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

Foundation Classes  {#user_guides__foundation_classes}
=================================

@tableofcontents

@section occt_fcug_1 Introduction

@subsection occt_fcug_1_1 Foundation Classes Overview

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  offerings on our web site at <a href="http://www.opencascade.org/support/training/">www.opencascade.org/support/training/</a>   
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 downcasting 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 the 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 the **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.


@subsection occt_fcug_1_2 Fundamental Concepts
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. 

In Open CASCADE Technology the  classes are usually defined using CDL (CASCADE Definition Language) that  provides a certain level of abstraction from pure C++ constructs and ensures a definite  level of similarity in the implementation of classes. See *CDL User’s Guide*  for more details. 

This chapter introduces some basic concepts most of which  are directly supported by CDL and used not only in Foundation Classes, but  throughout the whole OCCT library. 

@subsubsection occt_fcug_1_2_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_1_2_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_1_2_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). 

#### Categories of Classes
Classes fall into three categories: 
  * Ordinary classes.
  * Deferred classes. A **deferred 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. The C++ equivalent of a deferred CDL  class is an abstract class. 
  * Generic classes. A **generic class** offers a set of functional behaviors  to manipulate other data types. Instantiation of a generic class requires that  a data type is given for its argument(s). The generic classes in CDL perform  the same mission as template classes in C++.
  
@subsubsection occt_fcug_1_2_4 Genericity
Generic classes are implemented in two steps. First you  declare the generic class to establish the model, then you instantiate this  class by giving information about the generic types. 

#### Declaring a Generic  Class

The generic classes in Open CASCADE Technology are similar  by their intent to C++ templates with explicit instantiation. 
A generic class is declared in CDL as operating on data  items of non-fixed types which are declared as arguments of the generic class.  It is possible to put a restriction on these data types to be of subtype of  some definite class. Definition of the generic class does not create new class  type in C++ terms; it only defines a pattern for generation (instantiation) of  the real classes.
 
#### Instantiation of a Generic Class

When a generic class is instantiated, its argument types are  substituted by actually existing data types (elementary types or classes). The  result of instantiation is a new C++ class with an arbitrary name (specified in  the instantiating declaration). By convention, the name of the instantiated class  is usually constructed from the name of the generic class and names of actual  argument types. As for any other class, the name of the class instantiating a generic  type is prefixed by the name of the package in which instantiation is declared. 
@code
class Array1OfReal instantiates Array1 from TCollection  (Real);
@endcode

This declaration located in a CDL file of the *TColStd*  package defines a new C++ class *TColStd_Array1OfReal* as the instantiation of  generic class *TCollection_Array1* for *Real* values. 
More than one class can be instantiated from the same  generic class with the same argument types. Such classes will be identical by  implementation, but considered as two different classes by C++.  
No class can inherit from a generic class. 
A generic class can be a deferred class. A generic class can  also accept a deferred class as its argument. In both these cases, any class  instantiated from it will also be deferred. The resulting class can then be  inherited by another class. 

#### Nested Generic Classes

It often happens that many classes are linked by a common  generic type. This is the case when a base structure furnishes an iterator. In  this context, it is necessary to make sure that the group of linked generic  classes is indeed instantiated for the same type of object. In order to group  the instantiation, you may declare certain classes as being nested. 
When generic class is instantiated, its nested classes are  instantiated as well. The name of the instantiation of the nested class is  constructed from the name of that nested class and name of the main generic  class, connected by ‘Of’. 
@code
class MapOfReal instantiates Map from TCollection  (Real,MapRealHasher);
@endcode
This declaration in *TColStd* defines not only class  *TColStd_MapOfReal*, but also class *TColStd_MapIteratorOfMapOfReal*, which is  instantiated from nested class *MapIterator* of the generic class  *TCollection_Map*. Note that instantiation of the nested class is separate class,  it is not nested class to the instantiation of the main class. 
**Nested classes**, even though they are described as  non-generic classes, are generic by construction being inside the class they  are a member of. 

@subsubsection occt_fcug_1_2_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 descendent 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 **deferred**. 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 descendent classes. 

