0027231: Obsolete OCCT features still mentioned in the documentation

[occt.git] / dox / user_guides / foundation_classes / foundation_classes.md

Foundation Classes  {#occt_user_guides__foundation_classes}
=================================

@tableofcontents

@section occt_fcug_1 Introduction

This manual explains how to use Open CASCADE Technology (**OCCT**)  Foundation Classes. It provides basic documentation on foundation classes. For  advanced information on foundation classes and their applications, see our <a href="http://www.opencascade.com/content/tutorial-learning">E-learning & Training</a> offerings.
   
Foundation Classes provide a variety of general-purpose  services such as automated dynamic memory management (manipulation of objects  by handle), collections, exception handling, genericity by down-casting and  plug-in creation. 

Foundation Classes include the following: 

### Root Classes
Root classes are the basic data types and classes on which all the  other classes are built. They provide: 
  * fundamental types such as Boolean, Character, Integer or Real,
  * safe handling of dynamically created objects, ensuring automatic  deletion of unreferenced objects (see  *Standard_Transient* class),
  * configurable optimized memory manager increasing the performance  of applications that intensively use dynamically created objects,
  * extended run-time type information (RTTI) mechanism facilitating  the creation of complex programs,
  * management of exceptions,
  * encapsulation of C++ streams.
Root classes are mainly implemented in *Standard* and  *MMgt* packages. 

### Strings
Strings are classes that handle dynamically sized sequences  of characters based on both ASCII (normal 8-bit character type) and Unicode  (16-bit character type).  
Strings may also be manipulated by handles, and consequently  be shared. 
Strings are implemented in the *TCollection* package. 

### Collections
Collections are the classes that handle dynamically sized  aggregates of data.  
Collection classes are *generic*, that is, they define  a structure and algorithms allowing to hold a variety of objects which do not  necessarily inherit from a unique root class (similarly to C++ templates). When  you need to use a collection of a given type of object, you must *instantiate* it for this specific type of element. Once this declaration is compiled, all functions available on the generic collection are available on your *instantiated  class*. 

Collections include a wide range of generic classes such as  run-time sized arrays, lists, stacks, queues, sets and hash maps. 
Collections are implemented in the *TCollection* and *NCollection* packages. 

### Collections of Standard Objects

The *TColStd* package provides frequently used  instantiations of generic classes from the *TCollection* package with  objects from the *Standard* package or strings from the *TCollection* package. 

### Vectors and Matrices

These classes provide commonly used mathematical algorithms  and basic calculations (addition, multiplication, transposition, inversion,  etc.) involving vectors and matrices. 

### Primitive Geometric Types

Open CASCADE Technology primitive geometric types are a  STEP-compliant implementation of basic geometric and algebraic entities.  
They provide: 
  * Descriptions of elementary geometric shapes:
  * Points,
  * Vectors,
  * Lines,
  * Circles and conics,
  * Planes and elementary surfaces,
  * Positioning of these shapes in space or in a plane by means of an  axis or a coordinate system,
  * Definition and application of geometric transformations to these  shapes:
  * Translations
  * Rotations
  * Symmetries
  * Scaling transformations
  * Composed transformations
  * Tools (coordinates and matrices) for algebraic computation.
  
### Common Math Algorithms

Open CASCADE Technology common math algorithms provide a C++  implementation of the most frequently used mathematical algorithms.  
These include: 
  * Algorithms to solve a set of linear algebraic equations,
  * Algorithms to find the minimum of a function of one or more  independent variables,
  * Algorithms to find roots of one, or of a set, of non-linear  equations,
  * Algorithms to find the eigen-values and eigen-vectors of a square  matrix.

### Exceptions

A hierarchy of commonly used exception classes is provided,  all based on class Failure, the  root of exceptions. 
Exceptions describe exceptional situations, which can arise  during the execution of a function. With the raising of an exception, the  normal course of program execution is abandoned. The execution of actions in  response to this situation is called the treatment of the exception. 

### Quantities

These are various classes supporting date and time  information and fundamental types representing most physical quantities such as  length, area, volume, mass, density, weight, temperature, pressure etc. 

### Application services

Foundation Classes also include implementation of several  low-level services that facilitate the creation of customizable and  user-friendly applications with Open CASCADE Technology. These include: 
  * Unit conversion tools, providing a uniform mechanism for dealing  with quantities and associated physical units: check unit compatibility,  perform conversions of values between different units and so on (see package  *UnitsAPI*);
  * Basic interpreter of expressions that facilitates the creation of  customized scripting tools, generic definition of expressions and so on (see  package *ExprIntrp*);
  * Tools for dealing with configuration resource files (see package  *Resource*) and customizable message files (see package *Message*), making it easy  to provide a multi-language support in applications;
  * Progress indication and user break interfaces, giving a  possibility even for low-level algorithms to communicate with the user in a  universal and convenient way.
  

@section occt_fcug_2 Basics
This chapter deals with basic services such as library organization, persistence, data types, memory management,  programming with handles, exception handling, genericity by downcasting and plug-in creation. 


@subsection occt_fcug_2_a Library organization

This chapter introduces some basic concepts, which are used not only in Foundation Classes, but  throughout the whole OCCT library. 

@subsubsection occt_fcug_2_a_1 Modules  and toolkits

The whole OCCT library is organized in a set of modules. The  first module, providing most basic services and used by all other modules, is  called Foundation Classes and described by this manual. 

Every module consists primarily of one or several toolkits  (though it can also contain executables, resource units etc.). Physically a toolkit  is represented by a shared library (e.g. .so or .dll). The toolkit is built  from one or several packages. 

@subsubsection occt_fcug_2_a_2 Packages
A **package** groups together a number of classes which  have semantic links. For example, a geometry package would contain Point, Line,  and Circle classes. A package can also contain enumerations, exceptions and  package methods (functions). In practice, a class name is prefixed with the  name of its package e.g.  
*Geom_Circle*. 
Data types described in a package may include one or  more of the following data types: 
  * Enumerations
  * Object classes
  * Exceptions
  * Pointers to other object classes
Inside a package, two data types cannot bear the same  name. 

@image html /user_guides/foundation_classes/images/foundation_classes_image003.png  "Contents of a package"
@image latex /user_guides/foundation_classes/images/foundation_classes_image003.png  "Contents of a package"

**Methods** are either **functions** or **procedures**.  Functions return an object, whereas procedures only communicate by passing arguments.  In both cases, when the transmitted object is an instance manipulated by a  handle, its identifier is passed. There are three categories of methods: 
* **Object  constructor** Creates an instance of the described class. A class  will have one or more object constructors with various different arguments or none. 
* **Instance method** Operates on the  instance which owns it. 
* **Class  method** Does not work on individual  instances, only on the class itself. 

@subsubsection occt_fcug_2_a_3 Classes
The fundamental software component in object-oriented software  development is the class. A class is the implementation of a **data type**.  It defines its **behavior** (the services offered by its functions) and its **representation** (the data structure of the class -- the fields, which store its data). 

Classes fall into three categories: 
* Ordinary classes.
* Abstract classes. An **abstract class** cannot be instantiated. The purpose  of having such classes is to have a given behavior shared by a hierarchy of  classes and dependent on the implementation of the descendants. This is a way  of guaranteeing a certain base of inherited behavior common to all the classes  based on a particular deferred class. 
* Template classes. A **template class** offers a set of functional behaviors  to manipulate other data types. Instantiation of a template class requires that  a data type is given for its argument(s).

@subsubsection occt_fcug_2_a_5 Inheritance
The purpose of inheritance is to reduce the development  workload. The inheritance mechanism allows a new class to be declared already  containing the characteristics of an existing class. This new class can then be  rapidly specialized for the task in hand. This avoids the necessity of  developing each component “from scratch”. 
For example, having already developed a class *BankAccount* you  could quickly specialize new classes: *SavingsAccount, LongTermDepositAccount,  MoneyMarketAccount, RevolvingCreditAccount*, etc.... 

The corollary of this is that when two or more classes  inherit from a parent (or ancestor) class, all these classes guarantee as a  minimum the behavior of their parent (or ancestor). For example, if the parent  class BankAccount contains the method Print which tells it to print itself out,  then all its descendant classes guarantee to offer the same service. 

One way of ensuring the use of inheritance is to declare  classes at the top of a hierarchy as being **abstract**. In such classes,  the methods are not implemented. This forces the user to create a new class  which redefines the methods. This is a way of guaranteeing a certain minimum of  behavior among descendant classes. 

@subsection occt_fcug_2_1 Data Types

An object-oriented language structures a system around data types rather than around the actions carried out on this data. In this context,  an **object** is an **instance** of a data type and its definition  determines how it can be used. Each data type is implemented by one or more  classes, which make up the basic elements of the system. 

The data types in Open CASCADE Technology fall into two  categories: 
  * Data types manipulated by handle (or reference)
  * Data types manipulated by value
  
@image html /user_guides/foundation_classes/images/foundation_classes_image004.png  "Manipulation of data types"
@image latex /user_guides/foundation_classes/images/foundation_classes_image004.png  "Manipulation of data types"
  
A data type is implemented as a class. The class not only  defines its data representation and the methods available on instances, but it  also suggests how the instance will be manipulated. 
  * A variable of a type manipulated by value contains the instance  itself.
  * A variable of a type manipulated by handle contains a reference  to the instance.
The first examples of types manipulated by values are the  predefined **primitive types**: *Boolean, Character, Integer, Real*, etc. 

A variable of a type manipulated by handle which is not  attached to an object is said to be **null**. To reference an object, we  instantiate the class with one of its constructors. For example, in C++: 

~~~~~
Handle(myClass)  m = new myClass; 
~~~~~

In Open CASCADE Technology, the  Handles are specific classes that are used to safely manipulate objects  allocated in the dynamic memory by reference, providing reference counting  mechanism and automatic destruction of the object when it is not referenced. 



@subsubsection occt_fcug_2_1_1 Primitive Types

The primitive types are predefined in the language and they  are **manipulated by value**. 

* **Boolean** is used to represent logical  data. It may have only two values: *Standard_True*  and *Standard_False*. 
* **Character** designates any ASCII  character. 
* **ExtCharacter** is an extended character. 
* **Integer** is a whole number. 
* **Real** denotes  a real number (i.e. one with whole and a fractional part, either of which may  be null). 
* **ShortReal** is a real with a smaller choice of  values and memory size. 
* **CString** is used for literal  constants. 
* **ExtString** is an extended string. 
* **Address** represents a byte address of  undetermined size. 

The services offered by each of these types are described in  the **Standard** Package. 
The table below presents the equivalence existing between  C++ fundamental types and OCCT primitive types. 

**Table 1: Equivalence between C++ Types and OCCT Primitive  Types** 

| C++ Types     | OCCT Types |
| :--------- | :----------- |
| int   | Standard_Integer |
| double        | Standard_Real |
| float | Standard_ShortReal |
| unsigned int  | Standard_Boolean |
| char  | Standard_Character |
| short | Standard_ExtCharacter |
| char\*        | Standard_CString |
| void\*        | Standard_Address |
| short\*       | Standard_ExtString |

\* The types with asterisk are pointers. 

**Reminder of the classes listed above:** 

* **Standard_Integer** : fundamental type representing 32-bit integers yielding  negative, positive or null values. *Integer* is implemented as a *typedef* of the C++ *int* fundamental type. As such, the algebraic operations  +, -, *, / as well as the ordering and equivalence relations <, <=, ==, !=, >=, >  are defined on it. 
* **Standard_Real** : fundamental type representing real numbers with finite  precision and finite size. **Real** is implemented as a *typedef* of  the C++ *double* (double precision) fundamental type. As such, the  algebraic operations +, -, *, /, unary- and the ordering and equivalence  relations <, <=, ==, !=, >=, >  are defined on reals. 
* **Standard_ShortReal** : fundamental type representing real numbers with finite  precision and finite size. *ShortReal* is implemented as a *typedef* of  the C++ *float* (simple precision) fundamental type. As such, the  algebraic operations +, -, *, /, unary- and the ordering and equivalence  relations <, <=, ==, !=, >=, >  are defined on reals. 
* **Standard_Boolean** : fundamental type representing logical  expressions. It has two values: *false* and *true*. *Boolean* is implemented  as a *typedef* of the C++ *unsigned int* fundamental type. As such,  the algebraic operations *and, or, xor* and *not* as well as equivalence relations == and != are defined on Booleans. 
* **Standard_Character** : fundamental type representing the  normalized ASCII character set. It may be assigned the values of the 128 ASCII  characters. *Character* is implemented as a *typedef* of the C++ *char* fundamental type. As such, the ordering and equivalence relations <, <=, ==, !=, >=, >  are defined on characters using the order of the  ASCII chart (ex: A B). 
* **Standard_ExtCharacter** : fundamental type representing the  Unicode character set. It is a 16-bit character type. *ExtCharacter* is  implemented as a *typedef* of the C++ *short* fundamental type. As  such, the ordering and equivalence relations <, <=, ==, !=, >=, >   are defined on extended characters using the order of the UNICODE chart (ex:  A B). 
* **Standard_CString** : fundamental type representing string  literals. A string literal is a sequence of ASCII (8 bits) characters enclosed  in double quotes. *CString* is implemented as a *typedef* of the C++ *char* fundamental type. 
* **Standard_Address** : fundamental type representing a generic  pointer. *Address* is implemented as a *typedef* of the C++ *void* fundamental  type. 
* **Standard_ExtString** is a fundamental type representing string  literals as sequences of Unicode (16 bits) characters. *ExtString* is  implemented as a *typedef* of the C++ *short* fundamental type. 

