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Revision: 2758
Author: anna.ata...@gmail.com
Date: Tue Feb 25 09:31:56 2014 UTC
Log: issue 133
Enhancement: forgotten to add the new files. Now they are added.
http://code.google.com/p/ellipsoids/source/detail?r=2758

Added:
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_ellTube.txt
/branches/issue_133_aatanesyan/doc/_build/html/chap_ellTube.html
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.aux
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.idx
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.log
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.out
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.pdf
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.toc
/branches/issue_133_aatanesyan/doc/_build/latex/python.ist

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--- /dev/null
+++
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_ellTube.txt
Tue Feb 25 09:31:56 2014 UTC
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+Ellipsoid tubes and touching curves
+===================================
+
+Touching curves
+---------------
+
+One of the basic insruments in the *Ellipsoidal Toolbox* are classes,
which allow to work with touching curves. These are the curves along which
the internal and external ellipsoidal approximations are touching. In
*Ellipsoidal Toolbox* there are two basic classes (*EllTubeTouchCurveBasic*
and *EllTubeTouchCurveProjBasic*) which allow us to keep touching curves
and their projections. These classes do not add any functionality, that we
can use, while working with the toolbox, (They do not have public methods.)
but they are further used in other classes, which inherit these ones.
+
+*EllTubeTouchCurveBasic* class
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+This class allows us to keep touch point curve objects. This kind of
objects have a lot of different fields, which store the information about
the touching curve.
+The first field of our object is:
+
+- *dim*: In this field the dimension of the space in which the touching
+ curves are defined is stored.
+
+Then there are several fields that are connecteld with time:
+
+- *timeVec*: Time vector in which the the touching curves are defined;
+
+- *sTime*: Specific point of time which is best suited to describe good
direction;
+
+- *indSTime*: The index of sTime point within timeVec is srored in this
field.
+
+It should be said that the *good direction* is the direction along which
the internal and external approximations of ellipsoid tubes are touching.
Next several fields specify the type of approximation which was used? while
creating these touching curves:
+
+- *approxSchemaName*: The name of the approximation schema;
+
+- *approxSchemaDescr*: The description of the approximation schema;
+
+- *approxType*: The type of approximation (External, Internal,
NotDefined) is stored in this field.
+
+Then there are two fields which keep the absolute tolerance and relative
tolerance used to create this object (*absTolerance* and *relTolerance*,
respectively). And finally come the fields which allow us to keep the
touching curves and good directions:
+
+- *ltGoodDirMat* field stores the matrix of good direction vectors at any
point of time from timeVec;
+
+- *lsGoodDirVec* field stores the good direction vector at sTime point of
time;
+
+- *ltGoodDirNormVec* field stores the norm of good direction vectors at
any point of time from timeVec;
+
+- *lsGoodDirNorm* field stores the norm of good direction vector at sTime
point of time;
+
+- *xTouchCurveMat* field stores the touch point curve for good direction
matrix;
+
+- *xTouchOpCurveMat* field stores the touch point curve oposite to the
xTouchCurveMat touch point curve;
+
+- *xsTouchVec* field stores the touch point at sTime point of time;
+
+- *xsTouchOpVec* field stores a point opposite to the xsTouchVec touch
point;
+
+- *isLsTouch* field stores a logical variable which indicates whether a
touch takes place along good direction at sTime point of time;
+
+- *isLtTouchVec* field stores a logical vector which indicates whether a
touch takes place along good direction at any point of time from
timeVec.
+
+*EllTubeTouchCurveProjBasic* class
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+This class allows us to keep the projections of touch point curves. This
kind of objects have a lot of different fields, which store the information
about the projection of touching curve. First of all it inherits all the
fields from *EllTubeTouchCurveBasic* class, and, secondly, it adds some of
its own fields. The inherited fields store the information about the
projection instead of the information about the original curve, but their
meaning is all the same.
+The first group of new fields is connected to the type of projection and
the space on which the curve is projected:
+
+- *projSMat* field stores the projection matrix at sTime point of time;
+
+- *projArray* field stores an array of projection matrices at any point
of time from timVec;
+
+- *projType* field stores the type of projection (Static or
DynamicAlongGoodCurve).
