DGtal  0.9.3beta
Iterators and ranges

Table of Contents

Author(s) of this documentation:
Tristan Roussillon

This part of the manual describes basic concepts of iterators and ranges. It also presents several tools available in DGtal to ease their use: traits class, useful functions, adapters, etc.

DGtal users usually have to play with ranges to iterate over finite sets of elements.

Introduction to iterators

The concept of iterator is one of the main concept introduced in the STL in order to make data structures and algorithms independent: a programmer would be able to apply one algorithm on different data structures. Algorithms typically take iterators as arguments, so a data structure is only required to provide a way to access its elements using iterators. An iterator is any object that, pointing to some element stored in a data structure, can be incremented so that it points to the next element. An iterator has at least, the dereference (*) and increment (++) operators, but can have more operators to implement extra functionalities. Depending on the functionality they implement, they belong to one of the several categories of iterators. Following The Boost.Iterator Library, which extends the hierarchy of concepts proposed in the STL and separates access and traversal functionalities, we consider in DGtal the following access and traversal categories:

  1. Incrementable iterator: dereference (*), indirection (->) and increment (++) operators.
  2. Single-pass iterator: equality operators (== and !=).
  3. Forward iterator: default constructor.
  4. Bidirectional iterator: decrement (--) operator.
  5. Random access iterator: arithmetic and comparison operators (<, <=, >, >=).

Each traversal category of level l obviously implements the functionalities of all the categories k < l and one or more extra functionalities. For each category, the main difference with the previous categories is provided in the above list, but The Boost.Iterator Library gives more details.

The following diagram sums up the main iterator concepts:

Introduction to ranges

A range of elements stored in a data structure (container) may be implicitly described by a well-chosen pair of iterators. Any pair does not define a valid range, even with iterators having nonsingular values. An iterator j is reachable from an iterator i if and only if i can be made equal to j with finitely many applications of the increment operator. If j is reachable from i, one can iterate over the range bounded by i and j, from the one pointed to by i and up to, but not including, the one pointed to by j. Such a range is valid and is denoted by [i,j).

In linear data structures, any iterator pointing to the last element is incremented so that it points to the past-the-end element, ie. it points past the last element (just as a regular pointer to an array guarantees that there is a pointer value pointing past the last element of the array).

If an iterator begin points to the first element of a data structure and an iterator end points to the past-the-end element, iterating over the range [begin,end) is a way of iterating over all the elements of the underlying data structure. Note that if the underlying data structure is empty, it only has a past-the-end element. As a consequence, a range [i,i) denotes an empty range. A range of a linear data structure is illustrated below (normal values are depicted with a small straight segment, whereas the past-the-end value is depicted with a cross). In this example, [i,j) is not a valid range because j cannot be reached from i and the whole range may be denoted by [begin,end).

Linear range

Main concepts

Some objects have the capability to provide a pair of iterators describing a (valid) range. For instance, methods begin() and end() of STL containers return two iterators bounding the range of elements contained in the data structure. Similarly, in DGtal, there are several concepts of range having at least these begin() and end() methods.

The concept CConstSinglePassRange describes any object for which, one can iterate at least one time over a range of elements. Models of concepts::CConstSinglePassRange have a nested type ConstIterator, which is a readable and (at least) single-pass iterator. Instances of ConstIterator are returned by begin() and end() methods.

The concept CConstBidirectionalRange, which is a refinement of concepts::CConstSinglePassRange, describes any collection of elements that can be scanned several times, either forward or backward. Models of this concept have obviously a nested type ConstIterator, but it is a readable and (at least) bidirectional iterator. They have in addition a nested type ConstReverseIterator, which is a readable and bidirectional iterator too. Finally, begin() and end() methods return instances of ConstIterator, whereas rbegin() and rend() methods return instances of ConstReverseIterator.

The concept CSinglePassRange (resp. CBidirectionalRange) is a refinement of concepts::CConstSinglePassRange (resp. concepts::CConstBidirectionalRange) for not constant, mutable elements. All their models have a nested type Iterator (resp. ReverseIterator), which are the readable and writable counterparts of ConstIterator (resp. ConstReverseIterator).

These four concepts and their links are depicted in the following figure:

Adapters to iterators

In DGtal, several adapters to iterators are provided.