@subsubsection occt_fcug_2_1_2 Types manipulated by value
There are three categories of types which are manipulated by  value: 
  * Primitive types
  * Enumerated types
  * Types defined by classes not inheriting from *Standard_Transient*, whether directly or not.
Types which are manipulated by value behave in a more direct  fashion than those manipulated by handle and thus can be expected to perform  operations faster, but they cannot be stored independently in a file. 

@image html /user_guides/foundation_classes/images/foundation_classes_image005.png   "Manipulation of a data type by value"
@image latex /user_guides/foundation_classes/images/foundation_classes_image005.png   "Manipulation of a data type by value"

@subsubsection occt_fcug_2_1_3 Types manipulated by reference (handle)

These are types defined by classes inheriting from the *Transient* class.
  
@image html /user_guides/foundation_classes/images/foundation_classes_image006.png   "Manipulation of a data type by reference"
@image latex /user_guides/foundation_classes/images/foundation_classes_image006.png   "Manipulation of a data type by reference"
  
@subsubsection occt_fcug_2_1_4 When is it necessary to use a handle?

When you design an object, it can be difficult to choose how to manipulate that
object: by value or by handle. The following ideas can help you to make up your mind: 

* If your object may have a long lifetime within the application and you want to make multiple 
references to it, it would be preferable to manipulate this object with a handle. The memory for the 
object will be allocated on the heap. The handle which points to that memory is a light object which 
can be rapidly passed in argument. This avoids the penalty of copying a large object. 
* If your object will have a limited lifetime, for example, used within a single algorithm, it would 
be preferable to manipulate this object by value, non-regarding its size, because this object is 
allocated on the stack and the allocation and de-allocation of memory is extremely rapid, which 
avoids the implicit calls to *new* and *delete* occasioned by allocation on the heap.
* Finally, if an object will be created only once during, but will exist throughout the lifetime of 
the application, the best choice may be a class manipulated by handle or a value declared as a 
global variable. 


@subsection occt_fcug_2_2 Programming with Handles

@subsubsection occt_fcug_2_2_1 Handle Definition

A handle is OCCT implementation of a smart pointer.
Several handles  can reference the same object.
Also, a single handle may reference several  objects, but only one at a time.
To have access to the object it refers to, the  handle must be de-referenced just as with a C++ pointer. 

#### Organization of Classes

Class *Standard_Transient* is a root of a big hierarchy of OCCT  classes that are said to be operable by handles. It provides a reference  counter field, inherited by all its descendant classes, that is used by  associated *Handle()* classes to track a number of handles pointing to this  instance of the object. 

Objects of classes derived (directly or indirectly) from *Transient*, are normally allocated in dynamic memory using operator **new**, and manipulated by handle.
Handle is defined as template class *opencascade::handle<>*.
Open CASCADE Technology  provides preprocessor macro *Handle()* that is historically used throughout OCCT code to name a handle:
~~~~~{.cpp}
Handle(Geom_Line) aLine; // "Handle(Geom_Line)" is expanded to "opencascade::handleL<Geom_Line>"
~~~~~

In addition, for standard OCCT classes additional *typedef* is defined for a handle, as the name of a class prefixed by *Handle_*.
For instance, the above example can be also coded as:
~~~~~{.cpp}
Handle_Geom_Line aLine; // "Handle_Geom_Line" is typedef to "opencascade::handleL<Geom_Line>"
~~~~~

#### Using a Handle


A handle is characterized by the object it references. 

Before performing any operation on a transient object, you  must declare the handle. For example, if Point and Line are two transient classes  from the Geom package, you  would write: 
~~~~~
Handle(Geom_Point)  p1, p2; 
~~~~~
Declaring a handle creates a null handle that does not refer  to any object. The handle may be checked to be null by its method *IsNull()*. To  nullify a handle, use method *Nullify()*. 

To initialize a handle, either a new object should be  created or the value of another handle can be assigned to it, on condition that  their types are compatible. 

**Note** that handles should only be used  for object sharing. For all local operations, it is advisable to use classes  manipulated by values. 

@subsubsection occt_fcug_2_2_2 Type Management

Open CASCADE Technology provides a means to describe the hierarchy  of data types in a generic way, with a possibility to check the exact type of  the given object at run-time (similarly to C++ RTTI). 

To enable this feature, a class declaration should include the declaration of OCCT RTTI.
Header *Standard_Type.hxx* provides two variants of preprocessor macros facilitating this:

* Inline variant, which declares and defines RTTI methods by a single line of code:
~~~~~{.cpp}
#include <Geom_Surface.hxx>
class Appli_ExtSurface : public Geom_Surface
{
. . .
public:
  DEFINE_STANDARD_RTTIEXT(Appli_ExtSurface,Geom_Surface)
};
~~~~~

* Out-of line variant, which uses one macro in the declaration (normally in the header file), and another in the implementation (in C++ source):

  In *Appli_ExtSurface.hxx* file:
~~~~~{.cpp}
#include <Geom_Surface.hxx>
class Appli_ExtSurface : public Geom_Surface
{
. . .
public:
  DEFINE_STANDARD_RTTIEXT(Appli_ExtSurface,Geom_Surface)
};
~~~~~

   In *Appli_ExtSurface.cxx* file:
~~~~~{.cpp}
#include <Appli_ExtSurface.hxx>
IMPLEMENT_STANDARD_RTTIEXT(Appli_ExtSurface,Geom_Surface)
~~~~~

These macros define method *DynamicType()* that returns a type descriptor - handle to singleton instance of the class *Standard_Type* describing the class.
The type descriptor stores the name of the class and the descriptor of its parent class.

Note that while inline version is easier to use, for widely used classes this method may lead to bloating of binary code of dependent libraries, due to multiple instantiations of inline method.

To get the type descriptor for a given class type, use macro *STANDARD_TYPE()* with the name of the class as argument.

Example of usage:
~~~~~{.cpp}
if (aCurve->IsKind(STANDARD_TYPE(Geom_Line))) // equivalent to "if (dynamic_cast<Geom_Line>(aCurve.get()) != 0)"
{
...
}
~~~~~

#### Type Conformity

The type used in the declaration of a handle is the static  type of the object, the type seen by the compiler. A handle can reference an  object instantiated from a subclass of its static type. Thus, the dynamic type  of an object (also called the actual type of an object) can be a descendant of  the type which appears in the handle declaration through which it is  manipulated. 

Consider the class *CartesianPoint*, a  sub-class of *Point*; the rule of type conformity can be illustrated as  follows: 

~~~~~
Handle (Geom_Point) p1;
Handle (Geom_CartesianPoint) p2;
p2 = new Geom_CartesianPoint;
p1 = p2;  // OK,  the types are compatible
~~~~~


The compiler sees p1 as a handle to *Point* though the  actual object referenced by *p1* is of the *CartesianPoint* type. 

#### Explicit Type Conversion

According to the rule of type conformity, it is always  possible to go up the class hierarchy through successive assignments of  handles. On the other hand, assignment does not authorize you to go down the  hierarchy. Consequently, an explicit type conversion of handles is required. 

A handle can be converted explicitly into one of its  sub-types if the actual type of the referenced object is a descendant of the  object used to cast the handle. If this is not the case, the handle is  nullified (explicit type conversion is sometimes called a “safe cast”).  Consider the example below. 

~~~~~~
Handle (Geom_Point) p1;
Handle (Geom_CartesianPoint) p2, p3;
p2 = new Geom_CartesianPoint;
p1 = p2; // OK, standard assignment
p3 = Handle (Geom_CartesianPoint)::DownCast (p1);
// OK, the actual type of p1 is CartesianPoint, although the static type of the handle is Point
~~~~~~

If conversion is not compatible with the actual type of the  referenced object, the handle which was “cast” becomes null (and no exception  is raised). So, if you require reliable services defined in a sub-class of the  type seen by the handle (static type), write as follows: 

~~~~~~
void MyFunction (const Handle(A) & a)
{
  Handle(B) b =  Handle(B)::DownCast(a);
  if (! b.IsNull()) {
    // we can use “b” if class B inherits from A
  }
  else {
    // the types are incompatible
  }
}
~~~~~~
Downcasting is used particularly with collections of objects  of different types; however, these objects should inherit from the same root  class. 

For example, with a sequence of transient objects *SequenceOfTransient* and two classes  A and B that both inherit from *Standard_Transient*, you get the  following syntax: 

~~~~~
Handle (A) a;
Handle (B) b;
Handle (Standard_Transient) t;
SequenceOfTransient s;
a = new A;
s.Append (a);
b = new B;
s.Append (b);
t = s.Value (1);
// here, you cannot write:
// a = t; // ERROR !
// so you downcast:
a = Handle (A)::Downcast (t)
if (! a.IsNull()) {
        // types are compatible, you can use a
}
else {
       // the types are incompatible
}
~~~~~

@subsubsection occt_fcug_2_2_3 Using  Handles to Create Objects

To create an object which is manipulated by handle, declare  the handle and initialize it with the standard C++ **new** operator,  immediately followed by a call to the constructor. The constructor can be any  of those specified in the source of the class from which the object is  instanced. 

~~~~~
Handle (Geom_CartesianPoint) p;
p = new Geom_CartesianPoint (0, 0, 0);
~~~~~

Unlike for a pointer, the **delete** operator does not  work on a handle; the referenced object is automatically destroyed when no  longer in use. 

@subsubsection occt_fcug_2_2_4 Invoking Methods
Once you have a handle to an object,  you can use it like a pointer in C++. To invoke a method which acts on the  referenced object, you translate this method by the standard *arrow* operator, or  alternatively, by function call syntax when this is available. 

To test or to modify the state of the handle, the method is  translated by the *dot* operator. 
The example below illustrates how to access the coordinates  of an (optionally initialized) point object: 

~~~~~
Handle (Geom_CartesianPoint) centre;
Standard_Real x, y, z;
if (centre.IsNull()) {
  centre = new PGeom_CartesianPoint (0, 0, 0);
}
centre->Coord(x, y, z);
~~~~~

The example below illustrates how to access the type object  of a Cartesian point: 

~~~~~
Handle(Standard_Transient)  p = new Geom_CartesianPoint(0.,0.,0.);
if ( p->DynamicType() ==  STANDARD_TYPE(Geom_CartesianPoint) )
  cout  << ;Type check OK;  << endl; 
else 
  cout << ;Type check FAILED; <<  endl;   
~~~~~

*NullObject* exception will be raised if  a field or a method of an object is accessed via a *Null* handle. 

#### Invoking Class Methods

A class method is called like a static C++ function, i.e. it  is called by the name of the class of which it is a member, followed by the “::” operator and the name of the  method. 

For example, we can find the maximum degree of a Bezier curve:

~~~~~
Standard_Integer  n; 
n = Geom_BezierCurve::MaxDegree();
~~~~~

@subsubsection occt_fcug_2_2_5 Handle deallocation

Before you delete an object, you must ensure it is no longer  referenced. To reduce the programming load related to this management of object  life, the delete function in Open CASCADE Technology is secured by a **reference counter** of classes manipulated by handle. A handle automatically deletes an object when it is no  longer referenced. Normally you never call the delete operator explicitly on  instances of subclasses of *Standard_Transient*. 

When a new handle to the same object is created, the  reference counter is incremented. When the handle is destroyed, nullified, or  reassigned to another object, that counter is decremented. The object is  automatically deleted by the handle when reference counter becomes 0. 

The principle of allocation can be seen in the example  below. 

~~~~~
...
{
Handle (TColStd_HSequenceOfInteger) H1 = new TColStd_HSequenceOfInteger;
  // H1 has one reference and corresponds to 48 bytes of  memory
  {
    Handle (TColStd_HSequenceOfInteger) H2;
    H2 = H1; // H1 has two references
    if (argc == 3) {
      Handle (TColStd_HSequenceOfInteger) H3;
      H3 = H1;
      // Here, H1 has three references
      ...
    }
    // Here, H1 has two references
  }
  // Here, H1 has 1 reference
}
// Here, H1 has no reference and the referred TColStd_HSequenceOfInteger object is deleted. 
~~~~~

You can easily cast a reference to the handle object to <i> void* </i> by defining the following:

~~~~
    void *pointer;
    Handle(Some_class) aHandle;
    // Here only a pointer will be copied
    Pointer = &aHandle;
    // Here the Handle object will be copied
    aHandle = * (Handle(Some_Class) *)pointer;
~~~~


@subsubsection occt_fcug_2_2_6  Cycles

Cycles appear if two or more objects reference each other by  handles (stored as fields). In this condition automatic destruction will not work. 

Consider for example a graph, whose objects (primitives)  have to know the graph object to which they belong, i.e. a primitive must have  a reference to complete graph object. If both primitives and the graph are  manipulated by handle and they refer to each other by keeping a handle as a  field, the cycle appears.  

The graph object will not be deleted when the last handle to  it is destructed in the application, since there are handles to it stored  inside its own data structure (primitives). 