+
+And then come the new fields which store some information about the
original curve:
+
+- *ltGoodDirNormOrigVec* field stores the norm of the original good
direction vectors at any point of time from timeVec;
+- *lsGoodDirNormOrig* field stores the norm of the original good
direction vector at sTime point of time;
+
+- *ltGoodDirOrigMat* field stores the matrix of the original good
direction vectors at any point of time from timeVec;
+
+- *lsGoodDirOrigVec* field stores the original good direction vector at
sTime point of time;
+
+- *ltGoodDirNormOrigProjVec* field stores the norm of the projection of
the original good direction curve;
+
+- *ltGoodDirOrigProjMat* field stores the projectition of the original
good direction curve.
+
+Ellipsoidal tubes
+-----------------
+
+Other basic insrument in the *Ellipsoidal Toolbox* are classes, which
allow to work with ellipsoidal tubes. In *Ellipsoidal Toolbox* there are
four classes (*EllTubeBasic*, *EllTube*, *EllTubeProjBasic* and
*EllTubeProj*) which give us the needed functionality to work with
ellipsoid tube objects.
+
+*EllTubeBasic* class
+~~~~~~~~~~~~~~~~~~~~
+
+This class inherits its fields from *EllTubeTouchCurveBasic* class and
adds some new fields which are:
+
+- *QArray* field which stores an array of nTimePoints ellipsoid matrices.
Each element from this
+ array specifies an ellipsoid matrix at nTimePoint point of time. Here
nTimePoints is number of elements in *timeVec* (It is one of the fields
inherited from *EllTubeTouchCurveBasic* class.);
+
+- *aMat* field which stores an array of nTimePoints ellipsoid centers.
Each center is specified for nTimePoint point of time;
+
+- scaleFactor field which stores the scale for the created ellipsoid tube;
+
+- MArray field which stores an array of nTimePoints regularization
matrices. Each element from this array specifies a regularization
matrix at nTimePoint point of time.
+
+This class gives us some methods which can be used to work with
ellipsoidal tubes. For example, if we have already created ellipsoid tube
object using one timeVec vector of time, then we can interpolate this tube,
using new time vector. Take notice that we have to make sure that the first
and the last elements in old and new vectors of time are the same.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_interp.m
+ :language: matlab
+ :linenos:
+
+Other method that we can use is *THINOUTTUPLES* method. It allows us to
thin out the already created ellipsoid tube, by saving only the ellipsoids
at specified points of time.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_thinOutTuples.m
+ :language: matlab
+ :linenos:
+
+Then we can also cut the created ellipsoid tube, leaving only part of it
at specified vector of time or point of time. Below are the exmples:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_cut1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_cut2.m
+ :language: matlab
+ :linenos:
+
+*EllTube* class
+~~~~~~~~~~~~~~~
+
+This class inherits its fields from *EllTubeBasic* class. It does not have
any new fields, but adds some functionality. First of all it gives us the
instruments to create ellipsoid tube objects. Here are these methods:
+
+- *fromQArrays* - creates nEllTubes ellipsoid tube objects using an array
of ellipsoid matrices and an array of ellipsoid centers specified at
any point of time from timeVec;
+
+- *fromQMArrays* - acts the same way as *fromQArrays* method, except for
this one requires to specify an array of regularization marices
specified at any point of time from timeVec;
+
+- *fromQMScaledArrays* - acts the same way as *fromQMArrays* method,
except for this one requires to also specify a vector of scale
factors specified for every created ellipsoid tube;
+
+- *fromEllArray* - creates ellipsoid tube object using an array of
ellipsoids;
+
+- *fromEllMArray* - creates ellipsoid tube object using an array of
ellipsoids and an array of regularisation matrices.
+
+Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices and an array of ellipsoid centers or an array of ellipsoids. Below
are some examples of the usage of these functions.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays2.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMArrays1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMScaledArrays1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllArray.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllMArray.m
+ :language: matlab
+ :linenos:
+
+As we can see in these examples, we can specify how many ellipsoid tubes
we want to create, which type of arrpoximation to use. also we can create
ellipsoid tube objects, which will contain several ellipsoid tubes with
different types of approximation.
