to space and momentum
+\end_layout
+
+\begin_layout Standard
+Once the reference point and the track parameters have been determined,
+ any point along the track can simply be parametrized by the length along
+ the trajectory
+\begin_inset Formula $L$
+\end_inset
+
+.
+ We find:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+x & =P_{x}^{\text{r}}+(r-d_{0})\sin(\phi_{0})-r\sin(\phi)\\
+y & =P_{y}^{\text{r}}-(r-d_{0})\cos(\phi_{0})+r\cos(\phi)\\
+z & =P_{z}^{\text{r}}+z_{0}+l\tan(\lambda)\\
+p_{x} & =p_{t}\cos(\phi)\\
+p_{y} & =p_{t}\sin(\phi)\\
+p_{z} & =p_{t}\tan(\lambda)\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+with the tracklength in the x-y plane
+\begin_inset Formula $l=L\cos(\lambda)=L/\sqrt{1+\tan^{2}(\lambda)}$
+\end_inset
+
+,
+\begin_inset Formula $\phi=\phi_{0}-\omega l$
+\end_inset
+
+,
+\begin_inset Formula $r=1/\omega$
+\end_inset
+
+.
+ It is noteworthy that the right-hand side of each equation is expressed
+ exclusively in terms of the track measurements and the tracklength parameter.
+\end_layout
+
+\begin_layout Subsection
+From space and momentum to track parameters
+\end_layout
+
+\begin_layout Standard
+This set of equations can be inverted to give the measurement in terms of
+ physical quantities:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+\tan(\lambda) & =\frac{p_{z}}{p_{t}}\\
+z_{0} & =z-P_{z}^{\text{r}}-l\frac{p_{z}}{p_{t}}\\
+\omega & =\frac{aqB_{z}}{p_{t}}\\
+\phi_{0} & =\text{atan2}(\tilde{p}_{y},\tilde{p}_{x})\\
+d_{0} & =\frac{p_{t}-\tilde{p}_{t}}{aqB_{z}}\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+with the abbreviations
+\begin_inset Formula $p_{t}=\sqrt{p_{x}^{2}+p_{y}^{2}}$
+\end_inset
+
+,
+\begin_inset Formula $\tilde{x}=x-P_{x}^{\text{r}}$
+\end_inset
+
+,
+\begin_inset Formula $\tilde{y}=y-P_{y}^{\text{r}}$
+\end_inset
+
+,
+\begin_inset Formula $\tilde{p}_{x}=p_{x}-aqB_{z}\tilde{y}$
+\end_inset
+
+,
+\begin_inset Formula $\tilde{p}_{y}=p_{y}+aqB_{z}\tilde{x}$
+\end_inset
+
+,
+\begin_inset Formula $\tilde{p}_{t}=\sqrt{\tilde{p}_{x}^{2}+\tilde{p}_{y}^{2}}$
+\end_inset
+
+,
+\begin_inset Formula $\phi=\text{atan2}(p_{y},p_{x})$
+\end_inset
+
+,
+\begin_inset Formula $l=(\phi_{0}-\phi)p_{t}/qaB_{z}$
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Subsection
+Derivatives of the track parameters wrt.
+ space and momentum components
+\end_layout
+
+\begin_layout Standard
+With these conventions established, the derivatives wrt.