There are two approaches how to avoid such situation: 
  * Use C++ pointer for one kind of references, e.g. from a primitive  to the graph
  * Nullify one set of handles (e.g. handles to a graph in  primitives) when a graph object needs to be destroyed
  
@subsection occt_fcug_2_3 Memory Management 

In a work session, geometric modeling  applications create and delete a considerable number of C++ objects allocated  in the dynamic memory (heap). In this context, performance of standard  functions for allocating and deallocating memory may be not sufficient. For this reason, Open CASCADE Technology employs a specialized memory manager implemented in the *Standard* package. 

The Memory Manager is based on the following principles:

* small memory arrays are grouped into clusters and then recycled (clusters are never released to the system),
* large arrays are allocated and de-allocated through the standard functions of the system (the arrays are released to system when they are no longer used).

As a general rule, it is advisable to allocate memory through significant blocks. In this way, the user can work with blocks of contiguous data and it facilitates memory page manager processing.

@subsubsection occt_fcug_2_3_1 Usage of Memory Manager

To  allocate memory in a C code with Open CASCADE Technology memory manager, simply use method *Standard::Allocate()* instead of  *malloc()* and method *Standard::Free()* instead of *free()*. In addition, method *Standard::Reallocate()* is provided to replace C function *realloc()*. 

In C++, operators *new()* and *delete()* for a class may be  defined so as to allocate memory using *Standard::Allocate()* and free it using  *Standard::Free()*. In that case all objects of that class and all inherited  classes will be allocated using the OCCT memory manager. 

Preprocessor macro *DEFINE_STANDARD_ALLOC* provided by header *Standard_DefineAlloc.hxx* defines *new()* and *delete()* in this way.
It is used for all OCCT classes (apart from a few exceptions) which thus are allocated using the OCCT memory manager. 
Since operators *new()* and *delete()* are inherited, this is  also true for any class derived from an OCCT class, for instance, for all  classes derived from *Standard_Transient*. 

**Note** that it is possible (though not  recommended unless really unavoidable) to redefine *new()* and *delete()* functions  for a class inheriting *Standard_Transient*. If that is done, the method  *Delete()* should be also redefined to apply operator *delete* to this pointer. This will ensure that appropriate *delete()* function will be called,  even if the object is manipulated by a handle to a base class.

@subsubsection occt_fcug_2_3_2 How to configure the Memory Manager

The OCCT memory manager may be configured to apply different  optimization techniques to different memory blocks (depending on their size),  or even to avoid any optimization and use C functions *malloc()* and *free()*  directly. 
The configuration is defined by numeric values of the  following environment variables: 
  * *MMGT_OPT*: if set to 0 (default) every memory block is allocated  in C memory heap directly (via *malloc()* and *free()* functions). In this case,  all other options except for *MMGT_CLEAR* are ignored; if set to 1 the memory manager  performs optimizations as described below; if set to 2, Intel ® TBB optimized  memory manager is used.
  * *MMGT_CLEAR*: if set to 1 (default), every allocated memory block  is cleared by zeros; if set to 0, memory block is returned as it is.
  * *MMGT_CELLSIZE*: defines the maximal size of blocks allocated in  large pools of memory. Default is 200.
  * *MMGT_NBPAGES*: defines the size of memory chunks allocated for  small blocks in pages (operating-system dependent). Default is 1000.
  * *MMGT_THRESHOLD*: defines the maximal size of blocks that are  recycled internally instead of being returned to the heap. Default is 40000.
  * *MMGT_MMAP*: when set to 1 (default), large memory blocks are  allocated using memory mapping functions of the operating system; if set to 0,  they will be allocated in the C heap by *malloc()*.

@subsubsection occt_fcug_2_3_3 Optimization Techniques

When *MMGT_OPT* is set to 1, the following optimization  techniques are used: 
  * Small blocks with a size less than *MMGT_CELLSIZE*, are not  allocated separately. Instead, a large pools of memory are allocated (the size  of each pool is *MMGT_NBPAGES* pages). Every new memory block is arranged in a  spare place of the current pool. When the current memory pool is completely  occupied, the next one is allocated, and so on.
  
In the current version memory  pools are never returned to the system (until the process finishes). However,  memory blocks that are released by the method *Standard::Free()* are remembered  in the free lists and later reused when the next block of the same size is  allocated (recycling). 

  * Medium-sized blocks, with a size greater than *MMGT_CELLSIZE* but  less than *MMGT_THRESHOLD*, are allocated directly in the C heap (using *malloc()*  and *free()*). When such blocks are released by the method *Standard::Free()* they  are recycled just like small blocks.
  
However, unlike small blocks, the  recycled medium blocks contained in the free lists (i.e. released by the  program but held by the memory manager) can be returned to the heap by method  *Standard::Purge()*. 

  * Large blocks with a size greater than *MMGT_THRESHOLD*, including  memory pools used for small blocks, are allocated depending on the value of  *MMGT_MMAP*: if it is 0, these blocks are allocated in the C heap; otherwise they  are allocated using operating-system specific functions managing memory mapped  files. Large blocks are returned to the  system immediately when *Standard::Free()* is called. 

@subsubsection occt_fcug_2_3_4 Benefits and drawbacks

The major benefit of the OCCT memory manager is explained  by its recycling of small and medium blocks that makes an application work much  faster when it constantly allocates and frees multiple memory blocks of similar  sizes. In practical situations, the real gain on the application performance  may be up to 50%. 

The associated drawback is that recycled memory is not  returned to the operating system during program execution. This may lead to  considerable memory consumption and even be misinterpreted as a memory leak. To  minimize this effect it is necessary to call the method *Standard::Purge* after the completion  of memory-intensive operations. 

The overhead expenses induced by the OCCT memory manager  are: 
  * size of every allocated memory block is rounded up to 8 bytes  (when *MMGT_OPT* is 0 (default), the rounding is defined by the CRT; the typical  value for 32-bit platforms is 4 bytes)
  * additional 4 bytes (or 8 on 64-bit platforms) are allocated in  the beginning of every memory block to hold its size (or address of the next  free memory block when recycled in free list) only when *MMGT_OPT* is 1.
  
Note that these overheads may be greater or less than  overheads induced by the C heap memory manager, so overall memory consumption  may be greater in either optimized or standard modes, depending on  circumstances. 

As a general rule, it is advisable to allocate memory  through significant blocks. In this way, you can work with blocks of contiguous  data, and processing is facilitated for the memory page manager. 

OCCT memory manager uses mutex to lock access to free lists, therefore it may have less  performance than non-optimized mode in situations when different threads often  make simultaneous calls to the memory manager.
The reason is that modern  implementations of *malloc()* and *free()* employ several allocation arenas and  thus avoid delays waiting mutex release, which are possible in such situations. 

@subsection occt_fcug_2_4 Exceptions 

@subsubsection occt_fcug_2_4_1 Introduction 

The behavior of any object is implemented by the methods,  which were defined in its class declaration. The definition of these methods  includes not only their signature (their programming interface) but also their domain of validity.  

This domain is expressed by **exceptions**. Exceptions  are raised under various error conditions to protect software quality. 

Exception handling provides a means of transferring control  from a given point in a program being executed to an **exception handler** associated  with another point previously executed. 

A method may raise an exception which interrupts its normal  execution and transfers control to the handler catching this exception. 

A hierarchy of commonly used exception classes is provided. The root class is *Standard_Failure* from the *Standard* package.  So each exception inherits from *Standard_Failure* either directly or by inheriting from another exception. Exception classes list all  exceptions, which can be raised by any OCCT function. 

Open CASCADE Technology also provides  support for converting system signals (such as access violation or division by  zero) to exceptions, so that such situations can be safely handled with the  same uniform approach. 
 
However, in order to support this functionality on various  platforms, some special methods and workarounds are used. Though the  implementation details are hidden and handling of OCCT exceptions is done  basically in the same way as with C++, some peculiarities of this approach  shall be taken into account and some rules must be respected. 

The following paragraphs describe recommended approaches for  using exceptions when working with Open CASCADE Technology.  

@subsubsection occt_fcug_2_4_2 Raising  an Exception

#### “C++ like” Syntax

To raise an exception of a definite type method Raise() of  the appropriate exception class shall be used. 
~~~~~
DomainError::Raise(“Cannot cope with this condition”);
~~~~~
raises an exception of *DomainError* type with the associated  message “Cannot cope with this condition”, the message being optional. This  exception may be caught by a handler of a *DomainError* type as follows: 
~~~~~
try {
  OCC_CATCH_SIGNALS
  // try block
}
catch(DomainError) {
// handle DomainError exceptions here
}
~~~~~

#### Regular usage

Exceptions should not be used as a programming technique, to  replace a “goto” statement for example, but as a way to protect methods against  misuse. The caller must make sure its condition is such that the method can  cope with it. 

Thus, 
  * No exception should be raised during normal execution of an  application.
  * A method which may raise an exception should be protected by  other methods allowing the caller to check on the validity of the call.
  
For example, if you consider the *TCollection_Array1* class  used with: 
  * *Value*  function to extract an element
  * *Lower*  function to extract the lower bound of the array
  * *Upper*  function  to extract the upper bound of the array. 
  
then, the *Value*  function may be implemented as follows: 

~~~~~
Item  TCollection_Array1::Value (const Standard_Integer&index) const
{
  // where r1 and r2 are  the lower and upper bounds of the array
  if(index < r1 || index > r2) {
    OutOfRange::Raise(“Index  out of range in Array1::Value”);
  }
  return contents[index];
}
~~~~~

Here validity of the index is first verified using the Lower and Upper functions in order to protect the call. 
Normally the caller ensures the index being in the valid  range before calling <i>Value()</i>. In this case the above implementation of *Value* is not optimal since the  test done in *Value* is  time-consuming and redundant. 
 
It is a widely used practice to include that kind of  protections in a debug build of the program and exclude in release (optimized)  build. To support this practice, the macros <i>Raise_if()</i> are provided for every OCCT  exception class: 
~~~~~
<ErrorTypeName>_Raise_if(condition,  “Error message”); 
~~~~~
where *ErrorTypeName* is the exception type, *condition*  is the logical expression leading to the raise of the exception, and *Error message* is the associated  message. 
  
The entire call may be removed by defining one of the preprocessor symbols *No_Exception* or <i>No_<ErrorTypeName></i> at compile-time: 

~~~~~
#define  No_Exception /* remove all raises */ 
~~~~~

Using this syntax, the *Value* function becomes: 

~~~~~
Item  TCollection_Array1::Value (const Standard_Integer&index) const
     { 
  OutOfRange_Raise_if(index < r1 || index > r2,
                      “index out of range in  Array1::Value”);
  return contents[index];
}
~~~~~

@subsubsection occt_fcug_2_4_3 Handling  an Exception

When an exception is raised, control is transferred to the  nearest handler of a given type in the call stack, that is: 
  * the handler whose try block was most recently entered and not yet  exited,
  * the handler whose type matches the raise expression.
  
A handler of T exception type is a match for a raise  expression with an exception type of E if: 
  * T and E are of the same type, or
  * T is a supertype of E.
  
In order to handle system signals as exceptions, make sure  to insert macro *OCC_CATCH_SIGNALS* somewhere in the beginning of the relevant  code. The recommended location for it is first statement after opening brace of  <i>try {}</i> block. 

As an example, consider the exceptions of type *NumericError, Overflow, Underflow* and *ZeroDivide*,  where *NumericError* is the parent type of the three others. 

~~~~~
void f(1)
 {
  try {
    OCC_CATCH_SIGNALS
    // try block
  }
  catch(Standard_Overflow) { // first handler
    // ...
  }
  catch(Standard_NumericError) { // second handler
    // ...
  }
}
~~~~~

Here, the first handler will catch exceptions of *Overflow* type and the second one -- exceptions of *NumericError* type and all exceptions derived from it, including *Underflow* and *ZeroDivide*. 

The handlers are checked in order of appearance, from the nearest to the try block to the most distant from it, until one matches the raise expression.  For a try block, it would be a mistake to place a handler for a base exception  type ahead of a handler for its derived type since that would ensure that the  handler for the derived exception would never be invoked.  

~~~~~
void f(1)
{
  int i = 0;
  {
    try {
      OCC_CATCH_SIGNALS
      g(i);// i is accessible
    }
    // statement here will produce compile-time errors !
    catch(Standard_NumericError) {
      // fix up with possible reuse of i
    }
    // statement here may produce unexpected side effect 
  }
  . . .
}
~~~~~

The exceptions form a hierarchy tree completely separated  from other user defined classes. One exception of type *Failure* is the root of the entire exception  hierarchy. Thus, using a handler with *Failure* type catches any OCCT exception. It is recommended to set up such a handler in  the main routine.  

The main routine of a program would look like this: 

~~~~~
#include <Standard_ErrorHandler.hxx>
#include <Standard_Failure.hxx>
#include <iostream.h>
int main (int argc, char* argv[])
{
  try {
    OCC_CATCH_SIGNALS
    // main block
    return 0;
  }
  catch(Standard_Failure) {
    Handle(Standard_Failure) error = Standard_Failure::Caught  ();
    cout  error  end1;
  }
  return 1;
}
~~~~~

In this example function *Caught* is a static member of *Failure* that  returns an exception object containing the error message built in the raise  expression. Note that this method of accessing a raised object is used in Open  CASCADE Technology instead of usual C++ syntax (receiving the exception in  catch argument). 