+We can also use *project* and *projectToOrths* methods to project our
ellipsoid tubes on the specified spaces. The first metod projects the
ellipsoid tube on specified space creating the specified type of projection.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_project.m
+ :language: matlab
+ :linenos:
+
+The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths2.m
+ :language: matlab
+ :linenos:
+
+*EllTubeProjBasic* class
+~~~~~~~~~~~~~~~~~~~~~~~~
+
+This class inherits its fields from *EllTubeBasic* and
*EllTubeTouchCurveProjBasic* classes. It does not have any new fields, but
holds not the original values of the fields, which were the values of the
original ellipsoid tube, it holds the values of the projection. We can use
*plot*, *plotInt* or *plotExt* methods to plot the projections.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plot.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotInt.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotExt.m
+ :language: matlab
+ :linenos:
+
+All the three methods have several properties connected to the properties
of the image, for example: transparency, color, line width and so on.
+
+*EllTubeProj* class
+~~~~~~~~~~~~~~~~~~~
+
+This class doesn't add any functionality to the *EllTubeProjBasic* class.
+
+Unions of ellipsoidal tubes
+---------------------------
+
+The last classes which will be discussed in this chapter are classes,
operating with unions of ellipsoid tubes. These are *EllUnionTubeBasic*,
*EllUnionTube* and *EllUnionTubeStaticProj* classes.
+
+*EllUnionTubeBasic* class
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+This class allows us to keep and work with unions of ellipsoid tubes. The
fields of this class are:
+
+- *ellUnionTimeDirection* which stores the direction in time along which
union is performed;
+
+- *timeTouchEndVec* which stores the points of time when touch is occured
in good direction;
+
+- *timeTouchOpEndVec* which stores the points of time when touch is
occured in direction opposite to good direction;
+
+- *isLsTouchOp* which stores a logical variable which indicates whether a
touch takes place along the direction opposite to the good direction at
sTime point of time;
+
+- *isLtTouchOpVec* which stores a logical variable which indicates
whether a touch takes place along the direction opposite to the good
direction at any point of time from timeVec.
+
+This class does not have any public methods.
+
+*EllUnionTube* class
+~~~~~~~~~~~~~~~~~~~~
+
+This class inherits its fields from *EllUnionTubeBasic* and *EllTubeBasic*
classes. Unlike *EllUnionTubeBasic* class, this class has one public method
- *fromEllTubes* method, which allows us to create an ellUnionTube object
using ellipsoid tubes.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllTubes.m
+ :language: matlab
+ :linenos:
+
+*EllUnionTubeStaticProj* class
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The last class connected to ellUnionTube objects is
*EllUnionTubeStaticProj* class. It inherits the fields and methods of
*EllUnionTubeBasic* and *EllTubeProjBasic* classes and allows us to work
with the static projections of ellUnionTubes.
+
+*TypifiedByFieldCodeRel* class
+----------------------------
+
+This is the last class that should be mentioned in this chapter. It is
inherited by *EllTube*, *EllTubeProj*, *EllUnionTube* and
*EllUnionTubeStaticProj* classes and adds some methods to them. For example
we can use *getData* method.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getData.m
+ :language: matlab
+ :linenos:
+
+Or we can compare objects from above mentioned classes using method
*isEqual*.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual1.m
+ :language: matlab
+ :linenos:
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual2.m
+ :language: matlab
+ :linenos:
=======================================
--- /dev/null
+++ /branches/issue_133_aatanesyan/doc/_build/html/chap_ellTube.html Tue
Feb 25 09:31:56 2014 UTC
@@ -0,0 +1,1276 @@
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+ <div class="body">
+
+ <div class="section" id="ellipsoid-tubes-and-touching-curves">
+<h1>Ellipsoid tubes and touching curves<a class="headerlink"
href="#ellipsoid-tubes-and-touching-curves" title="Permalink to this
headline">¶</a></h1>
+<div class="section" id="touching-curves">
+<h2>Touching curves<a class="headerlink" href="#touching-curves"
title="Permalink to this headline">¶</a></h2>
+One of the basic insruments in the Ellipsoidal Toolbox are
classes, which allow to work with touching curves. These are the curves
along which the internal and external ellipsoidal approximations are
touching. In Ellipsoidal Toolbox there are two basic classes
(EllTubeTouchCurveBasic and EllTubeTouchCurveProjBasic)
which allow us to keep touching curves and their projections. These classes
do not add any functionality, that we can use, while working with the
toolbox, (They do not have public methods.) but they are further used in
other classes, which inherit these ones.
