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OpenSim::FiberCompressiveForceCosPennationCurve Class Reference

This class serves as a serializable FiberCompressiveForceCosPennationCurve, which is used to ensure that the pennation angle approaches but never reaches an angle of 90 degrees. More...

+ Inheritance diagram for OpenSim::FiberCompressiveForceCosPennationCurve:

Public Member Functions

 FiberCompressiveForceCosPennationCurve ()
 Default constructor creates an curve with the default property values, and assigns it a default name. More...
 
 FiberCompressiveForceCosPennationCurve (double engagementAngleInDegrees, double stiffnessAtPerpendicular, double curviness, const std::string &muscleName)
 Constructs a C2 continuous compressive fiber force cos pennation curve. More...
 
 FiberCompressiveForceCosPennationCurve (double engagementAngleInDegrees, const std::string &muscleName)
 Constructs a C2 continuous compressive fiber force cos pennation curve using only the manditory property, engagmentAngleInDegrees. More...
 
double getEngagementAngleInDegrees () const
 
double getStiffnessAtPerpendicularInUse () const
 
double getCurvinessInUse () const
 
bool isFittedCurveBeingUsed () const
 
void setEngagementAngleInDegrees (double aEngagementAngleInDegrees)
 
void setOptionalProperties (double aStiffnessAtPerpendicular, double aCurviness)
 
double calcValue (double cosPennationAngle) const
 Calculates the value of the curve evaluated at cosPennationAngle. More...
 
double calcValue (const SimTK::Vector &x) const override
 Implement the generic OpenSim::Function interface. More...
 
double calcDerivative (double cosPennationAngle, int order) const
 Calculates the derivative of the fiber compressive force pennation angle curve w.r.t. More...
 
double calcIntegral (double cosPennationAngle) const
 
SimTK::Vec2 getCurveDomain () const
 This function returns a SimTK::Vec2 that contains in its 0th element the lowest value of the curve domain, and in its 1st element the highest value in the curve domain of the curve. More...
 
void printMuscleCurveToCSVFile (const std::string &path)
 This function will generate a csv file with a name that matches the curve name (e.g. More...
 
void ensureCurveUpToDate ()
 
Property declarations

These are the serializable properties associated with this class.

 OpenSim_DECLARE_PROPERTY (engagement_angle_in_degrees, double,"Engagement angle of the compressive pennation spring in degrees")
 
 OpenSim_DECLARE_OPTIONAL_PROPERTY (stiffness_at_perpendicular, double,"Stiffness of the curve at pennation angle of 90 degrees")
 
 OpenSim_DECLARE_OPTIONAL_PROPERTY (curviness, double,"Fiber curve bend, from linear to maximum bend (0-1)")
 
- Public Member Functions inherited from OpenSim::Function
 Function ()
 
 Function (const Function &aFunction)
 
virtual ~Function ()
 
virtual void init (Function *aFunction)
 
Functionoperator= (const Function &aFunction)
 
virtual double calcDerivative (const std::vector< int > &derivComponents, const SimTK::Vector &x) const
 Calculate a partial derivative of this function at a particular point. More...
 
virtual int getArgumentSize () const
 Get the number of components expected in the input vector. More...
 
virtual int getMaxDerivativeOrder () const
 Get the maximum derivative order this Function object can calculate. More...
 
- Public Member Functions inherited from OpenSim::Object
virtual ~Object ()
 Virtual destructor for cleanup. More...
 
virtual Objectclone () const =0
 Create a new heap-allocated copy of the concrete object to which this Object refers. More...
 
virtual const std::string & getConcreteClassName () const =0
 Returns the class name of the concrete Object-derived class of the actual object referenced by this Object, as a string. More...
 
virtual const VisibleObjectgetDisplayer () const
 Methods to support making the object displayable in the GUI or Visualizer Implemented only in few objects. More...
 
virtual VisibleObjectupdDisplayer ()
 get Non const pointer to VisibleObject More...
 
bool isEqualTo (const Object &aObject) const
 Equality operator wrapper for use from languages not supporting operator overloading. More...
 