@subsubsection occt_fcug_1_2_6 Categories  of Data Types
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_1_2_7 Exceptions
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. This mechanism is a safeguard of  software quality. 

@subsubsection occt_fcug_1_2_8 Persistence  and Data Schema
The data schema is the structure used by an application to  store its data. Data schemas consist of persistent classes. 

An object is called **persistent** if it can be  permanently stored. Thus, the object can be reused at a later date by the  application, which created it, or by another application.
 
In order for an object to be persistent for CDL, its type  must be declared as inheriting from the class *Standard_Persistent* or have a  parent class inheriting from the *Standard_Persistent* class. Note that classes  inheriting from *Standard_Persistent* are handled by a reference. 

Objects instantiated from classes which inherit from the  Standard_Storable class cannot themselves be stored individually, but they can  be stored as fields of an object which inherits from *Standard_Persistent*. Note  that objects inheriting from *Standard_Storable* are handled by a value. 

@section occt_fcug_2 Basics
This chapter deals with basic services such as memory management,  programming with handles, primitive types, exception handling, genericity by  downcasting and plug-in creation. 
@subsection occt_fcug_2_1 Data Types
@subsubsection occt_fcug_2_1_1 Primitive Types
The primitive types are predefined in the language and they  are **manipulated by value**. 
Some of these primitives inherit from the **Storable** class.  This means they can be used in the implementation of persistent objects, either  contained in entities declared within the methods of the object, or they form  part of the internal representation of the object. 

The primitives inheriting from *Standard_Storable* are the  following: 
* **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. 
There are also non-Storable primitives. They are: 
* **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: **Boolean** is a 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, not as well as equivalence relations ==,  != are defined on Booleans. 
* Standard_Character: **Character** is a 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: **ExtCharacter** is a 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: **CString** is a 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  : **Address** is a fundamental type representing a generic  pointer. **Address** is implemented as a **typedef** of the C++ *void* fundamental  type. 
* Standard_ExtString  : **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_Persistent  or 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"

Types that are known to the schema (i.e. they are either **primitives** or they inherit from **Storable**) and are manipulated by value, can be  stored inside a persistent object as part of the representation. Only in this  way can a “manipulated by value” object be stored in a file. 

@subsubsection occt_fcug_2_1_3 Types manipulated by reference (handle)
There are two categories of types which are manipulated by  handle: 
  * Types defined by classes inheriting from the **Persistent** class,  which are therefore storable in a file.
  * 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 Summary of properties

The following table summarizes how various data types are handled and stored.

| Type        | Manipulated by handle | Manipulated by value |
| :------- | :-------------------- | :-------------------- |
| storable |     Persistent	| Primitive, Storable (if nested in a persistent class)|
|temporary | Transient	| Other |


@subsection occt_fcug_2_2 Programming with Handles
@subsubsection occt_fcug_2_2_1 Handle Definition
A handle may be compared with a C++ 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. 

Transient and Persistent classes may be manipulated either  with handles or with values. Handles which reference non-persistent objects are  called non-storable handles; therefore, a persistent object cannot contain a  non-storable handle.  

Organization of Classes
-----------------------
Classes used with handles are persistent or transient. 

Classes that inherit from *Standard_Transient*  are transient while classes that inherit from *Standard_Persistent*  are persistent. 

In this chapter we will discuss only transient classes and  relevant handles. Persistent classes and their handles are organized in a similar  manner. 

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. 

For every class derived (directly or indirectly) from *Transient*, CDL extractor creates associated class *Handle()* whose name is the  same as the name of that class prefixed by *Handle_*. Open CASCADE Technology  provides pre-processor macro *Handle()* that produces a name of a *Handle()* class  for a given transient class name. 

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

General
-------

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). For every class type  derived from *Standard_Transient*, CDL extractor creates a code instantiating single  instance of the class *Standard_Type* (type descriptor) that holds information on  that type: its name and list of ancestor types. 
That instance (actually, a handle on it) is returned by the  virtual method *DynamicType()* of the class derived from *Standard_Transient*. The  other virtual method *IsKind()* provides a means to check whether a given object  has specified type or inherits it. 