+<div class="section" id="elltubetouchcurvebasic-class">
+<h3>EllTubeTouchCurveBasic class<a class="headerlink"
href="#elltubetouchcurvebasic-class" title="Permalink to this
headline">¶</a></h3>
+This class allows us to keep touch point curve objects. This kind of
objects have a lot of different fields, which store the information about
the touching curve.
+The first field of our object is:
+<ul class="simple">
+<li>dim: In this field the dimension of the space in which the
touching
+curves are defined is stored.</li>
+</ul>
+Then there are several fields that are connecteld with time:
+<ul class="simple">
+<li>timeVec: Time vector in which the the touching curves are
defined;</li>
+<li>sTime: Specific point of time which is best suited to
describe good direction;</li>
+<li>indSTime: The index of sTime point within timeVec is srored
in this field.</li>
+</ul>
+It should be said that the good direction is the direction
along which the internal and external approximations of ellipsoid tubes are
touching. Next several fields specify the type of approximation which was
used? while creating these touching curves:
+<ul class="simple">
+<li>approxSchemaName: The name of the approximation schema;</li>
+<li>approxSchemaDescr: The description of the approximation
schema;</li>
+<li>approxType: The type of approximation (External, Internal,
NotDefined) is stored in this field.</li>
+</ul>
+Then there are two fields which keep the absolute tolerance and
relative tolerance used to create this object (absTolerance and
relTolerance, respectively). And finally come the fields which
allow us to keep the touching curves and good directions:
+<ul class="simple">
+<li>ltGoodDirMat field stores the matrix of good direction
vectors at any point of time from timeVec;</li>
+<li>lsGoodDirVec field stores the good direction vector at sTime
point of time;</li>
+<li>ltGoodDirNormVec field stores the norm of good direction
vectors at any point of time from timeVec;</li>
+<li>lsGoodDirNorm field stores the norm of good direction vector
at sTime point of time;</li>
+<li>xTouchCurveMat field stores the touch point curve for good
direction matrix;</li>
+<li>xTouchOpCurveMat field stores the touch point curve oposite
to the xTouchCurveMat touch point curve;</li>
+<li>xsTouchVec field stores the touch point at sTime point of
time;</li>
+<li>xsTouchOpVec field stores a point opposite to the xsTouchVec
touch point;</li>
+<li>isLsTouch field stores a logical variable which indicates
whether a touch takes place along good direction at sTime point of
time;</li>
+<li>isLtTouchVec field stores a logical vector which indicates
whether a touch takes place along good direction at any point of
time from timeVec.</li>
+</ul>
+</div>
+<div class="section" id="elltubetouchcurveprojbasic-class">
+<h3>EllTubeTouchCurveProjBasic class<a class="headerlink"
href="#elltubetouchcurveprojbasic-class" title="Permalink to this
headline">¶</a></h3>
+This class allows us to keep the projections of touch point curves.
This kind of objects have a lot of different fields, which store the
information about the projection of touching curve. First of all it
inherits all the fields from EllTubeTouchCurveBasic class, and,
secondly, it adds some of its own fields. The inherited fields store the
information about the projection instead of the information about the
original curve, but their meaning is all the same.