Though standard C++ scoping  rules and syntax apply to try block and handlers, note that on some platforms Open  CASCADE Technology may be compiled in compatibility mode when exceptions are  emulated by long jumps (see below). In this mode it is required that no  statement precedes or follows any handler. Thus it is highly recommended to  always include a try block into additional {} braces. Also this mode requires  that header file *Standard_ErrorHandler.hxx* be included in your program before a  try block, otherwise it may fail to handle Open CASCADE Technology exceptions;  furthermore *catch()* statement does not allow passing exception object as  argument. 

#### Catching signals

In order for the application to be able to catch system  signals (access violation, division by zero, etc.) in the same way as other  exceptions, the appropriate signal handler shall be installed in the runtime by  the method *OSD::SetSignal()*.
 
Normally this method is called in the beginning of the  main() function. It installs a handler that will convert system signals into OCCT  exceptions. 

In order to actually convert signals to exceptions, macro *OCC_CATCH_SIGNALS* needs to be inserted in the source code. The typical place where  this macro is put is beginning of the *try{}* block which catches such exceptions.   

@subsubsection occt_fcug_2_4_4 Implementation on various platforms. 

The exception handling mechanism in Open CASCADE Technology  is implemented in different ways depending on the preprocessor macros *NO_CXX_EXCEPTIONS*  and *OCC_CONVERT_SIGNALS*, which shall be consistently defined by compilation  procedures for both Open CASCADE Technology and user applications: 

1. On  Windows, these macros are not defined by default, and normal C++  exceptions are used in all cases, including throwing from signal handler. Thus the  behavior is as expected in C++. 

2. On  Linux, macro *OCC_CONVERT_SIGNALS* is defined by default. The C++  exception mechanism is used for catching exceptions and for throwing them from  normal code. Since it is not possible to throw C++ exception from system signal  handler function, that function makes a long jump to the nearest (in the  execution stack) invocation of macro *OCC_CATCH_SIGNALS*, and only there the C++  exception gets actually thrown. The macro *OCC_CATCH_SIGNALS* is defined in the  file *Standard_ErrorHandler.hxx*. Therefore, including this file is necessary for  successful compilation of a code containing this macro. 

   This mode differs from standard  C++ exception handling only for signals:
 
   * macro *OCC_CATCH_SIGNALS* is necessary (besides call to  *OSD::SetSignal()* described above) for conversion of signals into exceptions;
   * the destructors for automatic C++ objects created in the code  after that macro and till the place where signal is raised will not be called in  case of signal, since no C++ stack unwinding is performed by long jump.

3. On  Linux Open CASCADE Technology can also be compiled in compatibility  mode. In that case macro  *NO_CXX_EXCEPTIONS* is defined and the C++ exceptions are simulated with C long  jumps. As a consequence, the behavior is slightly different from that expected  in the C++ standard.  

While exception handling with  *NO_CXX_EXCEPTIONS* is very similar to C++ by syntax, it has a number of  peculiarities that should be taken into account: 

* try and catch are actually macros defined in the file *Standard_ErrorHandler.hxx*. Therefore, including this file is necessary for  handling OCCT exceptions;
* due to being a macro, catch cannot contain a declaration of the  exception object after its type; only type is allowed in the catch statement.  Use method *Standard_Failure::Caught()* to access an exception object;
* catch macro may conflict with some STL classes that might use  catch(...) statements in their header files. So STL headers should not be  included after *Standard_ErrorHandler.hxx*;
* Open CASCADE Technology try/catch block will not handle normal  C++ exceptions; however this can be achieved using special workarounds;
* the try macro defines a C++ object that holds an entry point in the  exception handler. Therefore if exception is raised by code located immediately  after the try/catch block but on the same nesting level as *try*, it may  be handled by that *catch*. This may lead to unexpected behavior,  including infinite loop. To avoid that, always surround the try/catch block with curved brackets;
* the destructors of C++ objects allocated on the stack after  handler initialization are not called by exception raising.

In general, for writing platform-independent code it is recommended  to insert macros *OCC_CATCH_SIGNALS* in try {} blocks or other code where signals  may happen. For compatibility with previous versions of Open CASCADE Technology  the limitations described above for *NO_CXX_EXCEPTIONS* shall be assumed. 

@subsection occt_fcug_2_5 Plug-In  Management

@subsubsection occt_fcug_2_5_1 Distribution by Plug-Ins

A plug-in is a component that can be loaded dynamically into  a client application, not requiring to be directly linked to it. The plug-in is  not bound to its client, i.e. the plug-in knows only how its connection  mechanism is defined and how to call the corresponding services. 

A plug-in can be used to: 
  * implement the mechanism of a *driver*, i.e dynamically  changing a driver implementation according to the current transactions (for  example, retrieving a document stored in another version of an application),
  * restrict processing resources to the minimum required (for  example, it does not load any application services at run-time as long as the  user does not need them),
  * facilitate modular development  (an application can be  delivered with base functions while some advanced capabilities will be added as  plug-ins when they are available).
  
The plug-in is identified with the help of the global  universal identifier (GUID). The GUID includes lower case characters and cannot  end with a blank space. 

Once it has been loaded, the call to the services provided  by the plug-in is direct (the client is implemented in the same language as the  plug-in). 

#### C++ Plug-In  Implementation

The C++ plug-in implements a service as an object with  functions defined in an abstract class (this abstract class and its parent  classes with the GUID are the only information about the plug-in implemented in  the client application). The plug-in consists of a sharable library including a  method named Factory which  creates the C++ object (the client cannot instantiate this object because the  plug-in implementation is not visible). 
Foundation classes provide in the package *Plugin* a  method named *Load()*, which enables the client to access the required service  through a library.  

That method reads the information regarding available  plug-ins and their locations from the resource file *Plugin* found by environment  variable *CSF_PluginDefaults*:

~~~~~ 
$CSF_PluginDefaults/.Plugin 
~~~~~

The *Load* method looks for the library name in the resource file or registry  through its GUID, for example, on UNIX:
~~~~~
! METADATADRIVER whose value must be OS or DM.

! FW
a148e300-5740-11d1-a904-080036aaa103.Location:
 
libFWOSPlugin.so
a148e300-5740-11d1-a904-080036aaa103.CCL:
/adv_44/CAS/BAG/FW-K4C/inc/FWOS.ccl

! FWDM
a148e301-5740-11d1-a904-080036aaa103.Location:
libFWDMPlugin.so
a148e301-5740-11d1-a904-080036aaa103.CCL:
/adv_44/CAS/BAG/DESIGNMANAGER-K4C/inc/DMAccess.ccl|/
adv_44/CAS/BAG/DATABASE-K4C/inc/FWDMCommands.ccl
a148e301-5740-11d1-a904-080036aaa103.Message:  /adv_44/CAS/
BAG/DESIGNMANAGER-K4C/etc/locale/DMAccess

! Copy-Paste
5ff7dc00-8840-11d1-b5c2-00a0c9064368.Location:
libCDMShapeDriversPlugin.so
5ff7dc01-8840-11d1-b5c2-00a0c9064368.Location:
libCDMShapeDriversPlugin.so
5ff7dc02-8840-11d1-b5c2-00a0c9064368.Location:
libCDMShapeDriversPlugin.so
5ff7dc03-8840-11d1-b5c2-00a0c9064368.Location:
libCDMShapeDriversPlugin.so
5ff7dc04-8840-11d1-b5c2-00a0c9064368.Location:
libCDMShapeDriversPlugin.so

! Plugs 2d plotters:
d0d722a2-b4c9-11d1-b561-0000f87a4710.location: FWOSPlugin
d0d722a2-b4c9-11d1-b561-0000f87a4710.CCL: /adv_44/CAS/BAG/
VIEWERS-K4C/inc/CCLPlotters.ccl
d0d722a2-b4c9-11d1-b561-0000f87a4710.Message: /adv_44/CAS/
BAG/VIEWERS-K4C/etc/locale/CCLPlotters

!SHAPES
e3708f72-b1a8-11d0-91c2-080036424703.Location:
libBRepExchangerPlugin.so
e3708f72-b1a8-11d0-91c2-080036424703.CCL: /adv_44/CAS/BAG/
FW-K4C/inc/BRep.ccl
~~~~~


Then the *Load* method loads the library according to the rules of the operating system  of the host machine (for example, by using environment variables such as  *LD_LIBRARY_PATH* with Unix and *PATH* with Windows). After that it invokes the *Factory*  method to return the object which supports the required service.
The client may then call the functions supported by this  object. 

#### C++ Client Plug-In  Implementation

To invoke one of the services provided by the plug-in, you  may call the *Plugin::ServiceFactory* global function with the *Standard_GUID* of the requested service as follows: 

~~~~~
Handle(FADriver_PartStorer)::DownCast 
(PlugIn::ServiceFactory 
(PlugIn_ServiceId(yourStandardGUID))) 
~~~~~

Let us take *FAFactory.cxx* as an example:

~~~~~
#include <FAFactory.ixx>

#include <FADriver_PartRetriever.hxx>
#include <FADriver_PartStorer.hxx>
#include <FirstAppSchema.hxx>
#include <Standard_GUID.hxx>
#include <Standard_Failure.hxx>
#include <FACDM_Application.hxx>
#include <Plugin_Macro.hxx>

PLUGIN(FAFactory)

static Standard_GUID 
       StorageDriver(“45b3c690-22f3-11d2-b09e-0000f8791463”);
static Standard_GUID 
       RetrievalDriver(“45b3c69c-22f3-11d2-b09e-0000f8791463”);
static Standard_GUID 
       Schema(“45b3c6a2-22f3-11d2-b09e-0000f8791463”);

//======================================================
// function : Factory
// purpose :
//======================================================
 
Handle(Standard_Transient)  FAFactory::Factory(const Standard_GUID& aGUID) 
{
  if(aGUID == StorageDriver) {
    cout  “FAFactory : Create store driver”   endl;
    static  Handle(FADriver_PartStorer) sd = new FADriver_PartStorer();
    return sd;
  }

  if(aGUID == RetrievalDriver) {
    cout  “FAFactory : Create retrieve driver”   endl;
    static Handle(FADriver_PartRetriever)
    rd = new FADriver_PartRetriever();
    return rd;
  }

  if(aGUID == Schema) {
    cout  “FAFactory : Create schema”   endl;
    static Handle(FirstAppSchema) s = new  FirstAppSchema();
    return s;
  }

  Standard_Failure::Raise(“FAFactory: unknown GUID”);
  Handle(Standard_Transient) t;
  return t;
}
~~~~~

#### Without using the Software  Factory

To create a factory without using the Software Factory,  define a *dll* project under Windows or a library under UNIX by using a  source file as specified above. The *FAFactory* class is implemented as follows: 

~~~~~
#include <Handle_Standard_Transient.hxx>
#include <Standard_Macro.hxx>
class Standard_Transient;
class Standard_GUID;
class FAFactory {
public:
  Standard_EXPORT  static Handle_Standard_Transient
                  Factory(const Standard_GUID& aGUID)  ;
  . . .
};
~~~~~


@section occt_fcug_3 Collections,  Strings, Quantities and Unit Conversion

@subsection occt_fcug_3_1 Collections

@subsubsection occt_fcug_3_1_1 Overview

The **Collections** component contains the classes that  handle dynamically sized aggregates of data. They include a wide range of  collections such as arrays, lists and maps. 

Collections classes are *generic* (C++ template-like), that is, they define  a structure and algorithms allowing to hold a variety of objects which do not  necessarily inherit from a unique root class (similarly to C++ templates). 

When you need to use a collection of a given type of object you must *instantiate* it for this specific type of element. Once this declaration is compiled,  all the functions available on the generic collection are available on your *instantiated  class*. 

However, note that: 
  * Each collection directly used as an argument in OCCT public  syntax is instantiated in an OCCT component.
  * The *TColStd* package (**Collections of Standard Objects** component)  provides numerous instantiations of these generic collections with objects from  the **Standard** package or from the **Strings** component.
The **Collections** component provides a wide range of  generic collections: 
  * **Arrays** are generally used for a quick access to the item,  however an array is a fixed sized aggregate.
  * **Sequences** are variable-sized structures, they avoid the  use of large and quasi-empty arrays. A sequence item is longer to access  than an array item: only an exploration in sequence is effective (but sequences  are not adapted for numerous explorations). Arrays and sequences are commonly  used as data structures for more complex objects.
  * **Maps** are dynamic structures, where the size is constantly adapted to the number of inserted items and access to an item is the fastest. Maps structures are commonly used in cases of numerous explorations: they are typically internal data structures for complex algorithms.
  * **Lists** are similar to sequences but have different algorithms to explore them. 
  * Specific iterators for sequences and maps. 
  
@subsubsection occt_fcug_3_1_2 Generic general-purpose Aggregates

#### TCollection_Array1

These are unidimensional arrays similar to C arrays, i.e. of fixed  size but dynamically dimensioned at construction time. 
As with a C array, the access time for an *Array1* indexed  item is constant and is independent of the array size. Arrays are commonly used  as elementary data structures for more complex objects. 

*Array1* is a generic class which depends on *Item*,  the type of element in the array. 

*Array1* indexes start and end at a user-defined  position. Thus, when accessing an item, you must base the index on the lower  and upper bounds of the array. 