Objectoperator= (const Object &aObject)
 Copy assignment copies he base class fields, including the properties. More...
 
virtual bool operator== (const Object &aObject) const
 Determine if two objects are equal. More...
 
virtual bool operator< (const Object &aObject) const
 Provide an ordering for objects so they can be put in sorted containers. More...
 
void setName (const std::string &name)
 Set the name of the Object. More...
 
const std::string & getName () const
 Get the name of this Object. More...
 
void setDescription (const std::string &description)
 Set description, a one-liner summary. More...
 
const std::string & getDescription () const
 Get description, a one-liner summary. More...
 
const std::string & getAuthors () const
 Get Authors of this Object. More...
 
void setAuthors (const std::string &authors)
 Set Authors of this object, call this method in your constructor if needed. More...
 
const std::string & getReferences () const
 Get references or publications to cite if using this object. More...
 
void setReferences (const std::string &references)
 Set references or publications to cite if using this object. More...
 
int getNumProperties () const
 Determine how many properties are stored with this Object. More...
 
const AbstractPropertygetPropertyByIndex (int propertyIndex) const
 Get a const reference to a property by its index number, returned as an AbstractProperty. More...
 
AbstractPropertyupdPropertyByIndex (int propertyIndex)
 Get a writable reference to a property by its index number, returned as an AbstractProperty. More...
 
bool hasProperty (const std::string &name) const
 Return true if this Object has a property of any type with the given name, which must not be empty. More...
 
const AbstractPropertygetPropertyByName (const std::string &name) const
 Get a const reference to a property by its name, returned as an AbstractProperty. More...
 
AbstractPropertyupdPropertyByName (const std::string &name)
 Get a writable reference to a property by its name, returned as an AbstractProperty. More...
 
template<class T >
bool hasProperty () const
 Return true if this Object contains an unnamed, one-object property that contains objects of the given template type T. More...
 
template<class T >
const Property< T > & getProperty (const PropertyIndex &index) const
 Get property of known type Property<T> as a const reference; the property must be present and have the right type. More...
 
template<class T >
Property< T > & updProperty (const PropertyIndex &index)
 Get property of known type Property<T> as a writable reference; the property must be present and have the right type. More...
 
void setObjectIsUpToDateWithProperties ()
 When an object is initialized using the current values of its properties, it can set a flag indicating that it is up to date. More...
 
bool isObjectUpToDateWithProperties () const
 Returns true if no property's value has changed since the last time setObjectIsUpToDateWithProperties() was called. More...
 
void readObjectFromXMLNodeOrFile (SimTK::Xml::Element &objectElement, int versionNumber)
 We're given an XML element from which we are to populate this Object. More...
 
virtual void updateFromXMLNode (SimTK::Xml::Element &objectElement, int versionNumber)
 Use this method to deserialize an object from a SimTK::Xml::Element. More...
 
virtual void updateXMLNode (SimTK::Xml::Element &parent)
 Serialize this object into the XML node that represents it. More...
 
bool getInlined () const
 Inlined means an in-memory Object that is not associated with an XMLDocument. More...
 
void setInlined (bool aInlined, const std::string &aFileName="")
 Mark this as inlined or not and optionally provide a file name to associate with the new XMLDocument for the non-inline case. More...
 
std::string getDocumentFileName () const
 If there is a document associated with this object then return the file name maintained by the document. More...
 
void setAllPropertiesUseDefault (bool aUseDefault)
 
bool print (const std::string &fileName)
 Write this Object into an XML file of the given name; conventionally the suffix to use is ".osim". More...
 
std::string dump (bool dumpName=false)
 dump the XML representation of this Object into an std::string and return it. More...
 
void clearObjectIsUpToDateWithProperties ()
 For testing or debugging purposes, manually clear the "object is up to date with respect to properties" flag. More...
 
virtual bool isA (const char *type) const
 The default implementation returns true only if the supplied string is "Object"; each Object-derived class overrides this to match its own class name. More...
 
const std::string & toString () const
 Wrapper to be used on Java side to display objects in tree; this returns just the object's name. More...
 
