CGAL 6.0 - 2D Generalized Barycentric Coordinates
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Free functions to compute barycentric weights and coordinates.
Functions | |
template<typename VertexRange , typename OutIterator , typename GeomTraits , typename PointMap > | |
std::pair< OutIterator, bool > | CGAL::Barycentric_coordinates::boundary_coordinates_2 (const VertexRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const PointMap point_map) |
computes 2D boundary coordinates. | |
template<typename VertexRange , typename Query_2 , typename OutIterator , typename PointMap = CGAL::Identity_property_map<Query_2>> | |
std::pair< OutIterator, bool > | CGAL::Barycentric_coordinates::boundary_coordinates_2 (const VertexRange &polygon, const Query_2 &query, OutIterator c_begin, const PointMap point_map=PointMap()) |
computes 2D boundary coordinates. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::discrete_harmonic_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES) |
computes 2D discrete harmonic weights. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::discrete_harmonic_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES) |
computes 2D discrete harmonic coordinates. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::mean_value_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES) |
computes 2D mean value weights. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::mean_value_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES) |
computes 2D mean value coordinates. | |
template<typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::segment_coordinates_2 (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits) |
computes segment coordinates. | |
template<typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::triangle_coordinates_2 (const typename GeomTraits::Point_2 &p0, const typename GeomTraits::Point_2 &p1, const typename GeomTraits::Point_2 &p2, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits) |
computes triangle coordinates. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::wachspress_weights_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator w_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::FAST_WITH_EDGE_CASES) |
computes 2D Wachspress weights. | |
template<typename PointRange , typename OutIterator , typename GeomTraits > | |
OutIterator | CGAL::Barycentric_coordinates::wachspress_coordinates_2 (const PointRange &polygon, const typename GeomTraits::Point_2 &query, OutIterator c_begin, const GeomTraits &traits, const Computation_policy_2 policy=Computation_policy_2::PRECISE_WITH_EDGE_CASES) |
computes 2D Wachspress coordinates. | |
std::pair< OutIterator, bool > CGAL::Barycentric_coordinates::boundary_coordinates_2 | ( | const VertexRange & | polygon, |
const Query_2 & | query, | ||
OutIterator | c_begin, | ||
const PointMap | point_map = PointMap() |
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) |
#include <CGAL/Barycentric_coordinates_2/boundary_coordinates_2.h>
computes 2D boundary coordinates.
This is an overload of the function boundary_coordinates_2
.
VertexRange | a model of ConstRange whose iterator type is RandomAccessIterator |
Query_2 | a model of Kernel::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
PointMap | a model of ReadablePropertyMap whose key type is VertexRange::value_type and value type is Query_2 . The default is CGAL::Identity_property_map . |
polygon | an instance of VertexRange with 2D points, which form a simple polygon |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
point_map | an instance of PointMap that maps a vertex from polygon to Query_2 ; the default initialization is provided |
std::pair< OutIterator, bool > CGAL::Barycentric_coordinates::boundary_coordinates_2 | ( | const VertexRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits, | ||
const PointMap | point_map | ||
) |
#include <CGAL/Barycentric_coordinates_2/boundary_coordinates_2.h>
computes 2D boundary coordinates.
This function computes boundary barycentric coordinates at a given query
point with respect to the vertices of a simple polygon
, that is one coordinate per vertex. The coordinates are stored in a destination range beginning at c_begin
.
If query
is at the vertex, the corresponding coordinate is set to one, while all other coordinates are zero. If query
is on the edge, the two corresponding coordinates are segment coordinates, while all other coordinates are set to zero. If query
is not on the boundary, all the coordinates are set to zero.
Internally, segment_coordinates_2()
are used.
VertexRange | a model of ConstRange whose iterator type is RandomAccessIterator |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
PointMap | a model of ReadablePropertyMap whose key type is VertexRange::value_type and value type is GeomTraits::Point_2 |
polygon | an instance of VertexRange with 2D points, which form a simple polygon |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
point_map | an instance of PointMap that maps a vertex from polygon to Point_2 |
OutIterator CGAL::Barycentric_coordinates::discrete_harmonic_coordinates_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::PRECISE_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Discrete_harmonic_coordinates_2.h>
computes 2D discrete harmonic coordinates.
This function computes 2D discrete harmonic coordinates at a given query
point with respect to the vertices of a strictly convex polygon
, that is one coordinate per vertex. The coordinates are stored in a destination range beginning at c_begin
.
Internally, the class Discrete_harmonic_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a strictly convex polygon |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::PRECISE_WITH_EDGE_CASES |
OutIterator CGAL::Barycentric_coordinates::discrete_harmonic_weights_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | w_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::FAST_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Discrete_harmonic_coordinates_2.h>
computes 2D discrete harmonic weights.
This function computes 2D discrete harmonic weights at a given query
point with respect to the vertices of a strictly convex polygon
, that is one weight per vertex. The weights are stored in a destination range beginning at w_begin
.