#### TCollection_Array2

These are bi-dimensional arrays of fixed size but dynamically  dimensioned at construction time. 

As with a C array, the access time for an *Array2* indexed  item is constant and is independent of the array size. Arrays are commonly used  as elementary data structures for more complex objects. 

*Array2* is a generic class which depends on *Item*,  the type of element in the array. 

*Array2* indexes start and end at a user-defined  position. Thus, when accessing an item, you must base the index on the lower  and upper bounds of the array. 

#### TCollection_HArray1

These are unidimensional arrays similar to C arrays, i.e. of fixed  size but dynamically dimensioned at construction time. 
As with a C array, the access time for an *HArray1* or *HArray2* indexed item is constant and is independent of the array size. Arrays are  commonly used as elementary data structures for more complex objects. 

*HArray1* objects are **handles** to arrays. 
  * *HArray1* arrays may be shared by several objects.
  * You may use a *TCollection_Array1* structure to have the  actual array.
  
*HArray1* is a generic class which depends on two parameters: 
  * **Item**, the type of element in the array,
  * **Array**, the actual type of array handled by *HArray1*.  This is an instantiation with **Item** of the *TCollection_Array1* generic  class.
  
*HArray1* indexes start and end at a user-defined  position. Thus, when accessing an item, you must base the index on the lower  and upper bounds of the array. 

#### TCollection_HArray2

These are bi-dimensional arrays of fixed size but dynamically  dimensioned at construction time. 

As with a C array, the access time for an *HArray2* indexed  item is constant and is independent of the array size. Arrays are commonly used  as elementary data structures for more complex objects. 

*HArray2* objects are **handles** to arrays. 
  * *HArray2* arrays may be shared by several objects.
  * You may use a *TCollection_Array2* structure to have the  actual array.
  
*HArray2* is a generic class which depends on two  parameters: 
  * *Item*, the type of element in the array,
  * *Array*, the actual type of array handled by *HArray2*.  This is an instantiation with *Item* of the *TCollection_Array2* generic  class.
  
#### TCollection_HSequence

This is a sequence of items indexed by an integer. 

Sequences have about the same goal as unidimensional arrays  *TCollection_HArray1*: they are commonly used as elementary data  structures for more complex objects. But a sequence is a structure of *variable  size*: sequences avoid the use of large and quasi-empty arrays. Exploring a  sequence data structure is effective when the exploration is done in  sequence; elsewhere a sequence item is longer to read than an array item.  Note also that sequences are not effective when they have to support numerous  algorithmic explorations: a map is better for that. 

*HSequence* objects are **handles** to sequences. 
  * *HSequence* sequences may be shared by several objects.
  * You may use a *TCollection_Sequence* structure to have the  actual sequence.
  
*HSequence* is a generic class which depends on two  parameters: 
  * *Item*, the type of element in the sequence,
  * *Seq*, the actual type of sequence handled by *HSequence*.  This is an instantiation with *Item* of the *TCollection_Sequence* generic  class.
  
#### TCollection_List

These are ordered lists of non-unique objects which can be accessed  sequentially using an iterator. 
Item insertion in a list is very fast at any position. But  searching for items by value may be slow if the list is long, because it  requires a sequential search. 

*List* is a generic class, which depends on *Item*,  the type of element in the structure. 
Use a *ListIterator* iterator to explore a *List* structure. 

An iterator class is automatically instantiated from the *TCollection_ListIterator* class at the time of instantiation of a *List* structure. 

A sequence is a better structure when searching for items by  value. 

Queues and stacks are other kinds of list with a different  access to data. 

#### TCollection_Sequence

This is a sequence of items indexed by an integer. 
Sequences have about the same goal as unidimensional arrays  (*TCollection_Array1*): they are commonly used as elementary data  structures for more complex objects. But a sequence is a structure of *variable  size*: sequences avoid the use of large and quasi-empty arrays. Exploring a  sequence data structure is effective when the exploration is done *in sequence*; elsewhere a sequence item is longer to read than an array item.  Note also that sequences are not effective when they have to support numerous  algorithmic explorations: a map is better for that. 

*Sequence* is a generic class which depends on *Item*,  the type of element in the sequence. 

@subsubsection occt_fcug_3_1_3 Generic Maps

Maps are dynamically extended data structures where data is  quickly accessed with a key. *TCollection_BasicMap* is a root class for maps. 

#### General properties of maps

Map items may contain complex non-unitary data, thus it can be difficult to manage them with an array. The map allows a data structure to be  indexed by complex data. 

The size of a map is dynamically extended. So a map may be  first dimensioned for a little number of items. Maps avoid the use of large and  quasi-empty arrays. 

The access time for a map item is much better than the one  for a sequence, list, queue or stack item. It is  comparable with the  access time for an array item. It depends on the size of the map and on the quality of the user redefinable function (the *hashing  function*) to find quickly where is the item. 

The performance of a map exploration may be better of an array exploration because the size of the map is adapted to the  number of inserted items. 

That is why maps are commonly used as  internal data structures for algorithms. 

#### Definitions 

A map is a data structure for which data are addressed by *keys*. 

Once inserted in the map, a map item is referenced as an *entry* of the map. 

Each entry of the map is addressed by a key. Two different  keys address two different entries of the map. 
The position of an entry in the map is called a *bucket*. 

A map is dimensioned by its number of buckets, i.e. the  maximum number of entries in the map. The performance of a map is conditioned  by the number of buckets. 

The *hashing function* transforms a key into a bucket  index. The number of values that can be computed by the hashing function is  equal to the number of buckets of the map. 

Both the hashing function and the equality test between two  keys are provided by a *hasher* object. 

A map may be explored by a *map iterator*. This  exploration provides only inserted entries in the map (i.e. non empty buckets). 

#### Collections of generic maps 

The *Collections* component provides numerous generic  derived maps. 

These maps include automatic management of the number of *buckets*:  they are automatically resized when the number of *keys* exceeds the  number of buckets. If you have a fair idea of the number of items in your map,  you can save on automatic resizing by specifying a number of buckets at the  time of construction, or by using a resizing function. This may be considered  for crucial optimization issues. 

*Keys, items* and *hashers* are parameters of  these generic derived maps. 

*TCollection_MapHasher* class describes the functions  required by any *hasher*, which is to be used with a map instantiated from  the **Collections** component. 

An iterator class is automatically instantiated at the time  of instantiation of a map provided by the *Collections* component if this  map is to be explored with an iterator. Note that some provided generic maps  are not to be explored with an iterator but with indexes (*indexed maps*). 

##### TCollection_DataMap

This is a map used to store keys with associated items. An entry of **DataMap** is composed of both the key and the item. 
The *DataMap* can be seen as an extended array where  the keys are the indexes.
 
*DataMap* is a generic class which depends on three  parameters: 
  * *Key* is the type of key for an entry in the map,
  * *Item* is the type of element associated with a key in the  map,
  * *Hasher* is the type of hasher on keys.
  
Use a *DataMapIterator* iterator to explore a *DataMap*  map. 

An iterator class is automatically instantiated from the *TCollection_DataMapIterator* generic class at the time  of instantiation of a *DataMap* map. 

*TCollection_MapHasher* class describes the functions required for a *Hasher* object. 

##### TCollection_DoubleMap

This is a map used to bind pairs of keys (Key1,Key2) and retrieve them in linear time. 

*Key1* is  referenced as the first key of the *DoubleMap* and *Key2* as the second key. 

An entry of a *DoubleMap* is composed of a pair of two  keys: the first key and the second key. 

*DoubleMap* is a generic class which depends on four  parameters: 
  * *Key1* is the type of the first key for an entry in the map,
  * *Key2* is the type of the second key for an entry in the  map,
  * *Hasher1* is the type of hasher on first keys,
  * *Hasher2* is the type of hasher on second keys.
  
Use *DoubleMapIterator* to explore a *DoubleMap* map. 

An iterator class is automatically instantiated from the *TCollection_DoubleMapIterator* class at the time of instantiation of a *DoubleMap* map. 

*TCollection_MapHasher* class describes the functions  required for a *Hasher1* or a *Hasher2* object. 

##### TCollection_IndexedDataMap

This is  map to store keys with associated items and to bind an  index to them. 

Each new key stored in the map is assigned an index. Indexes  are incremented as keys (and items) stored in the map. A key can be found by  the index, and an index can be found by the key. No key but the last can be  removed, so the indexes are in the range 1...Upper,  where *Upper* is the number of  keys stored in the map. An item is stored with each key. 

An entry of an *IndexedDataMap* is composed of both the  key, the item and the index. An *IndexedDataMap* is an ordered map, which  allows a linear iteration on its contents. It combines the interest: 
  * of an array because data may be accessed with an index,
  * and of a map because data may also be accessed with a key.

*IndexedDataMap* is a generic class which depends on  three parameters: 
        * *Key* is the type of key for an entry in the map,
        * *Item* is the type of element associated with a key in the map,
        * *Hasher* is the type of hasher on keys.

##### TCollection_IndexedMap

This is map used to store keys and to bind an index to them. 

Each new key stored in the map is assigned an index. Indexes  are incremented as keys stored in the map. A key can be found by the index, and  an index by the key. No key but the last can be removed, so the indexes are in  the range 1...Upper where Upper is the number of keys stored  in the map. 

An entry of an *IndexedMap* is composed of both the key  and the index. An *IndexedMap* is an ordered map, which allows a linear  iteration on its contents. But no data is attached to the key. An *IndexedMap* is typically used by an algorithm to know if some action is still performed  on components of a complex data structure. 

*IndexedMap* is a generic class which depends on two  parameters: 
  * *Key* is the type of key for an entry in the map,
  * *Hasher* is the type of hasher on keys.

##### TCollection_Map

This is a basic hashed map, used to store and retrieve keys in  linear time. 

An entry of a *Map* is composed of the key only. No  data is attached to the key. A *Map* is typically used by an algorithm to  know if some action is still performed on components of a complex data  structure. 

*Map* is a generic class which depends on two  parameters: 
  * *Key* is the type of key in the map,
  * *Hasher* is the type of hasher on keys.

Use a *MapIterator* iterator to explore a *Map* map. 

##### TCollection_MapHasher

This is a hasher on the *keys* of a map instantiated from the *Collections* component. 

A hasher provides two functions: 
* *HashCode()* function transforms a key into a bucket index in the map. The number of values that can be  computed by the hashing function is equal to the number of buckets in the map.
* *IsEqual* is the equality test between two keys. Hashers are  used as parameters in generic maps provided by the **Collections** component.

*MapHasher* is a generic class which depends on the  type of keys, providing that *Key* is a type from the *Standard* package.  In such cases *MapHasher* may be directly instantiated with *Key*.  Note that the package *TColStd* provides some of these instantiations. 

Elsewhere, if *Key* is not a type from the *Standard* package  you must consider *MapHasher* as a template and build a class which  includes its functions, in order to use it as a hasher in a map instantiated  from the *Collections* component. 

Note that *TCollection_AsciiString* and *TCollection_ExtendedString* classes correspond to these specifications, in consequence they may be used  as hashers: when *Key* is one of these two types you may just define the  hasher as the same type at the time of instantiation of your map. 

@subsubsection occt_fcug_3_1_4 Iterators

#### TCollection_BasicMapIterator

This is a root class for map iterators. A map iterator provides a step  by step exploration of all the entries of a map. 

#### TCollection_DataMapIterator

These are functions used for iterating the contents of a *DataMap* map. 

A map is a non-ordered data structure. The order in which  entries of a map are explored by the iterator depends on its contents and  change when the map is edited. It is not recommended to modify the contents of a map during  the iteration: the result is unpredictable. 

#### TCollection_DoubleMapIterator

These are functions used for iterating the contents of a *DoubleMap* map. 

#### TCollection_ListIterator

These are unctions used for iterating the contents of a *List* data  structure. 

A *ListIterator* object can be used to go through a  list sequentially, and as a bookmark to hold a position in a list. It is not an  index, however. Each step of the iteration gives the current position of  the iterator, to which corresponds the current item in the list. The current  position is not defined if the list is empty, or when the exploration  is finished. 

An iterator class is automatically instantiated from this  generic class at the time of instantiation of a *List* data structure. 

#### TCollection_MapIterator

These are functions used for iterating the contents of a *Map* map. 
An iterator class is automatically instantiated from this  generic class at the time of instantiation of a *Map* map. 

#### TCollection_SetIterator

These are functions used for iterating the contents of a *Set* data  structure. 
An iterator class is automatically instantiated from this  generic class at the time of instantiation of a *Set* structure. 

#### TCollection_StackIterator

These are functions used for iterating the contents of a **Stack** data  structure. 

An iterator class is automatically instantiated from this  generic class at the time of instantiation of a *Stack* structure. 

@subsection occt_fcug_3_2 Collections of Standard Objects
@subsubsection occt_fcug_3_2_1 Overview
While generic classes of the *TCollection* package are the  root classes that describe the generic purpose of every type of collection, classes effectively used are extracted from the *TColStd* package. 
The *TColStd* and *TShort* packages provide  frequently used instantiations of generic classes with objects from the *Standard* package or strings from the *TCollection* package. 