PropertySetgetPropertySet ()
 OBSOLETE: Get a reference to the PropertySet maintained by the Object. More...
 
const PropertySetgetPropertySet () const
 

Additional Inherited Members

- Static Public Member Functions inherited from OpenSim::Function
static FunctionmakeFunctionOfType (Function *aFunction, const std::string &aNewTypeName)
 
- Static Public Member Functions inherited from OpenSim::Object
static void registerType (const Object &defaultObject)
 Register an instance of a class; if the class is already registered it will be replaced. More...
 
static void renameType (const std::string &oldTypeName, const std::string &newTypeName)
 Support versioning by associating the current Object type with an old name. More...
 
static const ObjectgetDefaultInstanceOfType (const std::string &concreteClassName)
 Return a pointer to the default instance of the registered (concrete) Object whose class name is given, or NULL if the type is not registered. More...
 
template<class T >
static bool isObjectTypeDerivedFrom (const std::string &concreteClassName)
 Return true if the given concrete object type represents a subclass of the template object type T, and thus could be referenced with a T*. More...
 
static ObjectnewInstanceOfType (const std::string &concreteClassName)
 Create a new instance of the concrete Object type whose class name is given as concreteClassName. More...
 
static void getRegisteredTypenames (Array< std::string > &typeNames)
 Retrieve all the typenames registered so far. More...
 
template<class T >
static void getRegisteredObjectsOfGivenType (ArrayPtrs< T > &rArray)
 Return an array of pointers to the default instances of all registered (concrete) Object types that derive from a given Object-derived type that does not have to be concrete. More...
 
static void PrintPropertyInfo (std::ostream &os, const std::string &classNameDotPropertyName)
 Dump formatted property information to a given output stream, useful for creating a "help" facility for registered objects. More...
 
static void PrintPropertyInfo (std::ostream &os, const std::string &className, const std::string &propertyName)
 Same as the other signature but the class name and property name are provided as two separate strings. More...
 
static ObjectmakeObjectFromFile (const std::string &fileName)
 Create an OpenSim object whose type is based on the tag at the root node of the XML file passed in. More...
 
static const std::string & getClassName ()
 Return the name of this class as a string; i.e., "Object". More...
 
static void setSerializeAllDefaults (bool shouldSerializeDefaults)
 Static function to control whether all registered objects and their properties are written to the defaults section of output files rather than only those values for which the default was explicitly overwritten when read in from an input file or set programmatically. More...
 
static bool getSerializeAllDefaults ()
 Report the value of the "serialize all defaults" flag. More...
 
static bool isKindOf (const char *type)
 Returns true if the passed-in string is "Object"; each Object-derived class defines a method of this name for its own class name. More...
 
static void setDebugLevel (int newLevel)
 Set the debug level to get verbose output. More...
 
static int getDebugLevel ()
 Get current setting of debug level. More...
 
static ObjectSafeCopy (const Object *aObject)
 Use the clone() method to duplicate the given object unless the pointer is null in which case null is returned. More...
 
static void RegisterType (const Object &defaultObject)
 OBSOLETE alternate name for registerType(). More...
 
static void RenameType (const std::string &oldName, const std::string &newName)
 OBSOLETE alternate name for renameType(). More...
 
- Static Public Attributes inherited from OpenSim::Object
static const std::string DEFAULT_NAME
 Name used for default objects when they are serialized. More...
 
- Protected Member Functions inherited from OpenSim::Function
void resetFunction ()
 This should be called whenever this object has been modified. More...
 
- Protected Member Functions inherited from OpenSim::Object
 Object ()
 The default constructor is only for use by constructors of derived types. More...
 
 Object (const std::string &fileName, bool aUpdateFromXMLNode=true) SWIG_DECLARE_EXCEPTION
 Constructor from a file, to be called from other constructors that take a file as input. More...
 
 Object (const Object &source)
 Copy constructor is invoked automatically by derived classes with default copy constructors; otherwise it must be invoked explicitly. More...
 
 Object (SimTK::Xml::Element &aElement)
 Construct the base class portion of an Object from a given Xml element that describes this Object. More...
 
template<class T >
PropertyIndex addProperty (const std::string &name, const std::string &comment, const T &value)
 Define a new single-value property of known type T, with the given name, associated comment, and initial value. More...
 
template<class T >
PropertyIndex addOptionalProperty (const std::string &name, const std::string &comment)
 Add an optional property, meaning it can contain either no value or a single value. More...
 
template<class T >
PropertyIndex addOptionalProperty (const std::string &name, const std::string &comment, const T &value)
 Add an optional property, meaning it can contain either no value or a single value. More...
 
template<class T >
PropertyIndex addListProperty (const std::string &name, const std::string &comment, int minSize, int maxSize)
 Define a new list-valued property of known type T, with the given name, associated comment, minimum (==0) and maximum (>0) allowable list lengths, and a zero-length initial value. More...
 
template<class T , template< class > class Container>
PropertyIndex addListProperty (const std::string &name, const std::string &comment, int minSize, int maxSize, const Container< T > &valueList)
 Define a new list-valued property as above, but assigning an initial value via some templatized container class that supports size() and indexing. More...
 