+ the components of space and momentum can be written as follows:
+\end_layout
+
+\end_body
+\end_document
lcsim/src/org/lcsim/contrib/JanStrube/vtxFitter
diff -N helixDef.svg
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ helixDef.svg 15 Jul 2006 09:12:47 -0000 1.1
@@ -0,0 +1,313 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+<svg
+ xmlns:dc="http://purl.org/dc/elements/1.1/"
+ xmlns:cc="http://web.resource.org/cc/"
+ xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+ xmlns:svg="http://www.w3.org/2000/svg"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:sodipodi="http://inkscape.sourceforge.net/DTD/sodipodi-0.dtd"
+ xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ width="612pt"
+ height="792pt"
+ id="svg2"
+ sodipodi:version="0.32"
+ inkscape:version="0.43"
+ sodipodi:docbase="/home/jstrube/Workspace/lcsim/src/org/lcsim/contrib/JanStrube/vtxFitter"
+ sodipodi:docname="helixDef.svg"
+ version="1.0"
+ inkscape:export-filename="/home/jstrube/Workspace/lcsim/src/org/lcsim/contrib/JanStrube/vtxFitter/helixDef.png"
+ inkscape:export-xdpi="90"
+ inkscape:export-ydpi="90">
+ <defs
+ id="defs4" />
+ <sodipodi:namedview
+ id="base"
+ pagecolor="#ffffff"
+ bordercolor="#666666"
+ borderopacity="1.0"
+ inkscape:pageopacity="0.0"
+ inkscape:pageshadow="2"
+ inkscape:zoom="1.4142136"
+ inkscape:cx="375"
+ inkscape:cy="720.37227"
+ inkscape:document-units="px"
+ inkscape:current-layer="layer1"
+ showgrid="true"
+ showguides="true"
+ inkscape:window-width="1390"
+ inkscape:window-height="971"
+ inkscape:window-x="0"
+ inkscape:window-y="25"
+ inkscape:grid-points="true"
+ inkscape:guide-bbox="true"
+ inkscape:guide-points="true" />
+ <metadata
+ id="metadata7">
+ <rdf:RDF>
+ <cc:Work
+ rdf:about="">
+ <dc:format>image/svg+xml</dc:format>
+ <dc:type
+ rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+ <cc:license
+ rdf:resource="http://artlibre.org/licence.php/lalgb.html" />
+ </cc:Work>
+ <cc:License
+ rdf:about="http://artlibre.org/licence.php/lalgb.html">
+ <cc:permits
+ rdf:resource="http://web.resource.org/cc/Reproduction" />
+ <cc:permits
+ rdf:resource="http://web.resource.org/cc/Distribution" />
+ <cc:permits
+ rdf:resource="http://web.resource.org/cc/DerivativeWorks" />
+ <cc:requires
+ rdf:resource="http://web.resource.org/cc/ShareAlike" />
+ <cc:requires
+ rdf:resource="http://web.resource.org/cc/Notice" />
+ <cc:requires
+ rdf:resource="http://web.resource.org/cc/Attribution" />
+ </cc:License>
+ </rdf:RDF>
+ </metadata>
+ <g
+ inkscape:label="Layer 1"
+ inkscape:groupmode="layer"
+ id="layer1">
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:2,2;stroke-dashoffset:0"
+ d="M 139,336 C 178,353 177.4838,353 177.4838,353 L 177.4838,353"
+ id="path7480" />
+ <path
+ sodipodi:type="arc"
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1.82930291;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+ id="path1307"
+ sodipodi:cx="290"
+ sodipodi:cy="379.50504"
+ sodipodi:rx="110"
+ sodipodi:ry="107.14286"
+ d="M 400 379.50504 A 110 107.14286 0 1 1 180,379.50504 A 110 107.14286 0 1 1 400 379.50504 z"
+ transform="matrix(1.081707,0,0,1.118968,-33.6928,-11.93845)" />
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ d="M 177,352.36218 C 229,352.36218 229,352.36218 229,352.36218"
+ id="path3065" />
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:2;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:8, 8;stroke-dashoffset:0;stroke-opacity:1"
+ d="M 177.30475,352.10099 C 214.69525,289.62338 214.69525,289.62338 214.69525,289.62338"
+ id="path3067" />
+ <path
+ sodipodi:type="arc"
+ style="fill:#0000e6;fill-opacity:1;stroke:none;stroke-width:2;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ id="path4837"
+ sodipodi:cx="119.50105"
+ sodipodi:cy="346.66962"
+ sodipodi:rx="2.1213202"
+ sodipodi:ry="2.1213202"
+ d="M 121.62237 346.66962 A 2.1213202 2.1213202 0 1 1 117.37973,346.66962 A 2.1213202 2.1213202 0 1 1 121.62237 346.66962 z"
+ transform="matrix(1.885618,0,0,1.885618,-47.74749,-301.3243)" />
+ <path
+ sodipodi:type="arc"
+ style="fill:#0000e6;fill-opacity:1;stroke:none;stroke-width:2;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ id="path6589"
+ sodipodi:cx="148.84598"
+ sodipodi:cy="306.01099"
+ sodipodi:rx="3.8890872"
+ sodipodi:ry="3.8890872"
+ d="M 152.73506 306.01099 A 3.8890872 3.8890872 0 1 1 144.95689,306.01099 A 3.8890872 3.8890872 0 1 1 152.73506 306.01099 z"
+ transform="translate(-7.735065,30.46211)" />
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="132.17383"
+ y="327.11023"
+ id="text7464"><tspan
+ sodipodi:role="line"
+ id="tspan7466"
+ x="132.17383"
+ y="327.11023">P</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="177.17383"
+ y="371.11023"
+ id="text7468"><tspan
+ sodipodi:role="line"
+ id="tspan7470"
+ x="177.17383"