@subsubsection occt_fcug_3_2_2 Description
These instantiations are the following: 
  * Unidimensional arrays: instantiations of the *TCollection_Array1* generic class with *Standard* Objects and *TCollection* strings.
  * Bidimensional arrays: instantiations of the *TCollection_Array2* generic class with *Standard* Objects.
  * Unidimensional arrays manipulated by handles: instantiations of  the *TCollection_HArray1* generic class with *Standard* Objects and *TCollection* strings.
  * Bidimensional arrays manipulated by handles: instantiations of  the *TCollection_HArray2* generic class with *Standard* Objects.
  * Sequences: instantiations of the *TCollection_Sequence* generic  class with *Standard* objects and *TCollection* strings.
  * Sequences manipulated by handles: instantiations of the *TCollection_HSequence* generic class with *Standard* objects and *TCollection* strings.
  * Lists: instantiations of the *TCollection_List* generic  class with *Standard* objects.
  * Queues: instantiations of the *TCollection_Queue* generic  class with *Standard* objects.
  * Sets: instantiations of the *TCollection_Set* generic class  with *Standard* objects.
  * Sets manipulated by handles: instantiations of the *TCollection_HSet* generic class with *Standard* objects.
  * Stacks: instantiations of the *TCollection_Stack* generic  class with *Standard* objects.
  * Hashers on map keys: instantiations of the *TCollection_MapHasher* generic class with *Standard* objects.
  * Basic hashed maps: instantiations of the *TCollection_Map* generic  class with *Standard* objects.
  * Hashed maps with an additional item: instantiations of the *TCollection_DataMap* generic class with *Standard* objects.
  * Basic indexed maps: instantiations of the *TCollection_IndexedMap* generic class with *Standard* objects.
  * Indexed maps with an additional item: instantiations of the *TCollection_IndexedDataMap* generic class with *Standard_Transient* objects.
  * Class *TColStd_PackedMapOfInteger* provides alternative  implementation of map of integer numbers, optimized for both performance and  memory usage (it uses bit flags to encode integers, which results in spending  only 24 bytes per 32 integers stored in optimal case). This class also provides  Boolean operations with maps as sets of integers (union, intersection,  subtraction, difference, checks for equality and containment).
  
@subsection occt_fcug_3_3 NCollections
@subsubsection occt_fcug_3_3_1 Overview  
  
The *NCollection* package provides a set of template collection classes used throughout OCCT.

Macro definitions of these classes are stored in *NCollection_Define\*.hxx* files. These definitions are now obsolete though still can be used, particularly for compatibility with the existing code.

@subsubsection occt_fcug_3_3_2 Instantiation of collection classes

Now we are going to implement the definitions from *NCollection* in the code, taking as an example a sequence of points (analogue of *TColgp_SequenceOfPnt*).
  
#### Definition of a new collection class

Let the header file be *MyPackage_SequenceOfPnt.hxx* :

Template class instantiaton
~~~~~
#include <NCollection_Sequence.hxx>
#include <gp_Pnt.hxx>
typedef NCollection_Sequence<gp_Pnt> MyPackage_SequenceOfPnt;
~~~~~

Macro instantiation
~~~~~
#include <NCollection_DefineSequence.hxx>
#include <gp_Pnt.hxx>
~~~~~

The following line defines the class "base collection of points"
~~~~~
DEFINE_BASECOLLECTION(MyPackage_BaseCollPnt, gp_Pnt)
~~~~~

The following line defines the class *MyPackage_SequenceOfPnt*

~~~~~
DEFINE_SEQUENCE (MyPackage_SequenceOfPnt, MyPackage_BaseCollPnt , gp_Pnt)  
~~~~~

#### Definition of a new collection class managed by Handle

It is necessary to provide relevant statements both in the header ( .hxx file) and the C++ source ( .cxx file). 

Header file MyPackage_HSequenceOfPnt.hxx:

~~~~~
#include <NCollection_DefineHSequence.hxx>
#include <gp_Pnt.hxx>
~~~~~

The following line defines the class "base collection of points"

~~~~~
DEFINE_BASECOLLECTION(MyPackage_BaseCollPnt, gp_Pnt)
~~~~~

The following line defines the class *MyPackage_SequenceOfPnt*

~~~~~
DEFINE_SEQUENCE (MyPackage_SequenceOfPnt, MyPackage_BaseCollPnt, gp_Pnt)
~~~~~

The following line defines the classes *MyPackage_HSequenceOfPnt* and *Handle(MyPackage_HSequenceOfPnt)*

~~~~~
DEFINE_HSEQUENCE (MyPackage_HSequenceOfPnt, MyPackage_SequenceOfPnt)
~~~~~

Source code file will be *MyPackage_HSequenceOfPnt.cxx* or any other .cxx file (once in the whole project):

~~~~~
IMPLEMENT_HSEQUENCE (MyPackage_HSequenceOfPnt)
~~~~~

@subsubsection occt_fcug_3_3_3 Arrays and sequences

Standard collections provided by OCCT are:
* *NCollection_Array1* -- fixed-size (at initialization) one-dimensional array; note that the index can start at any value, usually 1;
* *NCollection_Array2* -- fixed-size (at initialization) two-dimensional array; note that the index can start at any value, usually 1;
* *NCollection_List* -- plain list;
* *NCollection_Sequence* -- double-connected list with access by index; note that the index starts at 1.

These classes provide STL-style iterators (methods begin() and end()) and thus can be used in STL algorithms.

@subsubsection occt_fcug_3_3_3x Maps

NCollection provides several classes for storage of objects by value, providing fast search due to use of hash:
* *NCollection_Map* -- hash set;
* *NCollection_IndexedMap* -- set with a prefixed order of elements, allowing fast access by index or by value (hash-based);
* *NCollection_DataMap* -- hash map;
* *NCollection_IndexedDataMap* -- map with a prefixed order of elements, allowing fast access by index or by value (hash-based);
* *NCollection_DoubleMap* -- two-side hash map (with two keys).

@subsubsection occt_fcug_3_3_4 Other collection types

There are 4 collection types provided as template classes:
* *NCollection_Vector*
* *NCollection_UBTree*
* *NCollection_SparseArray*
* *NCollection_CellFilter*

#### Vector

This type is implemented internally as a list of arrays of the same size. Its properties:
* Direct (constant-time) access to members like in Array1 type; data are allocated in compact blocks, this provides faster iteration.
* Can grow without limits, like List, Stack or Queue types.
* Once having the size LEN, it cannot be reduced to any size less than LEN -- there is no operation of removal of items.

Insertion in a Vector-type class is made by two methods:
* _SetValue(ind, theValue)_ -- array-type insertion, where ind is the index of the inserted item, can be any non-negative number. If it is greater than or equal to Length(), then the vector is enlarged (its Length() grows).
* _Append(theValue)_ -- list-type insertion equivalent to _myVec.SetValue(myVec.Length(), theValue)_, incrementing the size of the collection.

Other essential properties coming from List and Array1 type collections:
* Like in *List*, the method *Clear()* destroys all contained objects and releases the allocated memory.
* Like in *Array1*, the methods *Value()* and *ChangeValue()* return a contained object by index. Also, these methods have the form of overloaded operator ().

#### UBTree

The name of this type stands for “Unbalanced Binary Tree”. It stores the members in a binary tree of overlapped bounding objects (boxes or else).
Once the tree of boxes of geometric objects is constructed, the algorithm is capable of fast geometric selection of objects. The tree can be easily updated by adding to it a new object with bounding box. 
The time of adding to the tree of one object is O(log(N)), where N is the total number of objects, so the time of building a tree of N objects is O(N(log(N)). The search time of one object is O(log(N)). 

Defining various classes inheriting *NCollection_UBTree::Selector* we can perform various kinds of selection over the same b-tree object.  

The object may be of any type allowing copying. Among the best suitable solutions there can be a pointer to an object, handled object or integer index of object inside some collection. The bounding object may have any dimension and geometry. The minimal interface of *TheBndType* (besides public empty and copy constructor and operator =) used in UBTree algorithm as follows: 

~~~~~
   class MyBndType
   {
    public:
     inline void                   Add (const MyBndType& other);
     // Updates me with other bounding type instance

     inline Standard_Boolean       IsOut (const MyBndType& other) const;
     // Classifies other bounding type instance relatively me

     inline Standard_Real          SquareExtent() const;
     // Computes the squared maximal linear extent of me (for a box it is the squared diagonal of the box).
   };
~~~~~
   

This interface is implemented in types of Bnd package: *Bnd_Box, Bnd_Box2d, Bnd_B2x, Bnd_B3x*.

To select objects you need to define a class derived from *UBTree::Selector* that should redefine the necessary virtual methods to maintain the selection condition. Usually this class instance is also used to retrieve selected objects after search.
The class *UBTreeFiller* is used to randomly populate a *UBTree* instance. The quality of a tree is better (considering the speed of searches) if objects are added to it in a random order trying to avoid the addition of a chain of nearby objects one following another. 
Instantiation of *UBTreeFiller* collects objects to be added, and then adds them at once to the given UBTree instance in a random order using the Fisher-Yates algorithm.
Below is the sample code that creates an instance of *NCollection_UBTree* indexed by 2D boxes (Bnd_B2f), then a selection is performed returning the objects whose bounding boxes contain the given 2D point.

~~~~~
typedef NCollection_UBTree<MyData, Bnd_B2f> UBTree;
typedef NCollection_List<MyData> ListOfSelected;
//! Tree Selector type
class MyTreeSelector : public UBTree::Selector
{
public:
  // This constructor initializes the selection criterion (e.g., a point)

  MyTreeSelector (const gp_XY& thePnt) : myPnt(thePnt) {}
  // Get the list of selected objects

  const ListOfSelected& ListAccepted () const
  { return myList; }
  // Bounding box rejection - definition of virtual method.  @return True if theBox is outside the selection criterion.

  Standard_Boolean Reject  (const Bnd_B2f& theBox) const
  { return theBox.IsOut(myPnt); }
  // Redefined from the base class. Called when the bounding of theData conforms to the selection criterion. This method updates myList.

  Standard_Boolean Accept  (const MyData& theData)
  { myList.Append(theData); }
  private:
  gp_XY          myPnt;
  ListOfSelected myList;
};
. . .
// Create a UBTree instance and fill it with data, each data item having the corresponding 2D box.

UBTree aTree;
NCollection_UBTreeFiller <MyData, Bnd_B2f> aTreeFiller(aTree);
for(;;) {
  const MyData& aData = …;
  const Bnd_B2d& aBox = aData.GetBox();
  aTreeFiller.Add(aData, aBox);
}
aTreeFiller.Fill();
. . .
// Perform selection based on ‘aPoint2d’
MyTreeSelector aSel(aPoint2d);
aTree.Select(aSel);
const ListOfSelected = aSel.ListAccepted();
~~~~~


#### SparseArray


This type has almost the same features as Vector but it allows to store items having scattered indices. In Vector, if you set an item with index 1000000, the container will allocate memory for all items with indices in the range 0-1000000. In SparseArray, only one small block of items will be reserved that contains the item with index 1000000.

This class can be also seen as equivalence of *DataMap<int,TheItemType>* with the only one practical difference: it can be much less memory-expensive if items are small (e.g. Integer or Handle). 

This type has both interfaces of DataMap and Vector to access items.

#### CellFilter

This class represents a data structure for sorting geometric objects in n-dimensional space into cells, with associated algorithm for fast checking of coincidence (overlapping, intersection, etc.) with other objects. It can be considered as a functional alternative to UBTree, as in the best case it provides the direct access to an object like in an n-dimensional array, while search with UBTree provides logarithmic law access time.

@subsubsection occt_fcug_3_3_5 Features

NCollection defines some specific features, in addition to the public API inherited from TCollection classes. 

#### Iterators

Every collection defines its Iterator class capable of iterating the members in some predefined order. Every Iterator is defined as a subtype of the particular collection type (e.g., MyPackage_StackOfPnt::Iterator ). The order of iteration is defined by a particular collection type. The methods of Iterator are: 

* _void Init (const MyCollection&)_ -- initializes the iterator on the collection object;
* _Standard_Boolean More () const_ -- makes a query if there is another non-iterated member;
* _void Next ()_ -- increments the iterator; 
* _const ItemType& Value () const_ -- returns the current member; 
* _ItemType& ChangeValue () const_ -- returns the mutable current member

~~~~~
typedef Ncollection_Sequence<gp_Pnt>
MyPackage_SequenceOfPnt
void Perform (const MyPackage_SequenceOfPnt& theSequence)
{
        MyPackage_SequenceOfPnt::Iterator anIter (theSequence);
        for (; anIter.More(); anIter.Next()) {
                const gp_Pnt aPnt& = anIter.Value();
....
        }
}
~~~~~

This feature is present only for some classes in *TCollection (Stack, List, Set, Map, DataMap, DoubleMap)*. In *NCollection* it is generalized. 


#### Class BaseCollection

There is a common abstract base class for all collections for a given item type (e.g., gp_Pnt). Developer X can arbitrarily name this base class like *MyPackage_BaseCollPnt* in the examples above. This name is further used in the declarations of any (non-abstract) collection class to designate the C++ inheritance. 