Reverse iterator

Any bidirectional iterator may have a reverse counterpart, ie. an adapter that enables a backward scanning by calling the decrement operator instead of the increment operator and conversely. Bidirectional ranges provide reverse iterators that can be used as follows:

template<typename Range>
void anyProcedure(const Range& aRange)
    BOOST_CONCEPT_ASSERT(( concepts::CBidirectionalRange<Range> )); 
    for (typename Range::ReverseIterator ri = r.rbegin(), 
         typename Range::ReverseIterator riEnd = r.rend(); 
         ri != riEnd; ++ri)

In order to take profit of the whole DGtal framework, you should use DGtal::ReverseIterator instead of std::reverse_iterator or even boost::reverse_iterator.

#include "DGtal/base/ReverseIterator.h"
template<typename Iterator>
void anyProcedure(const Iterator& anIterator)
    DGtal::ReverseIterator<Iterator> ri(anIterator); 
    ASSERT( ri.base() == anIterator ); //ie. anIterator is the underlying iterator of ri
Reverse iterators are a little tricky because *ri == *--ri.base() (or equivalently *++ri == *ri.base()), so that when an iterator is reversed, the reversed version does not point to the same element in the range, but to the one preceding it.
Developer trick: there is no erase or insert method taking a reverse iterator as input argument in STL containers. Static methods are provided to do that in a small struct called OpInSTLContainers.

On-line transformations

DGtal also provides adapters to iterators that transforms the data returned by the dereference (and indirection) operator into other data, possibly of different type. The transformation is delegated to a functor. Dereferencing any adapted iterator consists in applying the functor on the data to which points the underlying iterator:

#include "DGtal/base/ConstIteratorAdapter.h"
template<typename Iterator, typename Functor, typename ReturnType>
void anyProcedure(const Iterator& anIterator, const Functor& aFunctor)
    DGtal::ConstAdapterIterator<Iterator, Functor, ReturnType> a(i, f);
    ASSERT( *a == f(*i) ); //ie. *a and f(*i) return equivalent instances of ReturnType  

The class ConstIteratorAdapter adapts any (at least) readable and (at least) incremental iterator with any functor, whereas the class IteratorAdapter adapts any readable, writable, Lvalue and (at least) incremental iterator.


Like Cgal, DGtal extends the concept of iterator to circular data structures by defining the concept of circular iterator or circulator for short.

The class Circulator is an adapter that creates a circulator from a classic iterator.

In circular data structures, any pairs of iterators [i,j) always describes a valid range (ie. j is always reachable from i) and there is no past-the-end element. A range of a circular data structure is illustrated below. In this example, [i,j) is of course a valid range.

Circular range
As long as i != j, circulators are quite similar to classic iterator in the subrange [i,j). More precisely, forward and bidirectional circulators behave exactly like classic forward and bidirectional iterators (note that there is no incrementable or single-pass circulator). However, there is a semantic difference between random access circulators and iterators for some arithmetic and comparison operators. Indeed, even if we have i + (j-i) = j, (ie. i must be incremented j-i times so that it reaches j) for both circulators and iterators, we have two major differences, sum up in the following table:

classic iterators circulators
(i <= j) iff ((j-i) >= 0) (i <= j) is always true
(i-j) + (j-i) = 0 (i-j) + (j-i) = range size

On the other hand, circulators and iterators are quite different for iterating over all the elements of a given range. In linear data structures, due to the existence of a past-the-end element, the whole range is not different from any subranges: it is described by a pair of iterators [i,j) such that j is reachable from i. If the data structure does not contain any element, an iterator k can point to the past-the-end element and [k,k) describes the valid and empty associated range.

However, in (truly) circular data structures, there is no past-the-end element. How to describe a whole range using circulators ? Circulators have a specific state in the case of an empty data structure so that it is enough to consider one circulator k to check whether the underlying data structure is empty or not. Note that any default-constructed circulator, by convention, is in the same state as circulators provided by empty data structures.

Since the empty case is managed by this internal state, [k,k) can be viewed then as describing a whole range of elements, if a whole range is required.