+The first group of new fields is connected to the type of projection and
the space on which the curve is projected:
+<ul class="simple">
+<li>projSMat field stores the projection matrix at sTime point of
time;</li>
+<li>projArray field stores an array of projection matrices at any
point of time from timVec;</li>
+<li>projType field stores the type of projection (Static or
DynamicAlongGoodCurve).</li>
+</ul>
+And then come the new fields which store some information about the
original curve:
+<ul class="simple">
+<li>ltGoodDirNormOrigVec field stores the norm of the original
good direction vectors at any point of time from timeVec;</li>
+<li>lsGoodDirNormOrig field stores the norm of the original good
direction vector at sTime point of time;</li>
+<li>ltGoodDirOrigMat field stores the matrix of the original good
direction vectors at any point of time from timeVec;</li>
+<li>lsGoodDirOrigVec field stores the original good direction
vector at sTime point of time;</li>
+<li>ltGoodDirNormOrigProjVec field stores the norm of the
projection of the original good direction curve;</li>
+<li>ltGoodDirOrigProjMat field stores the projectition of the
original good direction curve.</li>
+</ul>
+</div>
+</div>
+<div class="section" id="ellipsoidal-tubes">
+<h2>Ellipsoidal tubes<a class="headerlink" href="#ellipsoidal-tubes"
title="Permalink to this headline">¶</a></h2>
+Other basic insrument in the Ellipsoidal Toolbox are classes,
which allow to work with ellipsoidal tubes. In Ellipsoidal Toolbox
there are four classes (EllTubeBasic, EllTube,
EllTubeProjBasic and EllTubeProj) which give us the
needed functionality to work with ellipsoid tube objects.
+<div class="section" id="elltubebasic-class">
+<h3>EllTubeBasic class<a class="headerlink"
href="#elltubebasic-class" title="Permalink to this headline">¶</a></h3>
+This class inherits its fields from EllTubeTouchCurveBasic
class and adds some new fields which are:
+<ul class="simple">
+<li>QArray field which stores an array of nTimePoints ellipsoid
matrices. Each element from this
+array specifies an ellipsoid matrix at nTimePoint point of time. Here
nTimePoints is number of elements in timeVec (It is one of the
fields inherited from EllTubeTouchCurveBasic class.);</li>
+<li>aMat field which stores an array of nTimePoints ellipsoid
centers. Each center is specified for nTimePoint point of time;</li>
+<li>scaleFactor field which stores the scale for the created ellipsoid
tube;</li>
+<li>MArray field which stores an array of nTimePoints regularization
matrices. Each element from this array specifies a regularization
matrix at nTimePoint point of time.</li>
+</ul>
+This class gives us some methods which can be used to work with
ellipsoidal tubes. For example, if we have already created ellipsoid tube
object using one timeVec vector of time, then we can interpolate this tube,
using new time vector. Take notice that we have to make sure that the first
and the last elements in old and new vectors of time are the same.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25</pre></div></td><td class="code"><div class="highlight"><pre>% An example of usage of INTERP function from EllTubeBasic class.
In this
+% example an ellipsoid tube object is created, using
oldTimeVec time
+% vector. Then it is interpolated on newTimeVec time
vector.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+newnPoints=100;
+newTimeVec = (1/nPoints):(1/newnPoints):1;
+interpEllTube = fromMatEllTube.interp(newTimeVec);
+</pre></div>
+</td></tr></table></div>
+Other method that we can use is THINOUTTUPLES method. It
allows us to thin out the already created ellipsoid tube, by saving only
the ellipsoids at specified points of time.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25</pre></div></td><td class="code"><div class="highlight"><pre>% An example of usage of THINOUTTUPLES function from EllTubeBasic
class. In
+% this example an ellipsoid tube object is created, using
TimeVec time
+% vector. Then it is thinned out using indVec vector of
indices of elements
+% from timeVec.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+indVec = randi(nPoints,1,5);
+thinOutEllTube = fromMatEllTube.thinOutTuples(indVec);
+</pre></div>
+</td></tr></table></div>
+Then we can also cut the created ellipsoid tube, leaving only part of
it at specified vector of time or point of time. Below are the exmples:
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24</pre></div></td><td class="code"><div class="highlight"><pre>% An example of usage of CUT function from EllTubeBasic class.