This base class has the following public API:
* abstract class Iterator as the base class for all Iterators descried above; 
* _Iterator& CreateIterator () const_ -- creates and returns the Iterator on this collection;
* _Standard_Integer Size () const_ -- returns the number of items in this collection;
* *void Assign (const NCollection_BaseCollection& theOther)* -- copies the contents of the Other to this collection object; 

These members enable accessing any collection without knowing its exact type. In particular, it makes possible to implement methods receiving objects of the abstract collection type: 

~~~~~
#include <NColection_Map.hxx>
typedef NCollection_Map<gp_Pnt> MyPackage_MapOfPnt;
typedef NCollection_BaseCollection<gp_Pnt> MyPackage_BaseCollPnt;
MyPackage_MapOfPnt aMapPnt;
....
gp_Pnt aResult = COG (aMapPnt);
....
gp_Pnt COG(const MyPackage_BaseCollPnt& theColl)
{
  gp_XYZ aCentreOfGravity(0., 0., 0.);
// create type-independent iterator (it is abstract type instance)
  MyPackage_BaseCollString::Iterator& anIter = theColl.CreateIterator();
  for (; anIter.More(); anIter.Next()) {
    aCentreOfGravity += anIter.Value().XYZ();
  }
  return aCentreOfGravity / theColl.Size();
}
~~~~~

Note that there are fundamental differences between the shown type-independent iterator and the iterator belonging to a particular non-abstract collection:
* Type-independent iterator can only be obtained via the call <i>CreateIterator()</i>; the typed iterator -- only via the explicit construction. 
* Type-independent iterator is an abstract class, so it is impossible to copy it or to assign it to another collection object; the typed iterators can be copied and reassigned using the method <i>Init()</i>. 
* Type-independent iterator is actually destroyed when its collection object is destroyed; the typed iterator is destroyed as any other C++ object in the corresponding C++ scope. 

The common point between them is that it is possible to create any number of both types of iterators on the same collection object. 

#### Heterogeneous Assign

The semantics of the method *Assign()* has been changed in comparison to *TCollection*. In *NCollection* classes the method *Assign()* is virtual and it receives the object of the abstract *BaseCollection* class (see the previous section). Therefore this method can be used to assign any collection type to any other if only these collections are instantiated on the same *ItemType*. 

For example, conversion of *Map* into *Array1* is performed like this:

~~~~~
#include <NCollection_Map.hxx>
#include <NCollection_Array1.hxx>
typedef NCollection_Map<gp_Pnt> MyPackage_MapOfPnt;
typedef NCollection_Array1<gp_Pnt> MyPackage_Array1OfPnt;
....
MyPackage_MapOfPnt aMapPnt;
....
MyPackage_Array1OfPnt anArr1Pnt (1, aMapPnt.Size());
anArr1Pnt.Assign (aMapPnt); // heterogeneous assignment
~~~~~

There are some aspects to mention:
* Unlike in *TCollection*, in *NCollection* the methods *Assign* and operator= do not coincide. The former is a virtual method defined in the *BaseCollection* class. The latter is always defined in instance classes as a non-virtual inline method and it corresponds exactly to the method *Assign* in *TCollection* classes. Therefore it is always profitable to use operator= instead of *Assign* wherever the types on both sides of assignment are known. 
* If the method *Assign* copies to *Array1* or *Array2* structure, it first checks if the size of the array is equal to the number of items in the copied collection object. If the sizes differ, an exception is thrown, as in *TCollection_Array1.gxx*. 
* Copying to *Map, IndexedMap, DataMap* and *IndexedDataMap* can bring about a loss of data: when two or more copied data items have the same key value, only one item is copied and the others are discarded. It can lead to an error in the code like the following:

~~~~~
MyPackage_Array1OfPnt anArr1Pnt (1, 100); 
MyPackage_MapOfPnt aMapPnt;
....
aMapPnt.Assign(anArr1Pnt);
anArr1Pnt.Assign(aMapPnt);
~~~~~

Objects of classes parameterised with two types (*DoubleMap, DataMap* and  *IndexedDataMap*) cannot be assigned. Their method *Assign* throws the exception *Standard_TypeMismatch* (because it is impossible to check if the passed *BaseCollection* parameter belongs to the same collection type).

#### Allocator

All constructors of *NCollection* classes receive the *Allocator* Object as the last parameter. This is an object of a type managed by Handle, inheriting *NCollection_BaseAllocator*, with the following (mandatory) methods redefined:

~~~~~
Standard_EXPORT virtual void* Allocate (const size_t size); 
Standard_EXPORT virtual void Free (void * anAddress);
~~~~~

It is used internally every time when the collection allocates memory for its item(s) and releases this memory. The default value of this parameter (empty *Handle*) designates the use of *NCollection_BaseAllocator* X where the functions *Standard::Allocate* and *Standard::Free* are called. Therefore if the user of *NCollection* does not specify any allocator as a parameter to the constructor of his collection, the memory management will be identical to the one in *TCollection* and other Open CASCADE Technology classes.

Nevertheless, the it is possible to define a custom *Allocator* type to manage the memory in the most optimal or convenient way for his algorithms.

As one possible choice, the class *NCollection_IncAllocator* is included. Unlike *BaseAllocator*, it owns all memory it allocates from the system. Memory is allocated in big blocks (about 20kB) and the allocator keeps track of the amount of occupied memory. The method *Allocate* just increments the pointer to non-occupied memory and returns its previous value. Memory is only released in the destructor of *IncAllocator*, the method *Free* is empty. If used efficiently, this Allocator can greatly improve the performance of OCCT collections.



@subsection occt_fcug_3_4 Strings

Strings are classes that handle dynamically sized sequences of characters based on
ASCII/Unicode UTF-8 (normal 8-bit character type) and UTF-16/UCS-2 (16-bit character type). They provide editing operations with built-in memory management which make the relative objects easier to use than ordinary character arrays.

String classes provide the following services to manipulate character strings:
 * Editing operations on string objects, using a built-in string manager 
 * Handling of dynamically-sized sequences of characters 
 * Conversion from/to ASCII and UTF-8 strings. 

Strings may also be manipulated by handles and therefore shared.

@subsubsection occt_fcug_3_4_1 Examples

#### TCollection_AsciiString

A variable-length sequence of ASCII characters (normal 8-bit  character type). It provides editing operations with built-in memory management  to make *AsciiString* objects easier to use than ordinary character  arrays. 
*AsciiString* objects follow value  semantics;, that is, they are the actual strings, not handles to strings,  and are copied through assignment. You may use *HAsciiString* objects to  get handles to strings. 

#### TCollection_ExtendedString

A variable-length sequence of "extended" (UNICODE)  characters (16-bit character type). It provides editing operations with  built-in memory management to make *ExtendedString* objects easier to use  than ordinary extended character arrays. 

*ExtendedString* objects follow value  semantics;, that is, they are the actual strings, not handles to strings,  and are copied through assignment. You may use *HExtendedString* objects  to get handles to strings. 

#### TCollection_HAsciiString

A variable-length sequence of ASCII characters (normal 8-bit  character type). It provides editing operations with built-in memory management  to make *HAsciiString* objects easier to use than ordinary character  arrays. 
*HAsciiString* objects are *handles* to strings. 
  * *HAsciiString* strings may be shared by several objects.
  * You may use an *AsciiString* object to get the actual  string.
*HAsciiString* objects use an *AsciiString* string  as a field. 

#### TCollection_HExtendedString

A variable-length sequence of extended; (UNICODE)  characters (16-bit character type). It provides editing operations with  built-in memory management to make *ExtendedString* objects easier to use  than ordinary extended character arrays. 
*HExtendedString* objects are *handles* to  strings. 
  * *HExtendedString* strings may be shared by several objects.
  * You may use an *ExtendedString* object to get the actual  string.
*HExtendedString* objects use an *ExtendedString* string  as a field. 

@subsubsection occt_fcug_3_4_2 Conversion

*Resource_Unicode* provides functions to convert a non-ASCII *C string* given  in ANSI, EUC, GB or SJIS format, to a Unicode string of extended characters, and vice  versa. 

@subsection occt_fcug_3_5 Quantities

Quantities are various classes supporting date and time information and fundamental types representing most physical quantities such as  length, area, volume, mass, density, weight, temperature, pressure etc. 

Quantity classes provide the following services:
  * Definition of primitive types representing most of mathematical and physical quantities;
  * Unit conversion tools providing a uniform mechanism for dealing  with quantities and associated physical units: check unit compatibility, perform conversions of values between different units, etc. (see package  *UnitsAPI*)    
  * Resources to manage time information such as dates and time periods 
  * Resources to manage color definition 

A mathematical quantity is characterized by the name and the value (real).

A physical quantity is characterized by the name, the value (real) and the unit. The unit may be either an international unit complying with the International Unit System (SI) or a user defined unit. The unit is managed by the physical quantity user.

The fact that both physical and mathematical quantities are manipulated as real values means that :
  * They are defined as aliases of real values, so all functions provided by the <i>Standard_Real</i> class are available on each quantity.
  * It is possible to mix several physical quantities in a mathematical or physical formula involving real values.

<i>Quantity</i> package includes all commonly used basic physical quantities. 

@subsection occt_fcug_3_6 Unit Conversion

The *UnitsAPI* global functions are used to convert a  value from any unit into another unit. Conversion is executed among three unit  systems: 
  * the **SI System**,
  * the user’s **Local System**,
  * the user’s **Current System**.
The **SI System** is the standard international unit  system. It is indicated by *SI* in the signatures of the *UnitsAPI* functions. 

The OCCT (former MDTV) System corresponds to the SI  international standard but the length unit and all its derivatives use the millimeter instead of the meter.  

Both systems are proposed by Open CASCADE Technology; the SI  System is the standard option. By selecting one of these two systems, you  define your **Local System** through the *SetLocalSystem* function. The  **Local System** is indicated by *LS* in the signatures of the *UnitsAPI* functions. 
The Local System units can be modified in the working  environment. You define your **Current System** by modifying its units  through the *SetCurrentUnit* function. The Current System is indicated by *Current* in the signatures of the *UnitsAPI* functions. 
A physical quantity is defined by a string (example:  LENGTH). 


@section occt_occt_fcug_4 Math Primitives and Algorithms

@subsection occt_occt_fcug_4_1 Overview

Math primitives and algorithms available in Open CASCADE  Technology include: 
  * Vectors and matrices
  * Geometric primitives
  * Math algorithms
  
@subsection occt_occt_fcug_4_2 Vectors and Matrices

The Vectors and Matrices component provides a C++  implementation of the fundamental types *Vector* and *Matrix*, which are regularly used to define more complex data structures. 

The <i> Vector</i> and <i> Matrix </i> classes provide commonly used mathematical algorithms which
include:

  * Basic calculations involving vectors and matrices; 
  * Computation of eigenvalues and eigenvectors of a square matrix; 
  * Solvers for a set of linear algebraic equations; 
  * Algorithms to find the roots of a set of non-linear equations; 
  * Algorithms to find the minimum function of one or more independent variables. 

These classes also provide a data structure to represent any expression,
relation, or function used in mathematics, including the assignment of variables.

Vectors and matrices have arbitrary ranges which must be defined at declaration time
and cannot be changed after declaration.

~~~~~
math_Vector  v(1, 3); 
//  a vector of dimension 3 with range (1..3) 
math_Matrix  m(0, 2, 0, 2); 
//  a matrix of dimension 3x3 with range (0..2, 0..2) 
math_Vector  v(N1, N2); 
//  a vector of dimension N2-N1+1 with range (N1..N2)
~~~~~

Vector and Matrix objects use value semantics. In other  words, they cannot be shared and are copied through assignment. 

~~~~~
math_Vector  v1(1, 3), v2(0, 2); 
v2  = v1; 
//  v1 is copied into v2. a modification of v1 does not affect  v2 
~~~~~

Vector and Matrix values may be initialized and obtained  using indexes which must lie within the range definition of the vector or the  matrix. 

~~~~~
math_Vector v(1, 3);
math_Matrix m(1, 3, 1, 3);
Standard_Real value;

v(2) = 1.0;
value = v(1);
m(1, 3) = 1.0;
value = m(2, 2);
~~~~~

Some operations on Vector and Matrix objects may not be  legal. In this case an exception is raised. Two standard exceptions are used: 
  * *Standard_DimensionError* exception is raised when two matrices or  vectors involved in an operation are of incompatible dimensions.
  * *Standard_RangeError* exception is raised if an access outside the  range definition of a vector or of a matrix is attempted.
  
~~~~~~
math_Vector v1(1, 3), v2(1, 2), v3(0, 2);
v1 = v2;
// error: Standard_DimensionError is raised

v1 = v3;
// OK: ranges are not equal but dimensions are
// compatible

v1(0) = 2.0;
// error: Standard_RangeError is raised
~~~~~~

@subsection occt_occt_fcug_4_3 Primitive Geometric Types

Open CASCADE Technology primitive geometric types are a  STEP-compliant implementation of basic geometric and algebraic entities.  
They provide: 
  * Descriptions of primitive geometric shapes, such as:
          * Points; 
          * Vectors; 
          * Lines; 
          * Circles and conics; 
          * Planes and elementary surfaces;
  * Positioning of these shapes in space or in a plane by means of an axis or a coordinate system;
  * Definition and application of geometric transformations to these shapes:
          * Translations; 
          * Rotations; 
          * Symmetries; 
          * Scaling transformations; 
          * Composed transformations;
  * Tools (coordinates and matrices) for algebraic computation.
  