PropertyIndex getPropertyIndex (const std::string &name) const
 Look up a property by name and return its PropertyIndex if it is found. More...
 
template<class T >
PropertyIndex getPropertyIndex () const
 Look up an unnamed property by the type of object it contains, and return its PropertyIndex if it is found. More...
 
void updateFromXMLDocument ()
 Use this method only if you're deserializing from a file and the object is at the top level; that is, primarily in constructors that take a file name as input. More...
 
void setDocument (XMLDocument *doc)
 Unconditionally set the XMLDocument associated with this object. More...
 
const XMLDocumentgetDocument () const
 Get a const pointer to the document (if any) associated with this object. More...
 
XMLDocumentupdDocument ()
 Get a writable pointer to the document (if any) associated with this object. More...
 
- Protected Attributes inherited from OpenSim::Function
SimTK::Function_function
 
- Protected Attributes inherited from OpenSim::Object
PropertySet _propertySet
 OBSOLETE: Property_Deprecated set for serializable member variables of this and derived classes. More...
 

Detailed Description

This class serves as a serializable FiberCompressiveForceCosPennationCurve, which is used to ensure that the pennation angle approaches but never reaches an angle of 90 degrees.

Preventing the fibers from achivieving a pennation angle of 90 degrees is important for equilibrium muscle models which have a singularity at this value.

This curve is designed to work with the muscle model in such a way that it acts like a spring that the pennated muscle fibers contact it as the fiber rotates (circuled in red). When the spring engages it will exert a force on the fiber that will prevent it from shortening further, thus preventing the pennation angle from reaching 90 degrees.

Note that this object should be updated through the set methods provided. These set methods will take care of rebuilding the curve correctly. If you modify the properties directly, the curve will not be rebuilt, and upon calling a function like calcValue, calcDerivative, or printCurveToCSVFile an exception will be thrown because the curve is out of date with its properties.

fig_FiberCompressiveForceCosPennationCurve.png
Author
Matt Millard

Constructor & Destructor Documentation

OpenSim::FiberCompressiveForceCosPennationCurve::FiberCompressiveForceCosPennationCurve ( )

Default constructor creates an curve with the default property values, and assigns it a default name.

OpenSim::FiberCompressiveForceCosPennationCurve::FiberCompressiveForceCosPennationCurve ( double  engagementAngleInDegrees,
double  stiffnessAtPerpendicular,
double  curviness,
const std::string &  muscleName 
)

Constructs a C2 continuous compressive fiber force cos pennation curve.

The sole purpose of this curve is to prevent the pennation angle from reaching an angle of 90 degrees. Details to appear in Millard et al. 2012.

Parameters
engagementAngleInDegreesThe pennation angle engagement angle of the fiber compressive force pennation curve. Making the spring engage too far from 90 degrees may unrealistically limit the force production capability of the muscle. An engagement angle of 80 degrees is a good place to start.
stiffnessAtPerpendicularThis is the stiffness of the compressive elastic force length spring when the pennation angle reaches 90 degrees. Note that the units of this stiffness are (normalized force) / cos(engagmentAngleInDegrees). If the engagement angle is 80 degrees, a good stiffness to start with is -2*(1/cosd(engagementAngleInDegrees))
curvinessA dimensionless parameter between [0-1] that controls how the curve is drawn: 0 will create a curve that is very close to a straight line segment while a value of 1 will create a curve that smoothly fills the corner formed by the linear extrapolation of 'stiffnessAtPerpendicularFiber' and the x axis as shown in the figure. A good curviness parameter value to start with is 0.5.
muscleNameThe name of the muscle this curve belongs to. This name is used to create the name of this curve, which is formed simply by appending "_FiberCompressiveForceCosPennationCurve" to the string in muscleName. This name is used for making intelligible error messages and also for naming the XML version of this curve when it is serialized.