In
+% this example an ellipsoid tube object is created, using
TimeVec time
+% vector. Then it is cut using cutTimeVec time
vector.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+cutTimeVec = [timeVec(2) timeVec(7)];
+cutVecEllTube = fromMatEllTube.cut(cutTimeVec);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25</pre></div></td><td class="code"><div class="highlight"><pre>% An example of usage of CUT function from EllTubeBasic class.
In
+% this example an ellipsoid tube object is created, using
TimeVec time
+% vector. Then it is cut using cutTimePoint point
+% of time.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+cutTimePoint = timeVec(randi(nPoints,1));
+cutPointEllTube = fromMatEllTube.cut(cutTimePoint);
+</pre></div>
+</td></tr></table></div>
+</div>
+<div class="section" id="elltube-class">
+<h3>EllTube class<a class="headerlink" href="#elltube-class"
title="Permalink to this headline">¶</a></h3>
+This class inherits its fields from EllTubeBasic class. It
does not have any new fields, but adds some functionality. First of all it
gives us the instruments to create ellipsoid tube objects. Here are these
methods:
+<ul class="simple">
+<li>fromQArrays - creates nEllTubes ellipsoid tube objects using
an array of ellipsoid matrices and an array of ellipsoid centers
specified at any point of time from timeVec;</li>
+<li>fromQMArrays - acts the same way as fromQArrays
method, except for this one requires to specify an array of
regularization marices specified at any point of time from timeVec;</li>
+<li>fromQMScaledArrays - acts the same way as
fromQMArrays method, except for this one requires to also
specify a vector of scale factors specified for every created ellipsoid
tube;</li>
+<li>fromEllArray - creates ellipsoid tube object using an array
of ellipsoids;</li>
+<li>fromEllMArray - creates ellipsoid tube object using an array
of ellipsoids and an array of regularisation matrices.</li>
+</ul>
+Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices and an array of ellipsoid centers or an array of ellipsoids. Below
are some examples of the usage of these functions.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromQArrays
+% function with the same type of approximation.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=3;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromQArrays
+% function with different types of approximation.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr={'Internal'; 'External'; 'External'};
+approxSchemaName={'Internal'; 'External'; 'External'};
+nDims=3;
+nTubes=3;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=[gras.ellapx.enums.EApproxType.Internal,...
+ gras.ellapx.enums.EApproxType.External,...
+ gras.ellapx.enums.EApproxType.External]';
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromQMArrays
+% function with the same type of approximation.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='External';
+approxSchemaName='External';
+nDims=3;
+nTubes=3;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.External;
+mArrayList=repmat({repmat(diag([0.1
0.2 0.3]),[1,1,nPoints])},...
+ 1,nTubes);
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatMEllTube=gras.ellapx.smartdb.rels.EllTube.fromQMArrays(...
+ qArrayList, aMat, mArrayList, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays
+% function with the same type of approximation.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=5;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+mArrayList=repmat({repmat(diag([0.1
0.2 0.3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+scaleFactor = ones(1,nTubes);
+fromQMScaledArraysEllTube =
...
+ gras.ellapx.smartdb.rels.EllTube.fromQMScaledArrays(...
+ qArrayList,aMat,mArrayList,timeVec,...
+ ltGoodDirArray,sTime,approxType,approxSchemaName,...
+ approxSchemaDescr,absTol, relTol,...
+ scaleFactor);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromEllArray
+% function.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+ellArray(nPoints) =
ellipsoid();
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},1,1);
+for iElem = 1:nPoints
+ ellArray(iElem) =
ellipsoid(aMat(:,iElem), qArrayList{1}(:,:,iElem));
+end;
+ellnArray = repmat(ellArray,nTubes,1);
+fromEllArrayEllTube = gras.ellapx.smartdb.rels.EllTube.fromEllArray(...
+ ellnArray,timeVec, ltGoodDirArray, sTime, approxType,...