All these functions are provided by geometric processor package <i> gp</i>. Its classes for 2d and 3d objects are handled by value rather than by reference. When this sort of object is copied, it is copied entirely. Changes in one instance will not be  reflected in another. 

The *gp* package defines the basic geometric entities used for algebraic calculation and basic analytical geometry  in 2d & 3d space. It also provides basic transformations such as identity,  rotation, translation, mirroring, scale transformations, combinations of  transformations, etc. Entities are handled by value.  

Please, note that <i> gp</i> curves and surfaces are analytic: there is no parameterization and no orientation on <i>gp</i> entities, i.e. these entities do not provide functions which work with these properties. 

If you need, you may use more evolved data structures provided by <i> Geom</i> (in 3D space) and <i> Geom2d</i> (in the plane). However, the definition of <i> gp</i> entities is identical to the one of equivalent <i> Geom</i> and <i> Geom2d</i> entities, and they are located in the plane or in space with the same kind of positioning systems. They implicitly contain the orientation, which they express on the <i> Geom </i> and <i> Geom2d </i> entities, and they induce the definition of their parameterization.

Therefore, it is easy to give an implicit parameterization to <i> gp</i> curves and surfaces, which is the parametrization of the equivalent <i> Geom</i> or <i> Geom2d</i> entity. This property is particularly useful when computing projections or intersections, or for operations involving complex algorithms where it is particularly important to manipulate the simplest data structures, i.e. those of <i> gp</i>. Thus,  <i> ElCLib</i> and <i> ElSLib</i> packages provide functions to compute:
  * the point of parameter u on a 2D or 3D gp curve,
  * the point of parameter (u,v) on a gp elementary surface, and
  * any derivative vector at this point.

Note: the <i> gp</i> entities cannot be shared when they are inside more complex data structures. 
  
@subsection occt_occt_fcug_4_4 Collections of Primitive Geometric Types

Before creating a geometric object, you must decide whether  you are in a 2d or in a 3d context and how you want to handle the object. 
If you do not need a single instance of a geometric  primitive but a set of them then the package which deals with collections of  this sort of object, *TColgp*, will provide the necessary functionality. 
In particular, this package provides standard and frequently  used instantiations of generic classes with geometric objects, i.e. *XY*, *XYZ*,  *Pnt*, *Pnt2d*, *Vec*, *Vec2d*, *Lin*, *Lin2d*, *Circ*,  *Circ2d.* 

@subsection occt_occt_fcug_4_5 Basic Geometric Libraries
There are various library packages available which offer a  range of basic computations on curves and surfaces. 
If you are dealing with objects created from the *gp* package,  the useful algorithms are in the elementary curves and surfaces libraries -- the  *ElCLib* and *ElSLib* packages.
* *EICLib* provides methods for analytic curves. This is a library of simple  computations on curves from the *gp* package (Lines, Circles and Conics).  It is possible to compute points with a given parameter or to compute the parameter for a point. 
* *EISLib* provides methods for analytic surfaces. This is a library of simple  computations on surfaces from the package *gp* (Planes, Cylinders,  Spheres, Cones, Tori). It is possible to compute points with a given pair of parameters or to compute the parameter for a point. There is a library for calculating normals  on curves and surfaces. 

Additionally, *Bnd* package provides a set of classes and tools to operate  with bounding boxes of geometric objects in 2d and 3d space. 

@subsection occt_occt_fcug_4_6 Common Math Algorithms
The common math algorithms library provides a C++  implementation of the most frequently used mathematical algorithms. These  include: 
  * Algorithms to solve a set of linear algebraic equations,
  * Algorithms to find the minimum of a function of one or more  independent variables,
  * Algorithms to find roots of one, or of a set, of non-linear  equations,
  * An algorithm to find the eigenvalues and eigenvectors of a square  matrix.
  
All mathematical algorithms are implemented using the same  principles. They contain: 
A constructor performing all, or most of, the calculation,  given the appropriate arguments. All relevant information is stored inside the  resulting object, so that all subsequent calculations or interrogations will be  solved in the most efficient way. 

A function *IsDone* returning the boolean true if the  calculation was successful. 
A set of functions, specific to each algorithm, enabling all  the various results to be obtained. 
Calling these functions is legal only if the function *IsDone*  answers **true**, otherwise the exception *StdFail_NotDone* is raised. 

The example below demonstrates the use of the Gauss class,  which implements the Gauss solution for a set of linear equations.The following  definition is an extract from the header file of the class *math_Gauss*: 

~~~~~~
class Gauss {
public:
  Gauss (const math_Matrix& A);
  Standard_Boolean IsDone() const;
  void Solve (const math_Vector& B,
  math_Vector& X) const;
};
~~~~~~

Now the main program uses the Gauss class to solve the  equations a*x1=b1 and a*x2=b2: 

~~~~~
#include <math_Vector.hxx> 
#include <math_Matrix.hxx>
main ()
{
  math_Vector a(1, 3, 1, 3);
  math_Vector b1(1, 3), b2(1, 3);
  math_Vector x1(1, 3), x2(1, 3);
  // a, b1 and b2 are set here to the appropriate values
  math_Gauss sol(a);              // computation of the
  // LU decomposition of A
  if(sol.IsDone()) {              // is it OK ?
    sol.Solve(b1, x1);      // yes, so compute x1
    sol.Solve(b2, x2);      // then x2
    ...
  } 
  else {                    // it is not OK:
    // fix up
    sol.Solve(b1, x1);            // error:
    // StdFail_NotDone is raised
  }
}
~~~~~

The next example demonstrates the use of the *BissecNewton* class, which implements a combination of the Newton and Bissection algorithms  to find the root of a function known to lie between two bounds. The definition is an extract from the header file of the class *math_BissecNewton*: 

~~~~~
class  BissecNewton { 
        public: 
                BissecNewton  (math_FunctionWithDerivative& f, 
                        const Standard_Real bound1, 
                        const Standard_Real bound2, 
                        const Standard_Real tolx); 
        Standard_Boolean IsDone() const; 
        Standard_Real Root(); 
}; 
~~~~~

The abstract class  *math_FunctionWithDerivative* describes the services which have to be implemented  for the function f which is to be used by a *BissecNewton* algorithm. The  following definition corresponds to the header file of the abstract class  *math_FunctionWithDerivative*: 

~~~~~
class  math_FunctionWithDerivative { 
        public: 
                virtual Standard_Boolean Value 
                        (const Standard_Real x, Standard_Real&  f) = 0; 
                virtual Standard_Boolean Derivative 
                        (const Standard_Real x, Standard_Real&  d) = 0; 
                virtual Standard_Boolean Values 
                        (const Standard_Real x, 
                        Standard_Real& f, 
                        Standard_Real& d) = 0; 
}; 
~~~~~

Now the test sample uses the *BissecNewton* class to find the  root of the equation *f(x)=x**2-4* in the interval [1.5, 2.5]: the function to  solve is implemented in the class *myFunction* which inherits from the class *math_FunctionWithDerivative*, then the main program finds the required root. 

~~~~~
#include <math_BissecNewton.hxx> 
#include <math_FunctionWithDerivative.hxx>
class myFunction : public math_FunctionWithDerivative 
{
  Standard_Real coefa, coefb, coefc;

  public:
    myFunction (const  Standard_Real a, const Standard_Real b,
                const Standard_Real c) :
      coefa(a), coefb(b), coefc(c)
    {}

    virtual  Standard_Boolean Value (const Standard_Real x, 
                                    Standard_Real& f)
    {
      f = coefa * x * x + coefb * x + coefc;
    }

    virtual  Standard_Boolean Derivative (const Standard_Real x,
                                         Standard_Real&  d)
    {
      d = coefa * x * 2.0 + coefb;
    }

    virtual  Standard_Boolean Values (const Standard_Real x,
                                     Standard_Real& f, Standard_Real& d)
    {
      f = coefa * x * x + coefb * x + coefc;
      d = coefa * x *  2.0 + coefb;
    }
};

main()
{
  myFunction f(1.0, 0.0, 4.0);
  math_BissecNewton sol(F, 1.5, 2.5, 0.000001);
  if(Sol.IsDone()) { // is it OK ?
    Standard_Real x = sol.Root(); // yes.
  }
  else { // no
  }
~~~~~

@subsection occt_occt_fcug_4_7 Precision

On the OCCT platform, each object stored in the database  should carry its own precision value. This is important when dealing with  systems where objects are imported from other systems as well as with various  associated precision values. 

The *Precision* package addresses the daily problem of  the geometric algorithm developer: what precision setting to use to compare two  numbers. Real number equivalence is clearly a poor choice. The difference  between the numbers should be compared to a given precision setting. 

Do not write _if  (X1 == X2),_  instead write _if  (Abs(X1-X2) < Precision)._ 

Also, to order real numbers, keep in mind that _if  (X1 < X2 - Precision)_ is incorrect. 
_if  (X2 - X1 > Precision)_ is far better when *X1* and *X2* are high numbers. 

This package proposes a set of methods providing precision  settings for the most commonly encountered situations. 

In Open CASCADE Technology, precision is usually not  implicit; low-level geometric algorithms accept precision settings as  arguments. Usually these should not refer directly to this package. 

High-level modeling algorithms have to provide a precision  setting to the low level geometric algorithms they call. One way is to use the  settings provided by this package. The high-level modeling algorithms can also  have their own strategy for managing precision. As an example the Topology Data  Structure stores precision values which are later used by algorithms. When a  new topology is created, it takes the stored value. 
Different precision settings offered by this package cover  the most common needs of geometric algorithms such as *Intersection* and *Approximation*. 
The choice of a precision value depends both on the algorithm  and on the geometric space. The geometric space may be either: 
  * a real space, 3d or 2d where the lengths are measured  in meters, micron, inches, etc.
  * a parametric space, 1d on a curve or 2d on a surface  where numbers have no dimension.
The choice of precision value for parametric space depends  not only on the accuracy of the machine, but also on the dimensions of the  curve or the surface. 
This is because it is desirable to link parametric precision  and real precision. If you are on a curve defined by the equation *P(t)*,  you would want to have equivalence between the following: 

~~~~~
Abs(t1-t2)  < ParametricPrecision 
Distance  (P(t1),P(t2)) < RealPrecision. 
~~~~~

@subsubsection occt_occt_fcug_4_7_1 The Precision package
The *Precision* package offers a number of package methods and  default precisions for use in dealing with angles, distances, intersections,  approximations, and parametric space. 
It provides values to use in comparisons to test for real  number equalities. 
  * Angular precision compares angles.
  * Confusion precision compares distances.
  * Intersection precision is used by intersection algorithms.
  * Approximation precision is used by approximation algorithms.
  * Parametric precision gets a parametric space precision from a 3D  precision.
  * *Infinite* returns a high number that can be considered to  be infinite. Use <i>-Infinite</i> for a high negative number. 
  
@subsubsection occt_occt_fcug_4_7_2 Standard Precision values
This package provides a set of real space precision values  for algorithms. The real space precisions are designed for precision to *0.1*  nanometers. The only unit available is the millimeter. 
The parametric precisions are derived from the real  precisions by the *Parametric* function. This applies a scaling factor which  is the length of a tangent to the curve or the surface. You, the user, provide  this length. There is a default value for a curve with <i>[0,1]</i> parameter  space and a length less than 100 meters. 
The geometric packages provide Parametric precisions for the  different types of curves. 
The *Precision* package provides methods to test whether a  real number can be considered to be infinite. 

#### Precision::Angular

This method is used to compare two angles. Its current value is *Epsilon(2 *  PI)* i.e. the smallest number *x* such that *2*PI + x* is  different of *2\*PI*. 

It can be used to check confusion  of two angles as follows:
_Abs(Angle1  - Angle2) < Precision::Angular()_ 

It is also possible to check parallelism  of two vectors (_Vec_ from _gp_) as follows _V1.IsParallel(V2,Precision::Angular())_ 

Note that *Precision::Angular()* can be used on both  dot and cross products because for small angles the *Sine* and the *Angle* are equivalent. So to test if two directions of type *gp_Dir* are  perpendicular, it is legal to use the following code: 
_Abs(D1 * D2) < Precision::Angular()_ 

#### Precision::Confusion

This method is used to test 3D distances. The current value is *1.e-7*, in other words, 1/10 micron if the unit used is the millimeter. 

It can be used to check confusion  of two points (_Pnt_ from _gp_) as follows: 
_P1.IsEqual(P2,Precision::Confusion())_ 

It is also possible to find a  vector of null length (_Vec_ from _gp_) :
_V.Magnitude() <  Precision::Confusion()_ 

#### Precision::Intersection

This is reasonable precision to pass to an Intersection process as  a limit of refinement of Intersection Points. *Intersection* is high  enough for the process to converge quickly. *Intersection* is lower than *Confusion* so that you still get a point on the intersected geometries. The current  value is *Confusion() / 100*. 

#### Precision::Approximation

This is a reasonable precision to pass to an approximation process  as a limit of refinement of fitting. The approximation is greater than the other  precisions because it is designed to be used when the time is at a premium. It has  been provided as a reasonable compromise by the designers of the Approximation  algorithm. The current value is *Confusion() * 10*. 
Note that Approximation is greater than Confusion, so care  must be taken when using Confusion in an approximation process.