+ y="371.11023">P</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="272.17383"
+ y="431.36218"
+ id="text7472"><tspan
+ sodipodi:role="line"
+ id="tspan7474"
+ x="272.17383"
+ y="431.36218">P</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="367.17383"
+ y="305"
+ id="text7476"><tspan
+ sodipodi:role="line"
+ id="tspan7478"
+ x="367.17383"
+ y="305">P</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:8px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="279.09766"
+ y="423.48047"
+ id="text8355"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan8357"
+ x="279.09766"
+ y="423.48047">c</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:8px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="184.47266"
+ y="363"
+ id="text8359"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan8361"
+ x="184.47266"
+ y="363">0</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:8px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="139.27344"
+ y="316.48047"
+ id="text8363"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan8365"
+ x="139.27344"
+ y="316.48047">r</tspan></text>
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1.40838194;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:5.63352749, 5.63352749;stroke-dashoffset:0;stroke-opacity:1"
+ d="M 358.07472,322.45517 C 396,353 396,353 396,353"
+ id="path9242" />
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ d="M 359,324 C 411,324 411,324 411,324"
+ id="path9244" />
+ <path
+ sodipodi:type="arc"
+ style="fill:#f7090b;fill-opacity:1;stroke:none;stroke-width:2;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ id="path8367"
+ sodipodi:cx="148.84598"
+ sodipodi:cy="306.01099"
+ sodipodi:rx="3.8890872"
+ sodipodi:ry="3.8890872"
+ d="M 152.73506 306.01099 A 3.8890872 3.8890872 0 1 1 144.95689,306.01099 A 3.8890872 3.8890872 0 1 1 152.73506 306.01099 z"
+ transform="translate(209.154,16.8781)" />
+ <path
+ sodipodi:type="arc"
+ style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:2, 2;stroke-dashoffset:0;stroke-opacity:1"
+ id="path9248"
+ sodipodi:cx="210"
+ sodipodi:cy="338.5"
+ sodipodi:rx="39.935421"
+ sodipodi:ry="39.935421"
+ d="M 245.13585,357.48184 A 39.935421,39.935421 0 0 1 208.6922,378.414 L 210,338.5 z"
+ sodipodi:start="0.49532013"
+ sodipodi:end="1.60355"
+ transform="matrix(0,-0.928762,1.023997,0,-167.623,546.6729)" />
+ <path
+ sodipodi:type="arc"
+ style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:2, 2;stroke-dashoffset:0;stroke-opacity:1"
+ id="path9250"
+ sodipodi:cx="324.5"
+ sodipodi:cy="274.5"
+ sodipodi:rx="37.629944"
+ sodipodi:ry="37.629944"
+ d="M 362.12794,274.88836 A 37.629944,37.629944 0 0 1 353.52973,298.44342 L 324.5,274.5 z"
+ sodipodi:start="0.010320726"
+ sodipodi:end="0.6896748"
+ transform="matrix(1,0,0,0.938489,34.5,66.38467)" />
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="146.33789"
+ y="355"
+ id="text1330"><tspan
+ sodipodi:role="line"
+ id="tspan1332"
+ x="146.33789"
+ y="355">d</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:8px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="155"
+ y="358"
+ id="text1334"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan1336"
+ x="155"
+ y="358">0</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:SF Math Ext"
+ x="192.34375"
+ y="342.11719"
+ id="text1338"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan1342"
+ x="192.34375"
+ y="342.11719">ϕ</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:SF Math Ext"
+ x="380.34375"
+ y="335.11719"
+ id="text1344"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan1346"
+ x="380.34375"
+ y="335.11719">ϕ</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-size:8px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="198.44141"
+ y="346.88672"
+ id="text1348"
+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan1350"
+ x="198.44141"
+ y="346.88672">0</tspan></text>
+ <path
+ style="fill:none;fill-opacity:0.75;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+ d="M 281,293.49984 C 281,409.46535 281,409.46535 281,409.46535"
+ id="path1352" />
+ <text
+ xml:space="preserve"
+ style="font-size:12px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ x="285.67114"
+ y="350.06839"
+ id="text1354"><tspan
+ sodipodi:role="line"
+ id="tspan1356"
+ x="285.67114"
+ y="350.06839">R</tspan></text>
+ <path
+ sodipodi:type="arc"
+ style="fill:#13b01a;fill-opacity:1;stroke:none;stroke-width:2;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ id="path6587"
+ sodipodi:cx="148.84598"
+ sodipodi:cy="306.01099"
+ sodipodi:rx="3.8890872"
+ sodipodi:ry="3.8890872"
+ d="M 152.73506 306.01099 A 3.8890872 3.8890872 0 1 1 144.95689,306.01099 A 3.8890872 3.8890872 0 1 1 152.73506 306.01099 z"
+ transform="translate(132.2649,104.0999)" />
+ </g>
+</svg>
CVSspam 0.2.8
