Segments

Models and functions that can be used when regularizing segments.

Classes
class	CGAL::Shape_regularization::Segments::Angle_regularization_2< GeomTraits, InputRange, SegmentMap >
	An angle-based regularization type for 2D segments that reinforces parallelism and orthogonality relationships. More...
class	CGAL::Shape_regularization::Segments::Delaunay_neighbor_query_2< GeomTraits, InputRange, SegmentMap >
	A neighbor query based on a Delaunay triangulation, which enables to find the nearest neighbors in a set of GeomTraits::Segment_2. More...
class	CGAL::Shape_regularization::Segments::Offset_regularization_2< GeomTraits, InputRange, SegmentMap >
	An offset-based regularization type for 2D segments that reinforces collinearity relationships. More...

Functions
template<typename InputRange , typename NeighQuery , typename RegType , typename QPSolver , typename NamedParameters = parameters::Default_named_parameters>
void	CGAL::Shape_regularization::Segments::regularize_segments (InputRange &input_range, NeighQuery &neighbor_query, RegType &regularization_type, QPSolver &quadratic_program, const NamedParameters &np=parameters::default_values())
	regularizes a set of 2D segments.
template<typename InputRange >
void	CGAL::Shape_regularization::Segments::regularize_angles (InputRange &input_range)
	regularizes angles in a set of 2D segments.
template<typename InputRange >
void	CGAL::Shape_regularization::Segments::regularize_offsets (InputRange &input_range)
	regularizes offsets in a set of 2D segments.
template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>
OutIterator	CGAL::Shape_regularization::Segments::parallel_groups (const InputRange &input_range, OutIterator groups, const NamedParameters &np=parameters::default_values())
	finds groups of parallel segments in a set of 2D segments.
template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>
OutIterator	CGAL::Shape_regularization::Segments::collinear_groups (const InputRange &input_range, OutIterator groups, const NamedParameters &np=parameters::default_values())
	finds groups of collinear segments in a set of 2D segments.
template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>
OutIterator	CGAL::Shape_regularization::Segments::orthogonal_groups (const InputRange &input_range, OutIterator groups, const NamedParameters &np=parameters::default_values())
	finds groups of orthogonal segments in a set of 2D segments.
template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>
OutIterator	CGAL::Shape_regularization::Segments::unique_segments (const InputRange &input_range, OutIterator segments, const NamedParameters &np=parameters::default_values())
	substitutes groups of 2D collinear segments by average segments.

Function Documentation

collinear_groups()

template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>

OutIterator CGAL::Shape_regularization::Segments::collinear_groups	(	const InputRange &	input_range,
		OutIterator	groups,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Shape_regularization/regularize_segments.h>

finds groups of collinear segments in a set of 2D segments.

This function enables to find groups of near collinear segments in a set of 2D segments. The groups are returned as vectors of indices. This algorithm first finds the groups of parallel segments using the function Segments::parallel_groups() and then splits these groups into groups of collinear segments.

This function does not regularize input segments, but only groups them.

Template Parameters

InputRange	a model of ConstRange whose iterator type is RandomAccessIterator
OutIterator	a model of OutputIterator that accepts elements of type std::vector<std::size_t>
NamedParameters	a sequence of Named Parameters

Parameters

input_range	a const range of input segments
groups	an output iterator with groups of segment indices
np	an optional sequence of Named Parameters among the ones listed below; this parameter can be omitted, the default values are then used

Optional Named Parameters

maximum_offset maximum allowed orthogonal distance between two parallel segments such that they are considered to be collinear Type: GeomTraits::FT Default: 0.2 unit length
preserve_order indicates whether the order of input segments should be preserved or not Type: boolean Default: false
segment_map a property map that maps an item from input_range to GeomTraits::Segment_2 Type: a model of ReadablePropertyMap whose key type is the value type of the input range and value type is GeomTraits::Segment_2 Default: CGAL::Identity_property_map
geom_traits an instance of geometric traits class Type: a model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits

Returns

an output iterator to the element in the destination range, one past the last group stored

Precondition

input_range.size() >= 1

maximum_offset >= 0

orthogonal_groups()

template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>

OutIterator CGAL::Shape_regularization::Segments::orthogonal_groups	(	const InputRange &	input_range,
		OutIterator	groups,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Shape_regularization/regularize_segments.h>

finds groups of orthogonal segments in a set of 2D segments.