+ approxSchemaName,approxSchemaDescr, absTol, relTol);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27</pre></div></td><td class="code"><div class="highlight"><pre>% An example of creating nTubes ellipsoid tube objects using
fromEllMArray
+% function.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+ellArray(nPoints) =
ellipsoid();
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},1,1);
+for iElem = 1:nPoints
+ ellArray(iElem) =
ellipsoid(aMat(:,iElem), qArrayList{1}(:,:,iElem));
+end;
+ellnArray = repmat(ellArray,nTubes,1);
+mArrayList=repmat({repmat(diag([0.1
0.2 0.3]),[1,1,nPoints])},...
+ 1,nTubes);
+fromEllMArrayEllTube=...
+ gras.ellapx.smartdb.rels.EllTube.fromEllMArray(...
+ ellArray, mArrayList{1}, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+</pre></div>
+</td></tr></table></div>
+As we can see in these examples, we can specify how many ellipsoid
tubes we want to create, which type of arrpoximation to use. also we can
create ellipsoid tube objects, which will contain several ellipsoid tubes
with different types of approximation.
+We can also use project and projectToOrths methods to
project our ellipsoid tubes on the specified spaces. The first metod
projects the ellipsoid tube on specified space creating the specified type
of projection.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26</pre></div></td><td class="code"><div class="highlight"><pre>% An example of calculating ellipsoid tube object projection
using project
+% function.
+nPoints=5;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr=char.empty(1,0);
+approxSchemaName=char.empty(1,0);
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=1:nPoints;
+sTime=nPoints;
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProjRel,indProj2OrigVec] = fromMatEllTube.project(projType,...
+ {projMat},p);
+</pre></div>
+</td></tr></table></div>
+The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25</pre></div></td><td class="code"><div class="highlight"><pre>% Examples of calculating ellipsoid tube object projection to
basic orths 
+% using PROJECTTOORTHS function. This is an example of
projectToOrths usage 
+% with one input variable. The default value of projection
type is used.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+ellTubeProjRel = fromMatEllTube.projectToOrths([1,2]);
+plObj=smartdb.disp.RelationDataPlotter();
+ellTubeProjRel.plot(plObj);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26</pre></div></td><td class="code"><div class="highlight"><pre>% Examples of calculating ellipsoid tube object projection to
basic orths 
+% using PROJECTTOORTHS function. This is an example of
projectToOrths usage 
+% with specified projection type.
+nPoints=10;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr='Internal';
+approxSchemaName='Internal';
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+projType = gras.ellapx.enums.EProjType.DynamicAlongGoodCurve;
+ellTubeProjRel = fromMatEllTube.projectToOrths([1,2], projType);
+plObj=smartdb.disp.RelationDataPlotter();
+ellTubeProjRel.plot(plObj);
+</pre></div>
+</td></tr></table></div>
+</div>
+<div class="section" id="elltubeprojbasic-class">
+<h3>EllTubeProjBasic class<a class="headerlink"
href="#elltubeprojbasic-class" title="Permalink to this headline">¶</a></h3>
+This class inherits its fields from EllTubeBasic and
EllTubeTouchCurveProjBasic classes. It does not have any new
fields, but holds not the original values of the fields, which were the
values of the original ellipsoid tube, it holds the values of the
projection. We can use plot, plotInt or plotExt
methods to plot the projections.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28</pre></div></td><td class="code"><div class="highlight"><pre>% An example of calculating ellipsoid tube object projection
using project
+% function.
+nPoints=5;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr=char.empty(1,0);
+approxSchemaName=char.empty(1,0);
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=1:nPoints;
+sTime=nPoints;
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProjRel,indProj2OrigVec] = fromMatEllTube.project(projType,...
+ {projMat},p);
+plObj=smartdb.disp.RelationDataPlotter();
+ellTubeProjRel.plot(plObj);
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27</pre></div></td><td class="code"><div class="highlight"><pre>% An example of plotting the projection of the ellipsoid tube
internal approximation
+% object using plotInt method.
+nPoints=5;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr=char.empty(1,0);
+approxSchemaName=char.empty(1,0);
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=1:nPoints;
+sTime=nPoints;
+approxType=gras.ellapx.enums.EApproxType.Internal;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProjRel,indProj2OrigVec] = fromMatEllTube.project(projType,...