In order to refer to the type descriptor object for a given  class type, use macros *STANDARD_TYPE()* with argument being a name of the class. 

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 persistent 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 on a persistent or transient 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 de-allocation
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. 
~~~~~

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
  
@subsubsection occt_fcug_2_2_6 Creating  Transient Classes without CDL

Though generation of Handle class and related C++ code is  normally performed by CDL extractor, it is also possible to define a class managed  by handle without CDL. To facilitate that, several macros are provided in the  file Standard_DefineHandle.hxx: 

* **DEFINE_STANDARD_HANDLE(class_name,ancestor_name)** - declares Handle class  for a class *class_name* that inherits class *ancestor_name* (for  instance, *Standard_Transient*). This macro should be put in a header file; the  declaration of the handle to a base class must be available (usually put before  or after the declaration of the class *class_name*, or into a separate  header file).  
* **IMPLEMENT_STANDARD_HANDLE(class_name,ancestor_name)** - implements method  *DownCast()* of the *Handle* class. Should be located in a C++ file (normally the  file where methods of the class *class_name* are implemented). 
* **DEFINE_STANDARD_RTTI(class_name)** - declares methods required for  RTTI in the class *class_name* declaration; should be in public: section. 
* **IMPLEMENT_STANDARD_RTTIEXT(class_name,ancestor_name)** - implements above methods. Usually  put into the C++ file implementing class class_name. 
Note that it is important to ensure correctness of macro  arguments, especially the ancestor name, otherwise the definition may be  inconsistent (no compiler warnings will be issued in case of mistake). 

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

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


@subsection occt_fcug_2_3 Memory  Management in Open CASCADE Technology
In the course of 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 de-allocating memory may be not sufficient. For  this reason, Open CASCADE Technology employs a specialized memory manager  implemented in the Standard package. 

@subsubsection occt_fcug_2_3_1. Usage
To use the Open CASCADE Technology memory manager to  allocate memory in a C code, just 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. 

CDL extractor defines *new()* and *delete()* in this way for all  classes declared with CDL. Thus all OCCT classes (apart from a few exceptions)  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 some 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 Configuring  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()*.
  * MMGT_REENTRANT: when set to 1 (default), all calls to the  optimized memory manager will be secured against possible simultaneous access  from different execution threads. This variable should be set in any  multithreaded application that uses an optimized memory manager (*MMGT_OPT=1*)  and has more than one thread potentially calling OCCT functions. If set to 0,  OCCT memory management and exception handling routines will skip the code protecting  from possible concurrency in multi-threaded environment. This can yield some  performance gain in some applications, but can lead to unpredictable results if  used in a multithreaded application.
  
**Note** it is  recommended to use options *MMGT_OPT=2* and *MMGT_REENTRANT=1* for applications that use OCCT  memory manager from more than one thread, on multiprocessor hardware.
 
@subsubsection occt_fcug_2_3_3 Implementation  details
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. 

#### 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, the method Standard::Purge() shall be called 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. 

In multithreaded mode *(MMGT_REENTRANT=1)*, the 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 Exception  Handling
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. 

Open CASCADE Technology provides a hierarchy of exception  classes with a root class being class Standard_Failure from the Standard  package. The CDL extractor generates exception classes with standardized  interface. 

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_1 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 Value(). 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 Raise_if() 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  pre-processor symbols No_Exception or No_<ErrorTypeName> 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_2 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  try {} 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 most distant try block, 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_3 Implementation  details

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 and DEC, 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  SUN and 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  SUN and Linux Open CASCADE Technology can also be compiled in compatibility  mode (which was default till Open CASCADE Technology 6.1.0). 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 in  {} braces;
  * the destructors of the 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 development de-synchronization (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 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*, that is, they can  hold a variety of objects which do not necessarily inherit from a unique root  class. 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.
  * On the other hand, **maps** are dynamic structures where the  size is constantly adapted to the number of inserted items and the access time  for an item is effective. Maps structures are commonly used in cases of  numerous explorations: they are typically internal data structures for complex  algorithms. **Sets** generate the same results as maps but computation time  is considerable.
  * **Lists, queues** and **stacks** are minor structures  similar to sequences but with other exploration algorithms.
  
Most collections follow value semantics: their  instances are the actual collections, not **handles** to a collection. Only  arrays and sequences may also be manipulated by handle, and therefore shared. 

@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_HSet

This is a collection of non-ordered items without any duplicates. At  each transaction, the system checks if  there are no duplicates. 
*HSet* objects are *handles* to sets. 
*HSet* is a generic class which depends on two  parameters: 
  * *Item*, the type of element in the set,
  * *Set*, the actual type of set handled by *HSet*. This  is an instantiation with *TCollection_Set* 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_Queue

This is a structure, where items are added at the end and removed  from the front. The first item entered will be the first removed (**FIFO**  structure: First In First Out). *Queue* is a generic class which depends  on *Item*, the type of element in the structure. 

#### 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. 

#### TCollection_Set

This is a collection of non-ordered items without any duplicates. At  each transaction, the system checks if there are no duplicates. 

A set generates the same result as a map. A map is more  effective; so it is advisable to use maps instead of sets. 

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

#### TCollection_Stack

This is a structure where items are added and removed from the top.  The last item entered will be the first removed. 

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

@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  
  
*NCollection* package allows to not use WOK development environment in projects. Though it is quite natural to develop a code based on OCCT in any environment accepted in the industry, there is still one limitation: the so-called OCCT generic classes provided in TCollection package require compilation of the definitions in the CDL language and therefore can only be instantiated in WOK development environment.

The NCollection library provides a full replacement of all TCollection generic classes so that any OCCT collection could be instantiated via C++ template or macro definitions. It can be used in WOK as a package development unit, or in any other configuration, since it only uses the standard capabilities of C++ compiler.

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. On the contrary, template classes in *NCollection_\*.hxx* files are recommended, they are supported by OPEN CASCADE Company and further developed according to various needs.

The technology used in this unit continues and complements the one offered in the header file *Standard_DefineHandle* – allowing to implement outside CDL the classes managed by Handle, also providing OCCT RTTI support.

@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 Class architecture


To understand the basic architecture of the classes instantiated from *NCollection* macros, please refer to the documentation on *TCollection* package, particularly to CDL files. Almost all API described there is preserved in *NCollection*. Changes are described in corresponding *NCollection_Define\*.hxx* files. 

Nevertheless the internal structure of NCollection classes is more complex than that of *TCollection* ones, providing more capabilities. The advanced layer of architecture is described in the next chapter Features.

There are two principal changes:
* In *TCollection* some classes ( Stack, List, Set, Map, DataMap, DoubleMap ) define the Iterator type, the name of Iterator being like *MyPackage_DoubleMapIteratorOfDoubleMapOfIntegerReal*. In *NCollection* each Iterator is always defined as subtype of the collection *MyPackage_DoubleMapOfIntegerReal::Iterator*. 
* Hashed collections (of type Map\* ) require in *TCollection* that the special class *Map\*Hasher* is defined. In *NCollection* it is only required that the global functions *IsEqual* and *HashCode* are defined. 

#### Interface to classes defined in CDL

The classes defined above can be used as types for fields, parameters of methods and return values in CDL definitions. In our example, if MyPackage is a CDL package, you will need to create the file *MyPackage_SequenceOfPnt.hxx* containing or including the above definitions, and then to add the line: imported *SequenceOfPnt* to file *MyPackage.cdl*;

Then the new collection type can be used in any CDL definition under the name *SequenceOfPnt* from *MyPackage*.

@subsubsection occt_fcug_3_3_4 New 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 CreateIterator(); 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 Init() . 
* 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 Array1or 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

The **Strings** component provides services to manipulate  character 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). They provide editing operations with built-in  memory management which make the relative objects easier to use than ordinary  character arrays. 
*Strings* may also be manipulated by *handle*, 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
----------------
Functions used 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 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  millimetre 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 Matrix and Vector, currently used to  define more complex data structures. The Vector and Matrix classes support  vectors and matrices of real values with standard operations such as addition,  multiplication, transposition, inversion etc. 
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
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. 
The *gp* package offers classes for both 2d and 3d  objects which 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 non-persistent  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.  
The available geometric entities are: 
  * 2d & 3d Cartesian coordinates (x, y, z)
  * Matrices
  * Cartesian points
  * Vector
  * Direction
  * Axis
  * Line
  * Circle
  * Ellipse
  * Hyperbola
  * Parabola
  * Plane
  * Infinite cylindrical surface
  * Spherical surface
  * Toroidal surface
  * Conical surface.
  
@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.* 
These are non-persistent classes. 

@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 *-Infinite* 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 *[0,1]* 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. 

@section occt_fcug_5 Data Storage
@subsection occt_fcug_5_1 Saving and Opening Files

@image html /user_guides/foundation_classes/images/foundation_classes_image007.png "Example of Saving-Opening workflow"
@image latex /user_guides/foundation_classes/images/foundation_classes_image007.png "Example of Saving-Opening workflow"
   
In the example, the roots of the transferable transient objects *TopoDS_Shape, Geom_Geometry* and *Geom2d_Geometry* are used in algorithms, they contain data and temporary results. 
The associated objects in the persistent domain are *PTopoDS_HShape, PGeom_Geometry* and *PGeom2d_Geometry*. They contain a real data  structure which is stored in a file. 
Note that when an object is stored, if it contains another  stored object, the references to the contained object are also managed. 
@image html /user_guides/foundation_classes/images/foundation_classes_image008.png "Saving-Opening mechanism"
@image latex /user_guides/foundation_classes/images/foundation_classes_image008.png "Saving-Opening mechanism"


@subsection occt_fcug_5_2 Basic Storage Procedures

@subsubsection occt_fcug_5_2_1 Saving

The storage procedure of a transient object follows five  main steps. 
1. Create  an I/O driver for files. For example, *FSD_File f()*; 
2. Instance the data schema, which will process your persistent information. The schema is  used for read/write operations. If ShapeSchema is the name of your schema: 
~~~~~
Handle(ShapeSchema) s = new ShapeSchema; 
~~~~~
3. Create a persistent shape from a transient shape. 
~~~~~
TopoDS_Shape  aShape; 
PTColStd_TransientPersistentMap  aMap; 
Handle(PTopoDS_HShape)  aPShape = MgtBRep::Translate 
  (aShape, aMap, MgtBRep_WithoutTriangle); 
~~~~~
4. Create  a new container and fill it using the *AddRoot()* method. 
~~~~~
Handle(Storage_Data)  d = new Storage_Data; 
d  -> AddRoot (“ObjectName”, aPShape); 
~~~~~
You may add as  many objects as you want in this container. 
5. Save  to the archive. 
~~~~~
s -> Write (f,d); 
~~~~~

@subsubsection occt_fcug_5_2_2 Opening
The retrieval mechanism is the opposite of the storage  mechanism. The procedure for retrieving an object is as follows:
 
1. Create  an I/O driver and instance a data schema (if not done). 
2. Read  the persistent object from the archive and get the list of objects using *Roots()* method. 
~~~~~
Handle(Storage_Data)  d = s -> Read(f); 
Handle(Storage_HSeqOfRoot)  roots = d-> Roots(); 
~~~~~
3. Loop  on root objects to get *Standard_Persistent* objects (the following sequence only  gets the first root). 
~~~~~
Handle(Standard_Persistent)  p; 
Handle(Standard_Root)  r; 
if(roots  -> Length() >= 1) { 
   r = roots -> Value(1); 
   p = r -> Object(); 
} 
~~~~~
4. DownCast  the persistent object to a *PTopoDS_Hshape*. 
~~~~~
Handle(PTopoDS_HShape) aPShape; 
aPShape =  Handle(PTopoDS_HShape)::DownCast(p); 
~~~~~
5. Create  the *TopoDS_Shape*. 
~~~~~
TopoDS_Shape aShape; 
PTColStd_PersistentTransientMap aMap;    
MgtBRep::Translate (aPShape, aMap,  aShape, MgtBRep_WithoutTriangle); 
~~~~~