Internally, the class Discrete_harmonic_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a strictly convex polygon |
query | a query point |
w_begin | the beginning of the destination range with the computed weights |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::FAST_WITH_EDGE_CASES |
OutIterator CGAL::Barycentric_coordinates::mean_value_coordinates_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::PRECISE_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Mean_value_coordinates_2.h>
computes 2D mean value coordinates.
This function computes 2D mean value coordinates at a given query
point with respect to the vertices of a simple polygon
, that is one coordinate per vertex. The coordinates are stored in a destination range beginning at c_begin
.
Internally, the class Mean_value_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a simple polygon |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::PRECISE_WITH_EDGE_CASES |
OutIterator CGAL::Barycentric_coordinates::mean_value_weights_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | w_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::FAST_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Mean_value_coordinates_2.h>
computes 2D mean value weights.
This function computes 2D mean value weights at a given query
point with respect to the vertices of a simple polygon
, that is one weight per vertex. The weights are stored in a destination range beginning at w_begin
.
Internally, the class Mean_value_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a simple polygon |
query | a query point |
w_begin | the beginning of the destination range with the computed weights |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::FAST_WITH_EDGE_CASES |
OutIterator CGAL::Barycentric_coordinates::segment_coordinates_2 | ( | const typename GeomTraits::Point_2 & | p0, |
const typename GeomTraits::Point_2 & | p1, | ||
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits | ||
) |
#include <CGAL/Barycentric_coordinates_2/segment_coordinates_2.h>
computes segment coordinates.
This function computes barycentric coordinates at a given query
point with respect to the end points p0
and p1
of a segment that is one coordinate per end point. The coordinates are stored in a destination range beginning at c_begin
.
After the coordinates \(b_0\) and \(b_1\) are computed, the query point \(q\) can be obtained as \(q = b_0p_0 + b_1p_1\). If \(q\) does not belong to the line through \(p_0\) and \(p_1\), it is projected onto this line, and only then the coordinates are computed. See more details in the user manual here.
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
p0 | the first vertex of a segment |
p1 | the second vertex of a segment |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
OutIterator CGAL::Barycentric_coordinates::triangle_coordinates_2 | ( | const typename GeomTraits::Point_2 & | p0, |
const typename GeomTraits::Point_2 & | p1, | ||
const typename GeomTraits::Point_2 & | p2, | ||
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits | ||
) |
#include <CGAL/Barycentric_coordinates_2/triangle_coordinates_2.h>
computes triangle coordinates.
This function computes barycentric coordinates at a given query
point with respect to the points p0
, p1
, and p2
, which form a triangle, that is one coordinate per point. The coordinates are stored in a destination range beginning at c_begin
.
After the coordinates \(b_0\), \(b_1\), and \(b_2\) are computed, the query point \(q\) can be obtained as \(q = b_0p_0 + b_1p_1 + b_2p_2\). See more details in the user manual here.
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
p0 | the first vertex of a triangle |
p1 | the second vertex of a triangle |
p2 | the third vertex of a triangle |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
OutIterator CGAL::Barycentric_coordinates::wachspress_coordinates_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | c_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::PRECISE_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Wachspress_coordinates_2.h>
computes 2D Wachspress coordinates.
This function computes 2D Wachspress coordinates at a given query
point with respect to the vertices of a strictly convex polygon
, that is one coordinate per vertex. The coordinates are stored in a destination range beginning at c_begin
.
Internally, the class Wachspress_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a strictly convex polygon |
query | a query point |
c_begin | the beginning of the destination range with the computed coordinates |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::PRECISE_WITH_EDGE_CASES |
OutIterator CGAL::Barycentric_coordinates::wachspress_weights_2 | ( | const PointRange & | polygon, |
const typename GeomTraits::Point_2 & | query, | ||
OutIterator | w_begin, | ||
const GeomTraits & | traits, | ||
const Computation_policy_2 | policy = Computation_policy_2::FAST_WITH_EDGE_CASES |
||
) |
#include <CGAL/Barycentric_coordinates_2/Wachspress_coordinates_2.h>
computes 2D Wachspress weights.
This function computes 2D Wachspress weights at a given query
point with respect to the vertices of a strictly convex polygon
, that is one weight per vertex. The weights are stored in a destination range beginning at w_begin
.
Internally, the class Wachspress_coordinates_2
is used. If one wants to process multiple query points, it is better to use that class. When using the free function, internal memory is allocated for each query point, while when using the class, it is allocated only once, which is much more efficient. However, for a few query points, it is easier to use this function. It can also be used when the processing time is not a concern.
PointRange | a model of ConstRange whose iterator type is RandomAccessIterator and value type is GeomTraits::Point_2 |
OutIterator | a model of OutputIterator that accepts values of type GeomTraits::FT |
GeomTraits | a model of BarycentricTraits_2 |
polygon | an instance of PointRange with 2D points, which form a strictly convex polygon |
query | a query point |
w_begin | the beginning of the destination range with the computed weights |
traits | a traits class with geometric objects, predicates, and constructions; this parameter can be omitted if the traits class can be deduced from the point type |
policy | one of the Computation_policy_2 ; the default is Computation_policy_2::FAST_WITH_EDGE_CASES |