+ {projMat},p);
+ellTubeProjRel.plotInt();
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27</pre></div></td><td class="code"><div class="highlight"><pre>% An example of plotting the projection of the ellipsoid tube
external approximation
+% object using plotExt method.
+nPoints=5;
+absTol=0.01;
+relTol=0.01;
+approxSchemaDescr=char.empty(1,0);
+approxSchemaName=char.empty(1,0);
+nDims=3;
+nTubes=1;
+lsGoodDirVec=[1;0;1];
+aMat=zeros(nDims,nPoints);
+timeVec=1:nPoints;
+sTime=nPoints;
+approxType=gras.ellapx.enums.EApproxType.External;
+qArrayList=repmat({repmat(diag([1
2 3]),[1,1,nPoints])},...
+ 1,nTubes);
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProjRel,indProj2OrigVec] = fromMatEllTube.project(projType,...
+ {projMat},p);
+ellTubeProjRel.plotExt();
+</pre></div>
+</td></tr></table></div>
+All the three methods have several properties connected to the
properties of the image, for example: transparency, color, line width and
so on.
+</div>
+<div class="section" id="elltubeproj-class">
+<h3>EllTubeProj class<a class="headerlink"
href="#elltubeproj-class" title="Permalink to this headline">¶</a></h3>
+This class doesn’t add any functionality to the
EllTubeProjBasic class.
+</div>
+</div>
+<div class="section" id="unions-of-ellipsoidal-tubes">
+<h2>Unions of ellipsoidal tubes<a class="headerlink"
href="#unions-of-ellipsoidal-tubes" title="Permalink to this
headline">¶</a></h2>
+The last classes which will be discussed in this chapter are classes,
operating with unions of ellipsoid tubes. These are
EllUnionTubeBasic, EllUnionTube and
EllUnionTubeStaticProj classes.
+<div class="section" id="elluniontubebasic-class">
+<h3>EllUnionTubeBasic class<a class="headerlink"
href="#elluniontubebasic-class" title="Permalink to this
headline">¶</a></h3>
+This class allows us to keep and work with unions of ellipsoid tubes.
The fields of this class are:
+<ul class="simple">
+<li>ellUnionTimeDirection which stores the direction in time
along which union is performed;</li>
+<li>timeTouchEndVec which stores the points of time when touch is
occured in good direction;</li>
+<li>timeTouchOpEndVec which stores the points of time when touch
is occured in direction opposite to good direction;</li>
+<li>isLsTouchOp which stores a logical variable which indicates
whether a touch takes place along the direction opposite to the good
direction at sTime point of time;</li>
+<li>isLtTouchOpVec which stores a logical variable which
indicates whether a touch takes place along the direction opposite to
the good direction at any point of time from timeVec.</li>
+</ul>
+This class does not have any public methods.
+</div>
+<div class="section" id="elluniontube-class">
+<h3>EllUnionTube class<a class="headerlink"
href="#elluniontube-class" title="Permalink to this headline">¶</a></h3>
+This class inherits its fields from EllUnionTubeBasic and
EllTubeBasic classes. Unlike EllUnionTubeBasic class,
this class has one public method - fromEllTubes method, which
allows us to create an ellUnionTube object using ellipsoid tubes.
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+10
***The diff for this file has been truncated for email.***
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--- /dev/null
+++ /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.aux Tue
Feb 25 09:31:56 2014 UTC
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***The diff for this file has been truncated for email.***
=======================================
--- /dev/null
+++ /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.log Tue
Feb 25 09:31:56 2014 UTC
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=======================================
--- /dev/null
+++ /branches/issue_133_aatanesyan/doc/_build/latex/python.ist Tue Feb 25
09:31:56 2014 UTC
@@ -0,0 +1,11 @@
+line_max 100
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+preamble "\\begin{theindex}
+\\def\\bigletter#1{{\\Large\\sffamily#1}\\nopagebreak\\vspace{1mm}}
+
+"
+
+symhead_positive "{Symbols}"
+numhead_positive "{Numbers}"

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