Conditions:

        0 < engagmentAngleInDegrees < 90
        stiffnessAtPerpendicular < -1/engagmentAngleInDegrees
        0 <= curviness <= 1

Computational Costs

        ~174,100 flops

Default Parameter Values

         engagmentAngleInDegrees = 80 

Example:

OpenSim::FiberCompressiveForceCosPennationCurve::FiberCompressiveForceCosPennationCurve ( double  engagementAngleInDegrees,
const std::string &  muscleName 
)

Constructs a C2 continuous compressive fiber force cos pennation curve using only the manditory property, engagmentAngleInDegrees.

The sole purpose of this curve is to prevent the pennation angle from reaching an angle of 90 degrees. Details to appear in Millard et al. 2012.

Parameters
engagementAngleInDegreesThe pennation angle engagement angle of the fiber compressive force pennation curve. Making the spring engage too far from 90 degrees may unrealistically limit the force production capability of the muscle. An engagement angle of 80 degrees is a good place to start.
muscleNameThe name of the muscle this curve belongs to. This name is used to create the name of this curve, which is formed simply by appending "_FiberCompressiveForceCosPennationCurve" to the string in muscleName. This name is used for making intelligible error messages and also for naming the XML version of this curve when it is serialized.

Optional Parameters If the optional parameters have not yet been set, they are computed when functions getStiffnessAtPerpendicularInUse(), and getCurvinessInUse() are called. See the documentation for these functions for details

Conditions:

        0 < engagmentAngleInDegrees < 90

Computational Costs

        ~174,100 flops

Default Parameter Values

         engagmentAngleInDegrees = 80 

Example:

Member Function Documentation

double OpenSim::FiberCompressiveForceCosPennationCurve::calcDerivative ( double  cosPennationAngle,
int  order 
) const

Calculates the derivative of the fiber compressive force pennation angle curve w.r.t.

to cosPennationAngle.

Parameters
cosPennationAngleThe cosine of the fiber pennation angle
orderthe order of the derivative. Only values of 0,1 and 2 are acceptable.
Returns
the derivative of the fiber compressive force pennation angle curve w.r.t. to cosPennationAngle

Computational Costs

    x in curve domain  : ~391 flops
    x in linear section:   ~2 flops       
double OpenSim::FiberCompressiveForceCosPennationCurve::calcIntegral ( double  cosPennationAngle) const
Parameters
cosPennationAngleThe cosine of the pennation angle
Returns
Computes the normalized area under the curve. For this curve, this quantity corresponds to the normalized potential energy stored in the fiber compressive force cos pennation spring - simply multiply this quantity by the number of NormForce (where NormForce corresponds to the number of Newtons that 1 normalized force corresponds to) to obtain the potental energy stored in the fiber in units of Joules. Note that NormDistance is omitted because the length dimension of this curve is not normalized, only the force dimension.

Computational Costs

    x in curve domain  : ~13 flops
    x in linear section: ~19 flops
double OpenSim::FiberCompressiveForceCosPennationCurve::calcValue ( double  cosPennationAngle) const

Calculates the value of the curve evaluated at cosPennationAngle.

Parameters
cosPennationAngleThe cosine of the fiber pennation angle
Returns
the normalized force generated by the compressive force element

Computational Costs

    x in curve domain  : ~282 flops
    x in linear section:   ~5 flops
double OpenSim::FiberCompressiveForceCosPennationCurve::calcValue ( const SimTK::Vector x) const
inlineoverridevirtual

Implement the generic OpenSim::Function interface.

Reimplemented from OpenSim::Function.

References OVERRIDE_11.

void OpenSim::FiberCompressiveForceCosPennationCurve::ensureCurveUpToDate ( )
SimTK::Vec2 OpenSim::FiberCompressiveForceCosPennationCurve::getCurveDomain ( ) const

This function returns a SimTK::Vec2 that contains in its 0th element the lowest value of the curve domain, and in its 1st element the highest value in the curve domain of the curve.

Outside of this domain the curve is approximated using linear extrapolation.

Returns
The minimum and maximum value of the domain, x, of the curve y(x). Within this range y(x) is a curve, outside of this range the function y(x) is a C2 (continuous to the second derivative) linear extrapolation
double OpenSim::FiberCompressiveForceCosPennationCurve::getCurvinessInUse ( ) const
Returns
A dimensionless parameter between [0-1] that controls how the curve is drawn: 0 will create a curve that is very close to a straight line segment while a value of 1 will create a curve that smoothly fills the corner formed by the linear extrapolation of 'StiffnessAtPerpendicularFiber'.