This function enables to find groups of near orthogonal segments in a set of 2D segments. The groups are returned as vectors of indices. This algorithm first finds the groups of parallel segments using the function Segments::parallel_groups() and then merges these groups into groups of orthogonal segments.

This function does not regularize input segments, but only groups them.

Template Parameters

InputRange	a model of ConstRange whose iterator type is RandomAccessIterator
OutIterator	a model of OutputIterator that accepts elements of type std::vector<std::size_t>
NamedParameters	a sequence of Named Parameters

Parameters

input_range	a const range of input segments
groups	an output iterator with groups of segment indices
np	an optional sequence of Named Parameters among the ones listed below; this parameter can be omitted, the default values are then used

Optional Named Parameters

maximum_angle maximum allowed angle deviation in degrees between two segments such that they are considered to be parallel or orthogonal Type: GeomTraits::FT Default: 5 degrees
preserve_order indicates whether the order of input segments should be preserved or not Type: boolean Default: false
segment_map a property map that maps an item from input_range to GeomTraits::Segment_2 Type: a model of ReadablePropertyMap whose key type is the value type of the input range and value type is GeomTraits::Segment_2 Default: CGAL::Identity_property_map
geom_traits an instance of geometric traits class Type: a model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits

Returns

an output iterator to the element in the destination range, one past the last group stored

Precondition

input_range.size() >= 1

maximum_angle >= 0 && maximum_angle <= 90

parallel_groups()

template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>

OutIterator CGAL::Shape_regularization::Segments::parallel_groups	(	const InputRange &	input_range,
		OutIterator	groups,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Shape_regularization/regularize_segments.h>

finds groups of parallel segments in a set of 2D segments.

This function enables to find groups of near parallel segments in a set of 2D segments. The groups are returned as vectors of indices. Note that two segments may be included at the same group even if they are far away from each other. This algorithm concerns only the angle relationship among segments, but not the distance.

This function does not regularize input segments, but only groups them.

Template Parameters

InputRange	a model of ConstRange whose iterator type is RandomAccessIterator
OutIterator	a model of OutputIterator that accepts elements of type std::vector<std::size_t>
NamedParameters	a sequence of Named Parameters

Parameters

input_range	a const range of input segments
groups	an output iterator with groups of segment indices
np	an optional sequence of Named Parameters among the ones listed below; this parameter can be omitted, the default values are then used

Optional Named Parameters

maximum_angle maximum allowed angle deviation in degrees between two segments such that they are considered to be parallel Type: GeomTraits::FT Default: 5 degrees
preserve_order indicates whether the order of input segments should be preserved or not Type: boolean Default: false
segment_map a property map that maps an item from input_range to GeomTraits::Segment_2 Type: a model of ReadablePropertyMap whose key type is the value type of the input range and value type is GeomTraits::Segment_2 Default: CGAL::Identity_property_map
geom_traits an instance of geometric traits class Type: a model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits

Returns

an output iterator to the element in the destination range, one past the last group stored

Precondition

input_range.size() >= 1

maximum_angle >= 0 && maximum_angle <= 90

Examples

Shape_regularization/regularize_100_segments_offsets.cpp.

regularize_angles()

template<typename InputRange >

void CGAL::Shape_regularization::Segments::regularize_angles

(

InputRange &

input_range

)

#include <CGAL/Shape_regularization/regularize_segments.h>

regularizes angles in a set of 2D segments.

Given a set of unordered 2D segments, this function enables to reinforce two types of regularities among these segments:

• Parallelism: segments, which are detected as near parallel, are made exactly parallel.
• Orthogonality: segments, which are detected as near orthogonal, are made exactly orthogonal.

This is an utility function based on regularize_segments() that is using default parameters.

Template Parameters

InputRange

a model of ConstRange whose iterator type is RandomAccessIterator

Parameters

input_range

a const range of input segments for angle regularization

Precondition

input_range.size() >= 2

See also

regularize_segments()

regularize_offsets()

regularize_offsets()

template<typename InputRange >

void CGAL::Shape_regularization::Segments::regularize_offsets

(

InputRange &

input_range

)

#include <CGAL/Shape_regularization/regularize_segments.h>

regularizes offsets in a set of 2D segments.

Given a set of parallel 2D segments, this function enables to reinforce the collinearity property among these segments that is all parallel segments, which are detected as near collinear, are made exactly collinear.

This is an utility function based on regularize_segments() that is using default parameters.

Template Parameters

InputRange

a model of ConstRange whose iterator type is RandomAccessIterator

Parameters

input_range

a const range of input segments for offset regularization

Precondition

input_range.size() >= 2

See also

regularize_segments()

regularize_angles()

regularize_segments()

template<typename InputRange , typename NeighQuery , typename RegType , typename QPSolver , typename NamedParameters = parameters::Default_named_parameters>

void CGAL::Shape_regularization::Segments::regularize_segments	(	InputRange &	input_range,
		NeighQuery &	neighbor_query,
		RegType &	regularization_type,
		QPSolver &	quadratic_program,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Shape_regularization/regularize_segments.h>

regularizes a set of 2D segments.

Given a set of unordered 2D segments, this function enables to reinforce three types of regularities among these segments:

• Parallelism: segments, which are detected as near parallel, are made exactly parallel.
• Orthogonality: segments, which are detected as near orthogonal, are made exactly orthogonal.
• Collinearity: parallel segments, which are detected as near collinear, are made exactly collinear.

The user has to provide a NeighborQuery model to access local neighbors of a segment and a RegularizationType model to define the type of regularities that should be addressed. The function is based on the class QP_regularization. Please refer to that class and these concepts for more information.

This class requires a QPSolver model which defaults to the OSQP library, which must be available on the system.

Template Parameters

InputRange	a model of ConstRange whose iterator type is RandomAccessIterator
NeighQuery	a model of NeighborQuery
RegType	a model of RegularizationType
QPSolver	a model of QuadraticProgramTraits
NamedParameters	a sequence of Named Parameters

Parameters

input_range	a const range of input segments for shape regularization
neighbor_query	an instance of NeighQuery that is used internally to access neighbors of a segment; this parameter can be omitted together with the regularization_type parameter, in this case, all types of regularities will be reinforced on the whole input range and the default solver will be used (see below)
regularization_type	an instance of RegType that is used internally to obtain bounds and target values required by the regularization; this parameter can be omitted together with the neighbor_query parameter, in this case, all types of regularities will be reinforced on the whole input range and the default solver will be used (see below)
quadratic_program	an instance of QPSolver to solve the quadratic programming problem; this parameter can be omitted, the default solver is CGAL::OSQP_quadratic_program_traits
np	an optional sequence of Named Parameters among the ones listed below; this parameter can be omitted, the default values are then used

Optional Named Parameters

geom_traits an instance of geometric traits class Type: a model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits

Precondition

input_range.size() >= 2

See also

regularize_angles()

regularize_offsets()

Examples

Shape_regularization/regularize_100_segments_angles.cpp, Shape_regularization/regularize_100_segments_offsets.cpp, Shape_regularization/regularize_real_data_2.cpp, and Shape_regularization/regularize_simple.cpp.

unique_segments()

template<typename InputRange , typename OutIterator , typename NamedParameters = parameters::Default_named_parameters>

OutIterator CGAL::Shape_regularization::Segments::unique_segments	(	const InputRange &	input_range,
		OutIterator	segments,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Shape_regularization/regularize_segments.h>

substitutes groups of 2D collinear segments by average segments.

This function first calls Segments::collinear_groups() and then substitutes each group of collinear segments by an average segment. The number of returned segments is the number of detected collinear groups.

This function does not regularize input segments, but only groups and then simplifies them.

Template Parameters

InputRange	a model of ConstRange whose iterator type is RandomAccessIterator
OutIterator	a model of OutputIterator that accepts segments of type GeomTraits::Segment_2
NamedParameters	a sequence of Named Parameters

Parameters

input_range	a const range of input segments
segments	an output iterator with the simplified segments
np	an optional sequence of Named Parameters among the ones listed below; this parameter can be omitted, the default values are then used

Optional Named Parameters

maximum_offset maximum allowed orthogonal distance between two parallel segments such that they are considered to be collinear Type: GeomTraits::FT Default: 0.2 unit length
preserve_order indicates whether the order of input segments should be preserved or not Type: boolean Default: false
segment_map a property map that maps an item from input_range to GeomTraits::Segment_2 Type: a model of ReadablePropertyMap whose key type is the value type of the input range and value type is GeomTraits::Segment_2 Default: CGAL::Identity_property_map
geom_traits an instance of geometric traits class Type: a model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits

Returns

an output iterator to the element in the destination range, one past the last segment stored

Precondition

input_range.size() >= 1

maximum_offset >= 0