The do-while structure is the basic way of circulating over a range of elements:

  } while( c != cEnd);   

The generic way of iterating over a range of elements whatever the type of iterators (either iterator or circulator) uses the generic function isNotEmpty():

#include "DGtal/base/IteratorFunctions.h"
template<typename IC>
void anyProcedure(const IC& ic1, const IC& ic2)
    if ( isNotEmpty( ic1, ic2 ) )
      { //if the range is not empty
        IC ic = ic1; 
          {//iterating over the range
          } while( ic != ic2);   

Iterator Utilities

To ease the use of iterators and circulators, several tools are available.

Useful functions

In the file DGtal/base/IteratorFunctions.h, there are several functions, like the isNotEmpty() function used above, that are specialized with respect to the type and category of iterators.

Here is the list of available functions:

Note that in the rangeXXX() methods, the range given as input argument is assumed to be the whole range of elements stored in a container possibly empty, whereas in the subRangeXXX() methods, the range given as input argument is assumed to be any subrange of an existing and not empty container. This distinction is only relevant for circulators and the subRangeXXX() functions are perfectly equivalent to the rangeXXX() functions for classic iterators.

Categories and other associated types

Sometimes, we need information about iterators. Is it a circulator ? What is its traversal category ? What is the type of the data ? In DGtal, the traits class IteratorCirculatorTraits provides this information thanks to the following nested types:

For instance, redefining the value type is done as follows:

#include "DGtal/base/IteratorTraits.h" 
template<typename IC>
void anyProcedure(const IC& ic)
    typedef typename IteratorCirculatorTraits<IC>::Value ValueType; 

For developers: Tag dispatching

If you want to specialize some classes or functions according to iterators tags (basically type and category), you may use function overloading. This technique is called tag dispatching. You may find examples of tag dispatching in IteratorFunctions.h and IteratorFunctions.ih

For developers: How to create new iterators ?

When you create a new iterator, you have to be sure that it contains all STL required nested types so that IteratorCirculatorTraits works fine:

By default, the type of any new iterator is IteratorType. If you create a new circulator, you have to define a nested type called Type as CirculatorType. The class Circulator is a good example of what a circulator should look like.

Moreover, you have to be sure that it implements all operators required by its category (dereference, indirection, pre- and post- incrementation, etc.). If your iterator should be readable and forward, you have to be sure that it is both a model of readable and forward iterator by concept checking.

For developers: interface completion for classes with random-access iterators over points

When you create a class that exposes a random-access iterator related to points, IteratorCompletion can help you to complete the iterator interface of your class: from a basic set of methods (begin() and end() returning mutable and constant iterators), IteratorCompletion adds to your class reverse iterators and ranges, and the corresponding access methods (rbegin, rend, range, etc.).

See the documentation of IteratorCompletion for more details and an usage example.

Concepts checking

The basic way of checking whether a given type is a model of a given concept or not is to use the BOOST_CONCEPT_ASSERT mechanism. In the following snippet, type I is expected to be a model of readable iterator and forward iterator. If it turns out that it is not a model of these concepts, a compilation error is raised.

template<typename I>
void anyProcedure(const I& i)
    BOOST_CONCEPT_ASSERT(( boost_concepts::ReadableIteratorConcept<I> )); 
    BOOST_CONCEPT_ASSERT(( boost_concepts::ForwardTraversalConcept<I> )); 


In DGtal, iterators and ranges are heavily used in several packages. We detail below their use in two packages: Geometry and Image.

Iterators and ranges in the Geometry package

One module of the geometry package is the analysis of one-dimensional discrete structures. This is a (not exhaustive) list of such structures used in digital geometry:

Since these structures are one-dimensional, discrete and finite, they can be viewed as linear or circular range of elements. Segmentation algorithms extract from the whole range of elements, possibly overlapping subranges called segments.

See Analysis of one-dimensional discrete structures for further details.

Iterators and ranges in the Image package

The concept of image is a refinement of the concept of point functor, which describes a mapping between the points of a digital space and a set of values. In addition, an image is bounded by a domain, ie. a finite and constant set of digital points.

All images provide an access to its domain (domain() method), which is a range of digital points, as well as an access to a range of values (constRange() or range() methods).

See Digital Spaces, Points, Vectors and Domains and Images for further details.