If this property is empty, then a value is computed and returned. The value is computed using the following:

           curviness = 0.1       
double OpenSim::FiberCompressiveForceCosPennationCurve::getEngagementAngleInDegrees ( ) const
Returns
The pennation angle engagement angle of the fiber compressive force pennation curve.
double OpenSim::FiberCompressiveForceCosPennationCurve::getStiffnessAtPerpendicularInUse ( ) const
Returns
This is the stiffness of the compressive elastic force length spring when the pennation angle reaches 90 degrees. If this property has been set, the property value is returned. If this property is empty, then a value is computed and returned. The value is computed using the following:
           stiffnessAtPerpendicular = -2 * 1/cosd(engagementAngleInDegrees)        

where cosd is a cosine function that takes its argument in units of degrees

bool OpenSim::FiberCompressiveForceCosPennationCurve::isFittedCurveBeingUsed ( ) const
Returns
true if the internal fitting routine (which takes only one argument, the engagementAngleInDegrees) is being used. False is returned if the user has set the optional parameters.
OpenSim::FiberCompressiveForceCosPennationCurve::OpenSim_DECLARE_OPTIONAL_PROPERTY ( stiffness_at_perpendicular  ,
double  ,
"Stiffness of the curve at pennation angle of 90 degrees"   
)
OpenSim::FiberCompressiveForceCosPennationCurve::OpenSim_DECLARE_OPTIONAL_PROPERTY ( curviness  ,
double  ,
"Fiber curve  bend,
from linear to maximum bend(0-1)"   
)
OpenSim::FiberCompressiveForceCosPennationCurve::OpenSim_DECLARE_PROPERTY ( engagement_angle_in_degrees  ,
double  ,
"Engagement angle of the compressive pennation spring in degrees"   
)
void OpenSim::FiberCompressiveForceCosPennationCurve::printMuscleCurveToCSVFile ( const std::string &  path)

This function will generate a csv file with a name that matches the curve name (e.g.

"bicepfemoris_FiberCompressiveForceCosPennationCurve.csv"). This function is not const to permit the curve to be rebuilt if it is out of date with its properties.

Parameters
pathThe full path to the location. Note '/' slashes must be used, and do not put a '/' after the last folder.

The file will contain the following columns:

 Col# 1, 2,     3,       4,  
      x, y, dy/dx, d2y/dx2,

The curve will be sampled from its linear extrapolation region (the region with normalized fiber velocities < -1), through the curve, out to the other linear extrapolation region (the region with normalized fiber velocities > 1). The width of each linear extrapolation region is 10% of the entire range of x, or 0.1*(x1-x0).

The curve is sampled quite densely: there are 200+20 rows

Computational Costs

      ~194,800 flops

Example To read the csv file with a header in from Matlab, you need to use csvread set so that it will ignore the header row. This is accomplished by using the extra two numerical arguments for csvread to tell the function to begin reading from the 1st row, and the 0th index (csvread is 0 indexed). This is necessary to skip reading in the text header

  data=csvread('bicepfemoris_FiberCompressiveForceCosPennationCurve.csv',1,0);
void OpenSim::FiberCompressiveForceCosPennationCurve::setEngagementAngleInDegrees ( double  aEngagementAngleInDegrees)
Parameters
aEngagementAngleInDegreesSets the pennation angle engagement angle of the fiber compressive force pennation curve. Cost The curve is rebuilt at a cost of ~174,100 flops
void OpenSim::FiberCompressiveForceCosPennationCurve::setOptionalProperties ( double  aStiffnessAtPerpendicular,
double  aCurviness 
)
Parameters
aStiffnessAtPerpendicularThis is the stiffness of the compressive elastic force length spring when the pennation angle reaches 90 degrees.
aCurvinessA dimensionless parameter between [0-1] that controls how the curve is drawn: 0 will create a curve that is very close to a straight line segment while a value of 1 will create a curve that smoothly fills the corner formed by the linear extrapolation of 'stiffnessAtOneNormForce' and the x axis as shown in the figure.

Cost The curve is rebuilt at a cost of ~174,100 flops


The documentation for this class was generated from the following file: