Namespace SFCGAL::algorithm#

Main algorithm namespace.

Classes#

Type	Name
class	BoundaryVisitor
class	Buffer3D Computes a 3D buffer around a Point orLineString .
struct	Circle
class	ConsistentOrientationBuilder
struct	LoopDetector
struct	NoValidityCheck
struct	Plane3DInexactUnsafe
struct	Sphere
class	SurfaceGraph
class	WeightedCentroid
struct	found_an_intersection
struct	intersects_cb <Dim>

Public Types#

Type	Name
enum	PartitionAlgorithm

Public Functions#

Type	Name
auto	alphaShapes (const Geometry & g, double alpha=1, bool allow_holes=false)
auto	alphaWrapping3D (const Geometry & geom, size_t relativeAlpha, size_t relativeOffset)
auto	approximate (const Offset_polygon_2 & polygon, const int & n=0) approximate an Offset_polygon_2 (filter null segments)
auto	approximate (const Offset_polygon_with_holes_2 & polygon, const int & n=0) approximate an Offset
auto	approximateMedialAxis (const Geometry & geom) build an approximate medial axis for a Polygon __
auto	area (const Geometry & g, NoValidityCheck) Compute the 2D area for a Geometry.
auto	area (const Geometry & g) Compute the 2D area for a Geometry.
auto	area (const Triangle & g)
auto	area (const Polygon & g)
auto	area (const GeometryCollection & g)
auto	area (const TriangulatedSurface & g)
auto	area (const PolyhedralSurface & g)
auto	area3D (const Geometry & g, NoValidityCheck)
auto	area3D (const Geometry & g)
auto	area3D (const Polygon & g)
auto	area3D (const Triangle & g)
auto	area3D (const GeometryCollection & g)
auto	area3D (const PolyhedralSurface & g)
auto	area3D (const TriangulatedSurface & g)
auto	boundingCircle (const Geometry & geom)
auto	boundingSphere (const Geometry & geom)
auto	centroid (const Geometry & g) Returns the 2D centroid for a Geometry.
auto	centroid3D (const Geometry & g) Returns the 3D centroid for a Geometry.
auto	circleToPolygon (const Kernel::Circle_2 & circle) helper to create a polygon from a circle
auto	collect (const Geometry & ga, const Geometry & gb)
std::unique_ptr< Geometry >	collect (GeometryIterator begin, GeometryIterator end)
auto	collectionExtractPolygons (std::unique_ptr< Geometry > coll)
auto	collectionHomogenize (std::unique_ptr< Geometry > coll)
auto	collectionToMulti (std::unique_ptr< Geometry > coll)
auto	convexHull (const Geometry & g)
auto	convexHull3D (const Geometry & g)
auto	covers (const Geometry & ga, const Geometry & gb)
bool	covers (const detail::GeometrySet< Dim > & a, const detail::GeometrySet< Dim > & b)
bool	covers (const detail::PrimitiveHandle< Dim > & a, const detail::PrimitiveHandle< Dim > & b)
auto	covers3D (const Geometry & ga, const Geometry & gb)
auto	difference (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	difference (const Geometry & ga, const Geometry & gb)
auto	difference3D (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	difference3D (const Geometry & ga, const Geometry & gb)
auto	distance (const Geometry & gA, const Geometry & gB, NoValidityCheck)
auto	distance (const Geometry & gA, const Geometry & gB)
auto	distance3D (const Geometry & gA, const Geometry & gB, NoValidityCheck)
auto	distance3D (const Geometry & gA, const Geometry & gB)
auto	distanceGeometryCollectionToGeometry (const Geometry & gA, const Geometry & gB)
auto	distanceGeometryCollectionToGeometry3D (const Geometry & gA, const Geometry & gB)
auto	distanceLineStringGeometry (const LineString & gA, const Geometry & gB)
auto	distanceLineStringGeometry3D (const LineString & gA, const Geometry & gB)
auto	distanceLineStringLineString (const LineString & gA, const LineString & gB)
auto	distanceLineStringLineString3D (const LineString & gA, const LineString & gB)
auto	distanceLineStringPolygon (const LineString & gA, const Polygon & gB)
auto	distanceLineStringPolygon3D (const LineString & gA, const Polygon & gB)
auto	distanceLineStringPolyhedralSurface3D (const LineString & lineA, const PolyhedralSurface & polySurfaceB)
auto	distanceLineStringSolid3D (const LineString & gA, const Solid & gB)
auto	distanceLineStringTriangle (const LineString & gA, const Triangle & gB)
auto	distanceLineStringTriangle3D (const LineString & gA, const Triangle & gB)
auto	distanceLineStringTriangulatedSurface3D (const LineString & lineA, const TriangulatedSurface & triangulatedSurfaceB)
auto	distancePointGeometry (const Point & gA, const Geometry & gB)
auto	distancePointGeometry3D (const Point & gA, const Geometry & gB)
auto	distancePointLineString (const Point & gA, const LineString & gB)
auto	distancePointLineString3D (const Point & gA, const LineString & gB)
auto	distancePointPoint (const Point & gA, const Point & gB)
auto	distancePointPoint3D (const Point & gA, const Point & gB)
auto	distancePointPolygon (const Point & gA, const Polygon & gB)
auto	distancePointPolygon3D (const Point & gA, const Polygon & gB)
auto	distancePointPolyhedralSurface3D (const Point & pointA, const PolyhedralSurface & polySurfaceB)
auto	distancePointSegment (const Point & p, const Point & a, const Point & b)
auto	distancePointSegment3D (const Point & p, const Point & a, const Point & b)
auto	distancePointSolid3D (const Point & gA, const Solid & gB)
auto	distancePointTriangle (const Point & gA, const Triangle & gB)
auto	distancePointTriangle3D (const Point & gA, const Triangle & gB)
auto	distancePointTriangle3D (const Point & p_, const Point & a_, const Point & b_, const Point & c_)
auto	distancePointTriangulatedSurface3D (const Point & pointA, const TriangulatedSurface & triangulatedSurfaceB)
auto	distancePolygonGeometry (const Polygon & gA, const Geometry & gB)
auto	distancePolygonGeometry3D (const Polygon & gA, const Geometry & gB)
auto	distancePolygonPolygon (const Polygon & gA, const Polygon & gB)
auto	distancePolygonTriangle (const Polygon & gA, const Triangle & gB)
auto	distancePolyhedralSurfaceGeometry3D (const PolyhedralSurface & polySurfaceA, const Geometry & geomB)
auto	distanceSegmentSegment (const Point & a, const Point & b, const Point & c, const Point & d)
auto	distanceSegmentSegment3D (const Point & a, const Point & b, const Point & c, const Point & d)
auto	distanceSegmentTriangle3D (const Point & sA_, const Point & sB_, const Point & tA_, const Point & tB_, const Point & tC_)
auto	distanceSolidGeometry3D (const Solid & gA, const Geometry & gB)
auto	distanceSolidSolid3D (const Solid & gA, const Solid & gB)
auto	distanceTriangleGeometry (const Triangle & gA, const Geometry & gB)
auto	distanceTriangleGeometry3D (const Triangle & gA, const Geometry & gB)
auto	distanceTrianglePolyhedralSurface3D (const Triangle & triangleA, const PolyhedralSurface & polySurfaceB)
auto	distanceTriangleSolid3D (const Triangle & gA, const Solid & gB)
auto	distanceTriangleTriangle3D (const Triangle & gA, const Triangle & gB)
auto	distanceTriangleTriangulatedSurface3D (const Triangle & triangleA, const TriangulatedSurface & triangulatedSurfaceB)
auto	distanceTriangulatedSurfaceGeometry3D (const TriangulatedSurface & triangulatedSurfaceA, const Geometry & geomB)
auto	extrude (const Geometry & g, const Kernel::Vector_3 & v) Returns a Geometry equal to the specified Geometry, extruded by the specified displacement vector.
auto	extrude (const Geometry & g, const Kernel::FT & dx, const Kernel::FT & dy, const Kernel::FT & dz, NoValidityCheck)
auto	extrude (const Geometry & g, const Kernel::FT & dx, const Kernel::FT & dy, const Kernel::FT & dz) Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.
SFCGAL_API auto	extrude (const Geometry & g, const double & dx, const double & dy, const double & dz) Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.
SFCGAL_API auto	extrude (const Polygon & g, const double & height)
SFCGAL_API std::unique_ptr< Geometry >	extrude (const Geometry & g, const Kernel::FT & dx, const Kernel::FT & dy, const Kernel::FT & dz, NoValidityCheck & nvc) Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.
auto	extrudeStraightSkeleton (const Polygon & geom, double height)
auto	extrudeStraightSkeleton (const Geometry & geom, double height)
auto	extrudeStraightSkeleton (const Geometry & geom, double building_height, double roof_height)
SFCGAL_API auto	extrudedStraightSkeleton (const Polygon & geom, double height) build a 3D straight skeleton extruded for a Polygon __
void	force2D (Geometry & g) force a geometry to be 2D (project on O,x,y)
void	force3D (Geometry & g, const Kernel::FT & defaultZ=0) force a 2D geometry to be 3D (replace undefined Z by defaultZ, existing Z values remains unchanged)
void	forceMeasured (Geometry & geometry, const double & defaultM=0) force a 2D or M geometry to be M (replace undefined M by defaultM, existing M values remains unchanged)
auto	hasConsistentOrientation3D (const TriangulatedSurface & g)
auto	hasConsistentOrientation3D (const PolyhedralSurface & g)
bool	hasPlane3D (const Polygon & polygon, CGAL::Point_3< Kernel > & a, CGAL::Point_3< Kernel > & b, CGAL::Point_3< Kernel > & c) Test if a 3D plane can be extracted from a Polygon .
bool	hasPlane3D (const Polygon & polygon)
auto	intersection (const CGAL::Triangle_3< Kernel > & a, const CGAL::Triangle_3< Kernel > & b)
void	intersection (const GeometrySet< Dim > & a, const GeometrySet< Dim > & b, GeometrySet< Dim > & output)
auto	intersection (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	intersection (const Geometry & ga, const Geometry & gb)
auto	intersection3D (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	intersection3D (const Geometry & ga, const Geometry & gb)
auto	intersects (const detail::PrimitiveHandle< Dim > & a, const detail::PrimitiveHandle< Dim > & b)
auto	intersects (const detail::GeometrySet< Dim > & a, const detail::GeometrySet< Dim > & b)
auto	intersects (const Geometry & ga, const Geometry & gb)
auto	intersects (const Geometry & ga, const Geometry & gb, NoValidityCheck)
bool	intersects (const detail::GeometrySet< Dim > & a, const detail::GeometrySet< Dim > & b)
bool	intersects (const detail::PrimitiveHandle< Dim > & a, const detail::PrimitiveHandle< Dim > & b)
auto	intersects3D (const Geometry & ga, const Geometry & gb)
auto	intersects3D (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	isClosed (const SurfaceGraph & graph)
auto	isConnected (const SurfaceGraph & graph)
auto	isCounterClockWiseOriented (const LineString & ls)
auto	isCounterClockWiseOriented (const Triangle & tri)
auto	isCounterClockWiseOriented (const Polygon & poly)
bool	isPlane3D (const Geometry & geom, const double & toleranceAbs)
auto	isSimple (const Geometry & g, const double & toleranceAbs=1e-9)
auto	isValid (const Point & p)
auto	isValid (const LineString & l, const double & toleranceAbs)
auto	isValid (const Polygon & p, const double & toleranceAbs)
auto	isValid (const Triangle & t, const double & toleranceAbs)
auto	isValid (const MultiLineString & ml, const double & toleranceAbs)
auto	isValid (const MultiPolygon & mp, const double & toleranceAbs)
auto	isValid (const GeometryCollection & gc, const double & toleranceAbs)
auto	isValid (const TriangulatedSurface & tin, const SurfaceGraph & graph, const double & toleranceAbs)
auto	isValid (const TriangulatedSurface & tin, const double & toleranceAbs)
auto	isValid (const PolyhedralSurface & s, const SurfaceGraph & graph, const double & toleranceAbs)
auto	isValid (const PolyhedralSurface & s, const double & toleranceAbs)
auto	isValid (const Solid & solid, const double & toleranceAbs)
auto	isValid (const MultiSolid & ms, const double & toleranceAbs)
auto	isValid (const Geometry & g, const double & toleranceAbs) Check validity of a geometry.
auto	length (const LineString & g) Compute the 2D length for a LineString .
auto	length (const GeometryCollection & g) Compute the 2D length for a GeometryCollection .
auto	length (const Geometry & g) Compute the 2D length for a Geometry (0 for incompatible types)
auto	length3D (const LineString & g) Compute the 3D length for a LineString .
auto	length3D (const GeometryCollection & g) Compute the 3D length for a GeometryCollection .
auto	length3D (const Geometry & g) Compute the 2D length for a geometry.
auto	lineSubstring (const LineString & ls, double start, double end) Retrieve a substring of a specified LineString , between the specified fractional distances from the start of the specifiedLineString .
void	makeConsistentOrientation3D (TriangulatedSurface & g)
void	makeValidOrientation (CGAL::Polygon_2< Kernel > & polygon)
void	makeValidOrientation (CGAL::Polygon_with_holes_2< Kernel > & polygon)
void	makeValidOrientation (Polygon & polygon)
auto	minkowskiSum (const Geometry & gA, const Polygon & gB, NoValidityCheck) 2D minkowski sum (p+q)
auto	minkowskiSum (const Geometry & gA, const Polygon & gB) 2D minkowski sum (p+q)
auto	minkowskiSum3D (const Geometry & gA, const Geometry & gB, NoValidityCheck) 3D Minkowski sum (p+q)
auto	minkowskiSum3D (const Geometry & gA, const Geometry & gB) 3D Minkowski sum (p+q)
CGAL::Vector_3< Kernel >	normal3D (const CGAL::Point_3< Kernel > & a, const CGAL::Point_3< Kernel > & b, const CGAL::Point_3< Kernel > & c)
CGAL::Vector_3< Kernel >	normal3D (const LineString & ls, bool exact=true)
CGAL::Vector_3< Kernel >	normal3D (const Polygon & polygon, bool exact=true)
void	offset (const Geometry & g, const double & radius, Offset_polygon_set_2 & polygonSet) dispatch a geometry
void	offset (const Point & g, const double & radius, Offset_polygon_set_2 & polygonSet) offset for a Point __
void	offset (const LineString & g, const double & radius, Offset_polygon_set_2 & polygonSet) offset for a LineString __
void	offset (const Polygon & g, const double & radius, Offset_polygon_set_2 & polygonSet) offset for a Polygon __
auto	offset (const Geometry & g, const double & r, NoValidityCheck) [experimental]compute polygon offset
auto	offset (const Geometry & g, const double & r) [experimental]compute polygon offset
void	offsetCollection (const Geometry & g, const double & radius, Offset_polygon_set_2 & polygonSet) offset for MultiPoint ,MultiLineString ,MultiPolygon ,TriangulatedSurface ,PolyhedralSurface __
auto	optimal_alpha_shapes (const Geometry & g, bool allow_holes=false, size_t nb_components=1)
auto	partition_2 (const Geometry & g, PartitionAlgorithm alg, NoValidityCheck)
auto	partition_2 (const Geometry & g, PartitionAlgorithm alg=y_monotone)
void	plane3D (const Polygon & polygon, CGAL::Point_3< Kernel > & a, CGAL::Point_3< Kernel > & b, CGAL::Point_3< Kernel > & c)
CGAL::Plane_3< Kernel >	plane3D (const Polygon & polygon)
CGAL::Plane_3< Kernel >	plane3D (const Polygon & polygon, const Plane3DInexactUnsafe &)
CGAL::Plane_3< Kernel >	plane3D (const Polygon & polygon, bool exact)
auto	polygonSetToMultiPolygon (const Offset_polygon_set_2 & polygonSet, const int & n) convert Offset_polygon_set_2 to MultiPolygon __
void	propagateValidityFlag (Geometry & g, bool valid)
void	rotate (Geometry & g, const Kernel::FT & angle) Rotate a geometry in 2D around the origin (0,0)
void	rotate (Geometry & g, const Kernel::FT & angle, const Point & origin) Rotate a geometry in 2D around a specified point.
void	rotate (Geometry & g, const Kernel::FT & angle, const Kernel::Vector_3 & axis, const Point & origin=Point(0, 0, 0)) Rotate a geometry in 3D around a specified axis and origin.
void	rotateX (Geometry & g, const Kernel::FT & angle) Rotate a geometry around the X axis.
void	rotateY (Geometry & g, const Kernel::FT & angle) Rotate a geometry around the Y axis.
void	rotateZ (Geometry & g, const Kernel::FT & angle) Rotate a geometry around the Z axis.
void	scale (Geometry & g, double s)
void	scale (Geometry & g, double sx, double sy, double sz=0.0)
void	scale (Geometry & g, double sx, double sy, double sz, double cx, double cy, double cz)
auto	selfIntersects (const LineString & l)
auto	selfIntersects (const PolyhedralSurface & s, const SurfaceGraph & g)
auto	selfIntersects (const TriangulatedSurface & s, const SurfaceGraph & g)
auto	selfIntersects3D (const LineString & l)
auto	selfIntersects3D (const PolyhedralSurface & s, const SurfaceGraph & g)
auto	selfIntersects3D (const TriangulatedSurface & s, const SurfaceGraph & g)
auto	signedArea (const Triangle & g) Compute the 2D signed area for a Triangle .
auto	signedArea (const LineString & g) Compute the 2D signed area for a closed LineString .
auto	simplify (const Geometry & geometry, double threshold, bool preserveTopology) Main entry point for geometry simplification.
auto	squaredDistancePointTriangle3D (const Point_3 & p, const Triangle_3 & abc)
auto	squaredDistanceSegmentTriangle3D (const Segment_3 & sAB, const Triangle_3 & tABC)
auto	squaredDistanceTriangleTriangle3D (const Triangle_3 & triangleA, const Triangle_3 & triangleB)
auto	straightSkeleton (const Geometry & geom, bool autoOrientation, NoValidityCheck, bool innerOnly=false, bool outputDistanceInM=false, const double & toleranceAbs=EPSILON) build a 2D straight skeleton for a Polygon __
auto	straightSkeleton (const Geometry & geom, bool autoOrientation=true, bool innerOnly=false, bool outputDistanceInM=false, const double & toleranceAbs=EPSILON) build a 2D straight skeleton for a Polygon __
auto	straightSkeleton (const Polygon & geom, bool autoOrientation=true, bool innerOnly=false, bool outputDistanceInM=false, const double & toleranceAbs=EPSILON) build a 2D straight skeleton for a Polygon __
auto	straightSkeleton (const MultiPolygon & geom, bool autoOrientation=true, bool innerOnly=false, bool outputDistanceInM=false, const double & toleranceAbs=EPSILON) build a 2D straight skeleton for a Polygon __
auto	straightSkeletonPartition (const Geometry & geom, bool autoOrientation=true) Build a 2D straight skeleton partition for a Geometry.
auto	straightSkeletonPartition (const MultiPolygon & geom, bool autoOrientation=true) Build a 2D straight skeleton partition for a MultiPolygon .
auto	straightSkeletonPartition (const Polygon & geom, bool autoOrientation=true) Build a 2D straight skeleton partition for a Polygon .
auto	tesselate (const Geometry & g, NoValidityCheck)
auto	tesselate (const Geometry & g)
void	translate (Geometry & g, const Kernel::Vector_3 & v) translate a geometry from a given vector
void	translate (Geometry & g, const Kernel::Vector_2 & v) translate a geometry from a given vector
void	translate (Geometry & g, const Kernel::FT & dx, const Kernel::FT & dy, const Kernel::FT & dz) translate a geometry from a given vector
void	translate (Geometry & g, const double & dx, const double & dy, const double & dz) translate a geometry from double-coordinates
auto	union3D (const Geometry & ga, const Geometry & gb, NoValidityCheck)
auto	union3D (const Geometry & ga, const Geometry & gb)
void	union_ (const detail::GeometrySet< Dim > & a, const detail::GeometrySet< Dim > & b, detail::GeometrySet< Dim > &)
void	union_ (const detail::PrimitiveHandle< Dim > & a, const detail::PrimitiveHandle< Dim > & b, detail::GeometrySet< Dim > &)
auto	visibility (const Geometry & polygon, const Geometry & point) build the visibility polygon of a Point inside aPolygon __
auto	visibility (const Geometry & polygon, const Geometry & point, NoValidityCheck) build the visibility polygon of a Point inside aPolygon __
auto	visibility (const Geometry & polygon, const Geometry & pointA, const Geometry & pointB) build the visibility polygon of the segment [pointA ; pointB] on a Polygon __
auto	visibility (const Geometry & polygon, const Geometry & pointA, const Geometry & pointB, NoValidityCheck) build the visibility polygon of a Point inside aPolygon __
auto	volume (const Solid & g, NoValidityCheck)
auto	volume (const Geometry & g)
auto	weightedCentroid (const Geometry & g, bool enable3DComputation=false)
auto	weightedCentroid (const Triangle & g, bool enable3DComputation=false)
auto	weightedCentroid (const Point & a, const Point & b, const Point & c, bool enable3DComputation=false)
auto	weightedCentroid (const LineString & g, bool enable3DComputation=false)
auto	weightedCentroid (const Polygon & g, bool enable3DComputation=false)
auto	weightedCentroid (const GeometryCollection & g, bool enable3DComputation=false)
auto	weightedCentroid (const TriangulatedSurface & g, bool enable3DComputation=false)
auto	weightedCentroid (const PolyhedralSurface & g, bool enable3DComputation=false)
auto	weightedCentroid (const Solid & g, bool enable3DComputation=false)

Public Types Documentation#

enum PartitionAlgorithm#

enum algorithm::PartitionAlgorithm {
    y_monotone,
    approx_convex,
    greene_approx_convex,
    optimal_convex
};

Partition algorithm available

Since:

1.4.2

Public Functions Documentation#

function alphaShapes#

auto algorithm::alphaShapes (
    const Geometry & g,
    double alpha=1,
    bool allow_holes=false
)

Compute the 2D alpha shapes for a geometry https://doc.cgal.org/latest/Alpha_shapes_2/index.html#Chapter_2D_Alpha_Shapes

Since:

1.4.1

function alphaWrapping3D#

auto algorithm::alphaWrapping3D (
    const Geometry & geom,
    size_t relativeAlpha,
    size_t relativeOffset
)

end of private section

Computes the 3D alpha wrapping of a geometry https://doc.cgal.org/latest/Alpha_wrap_3/index.html

Since:

2.1

Parameters:

geom input geometry
relativeAlpha This parameter is used to determine which features will appear in the output A small relativeAlpha will produce an output less complex but less faithful to the input
relativeOffset This parameter controls the tightness of the result A large relativeOffset parameter will tend to better preserve sharp features as projection If this parameter is equal to 0, it is computed from the alpha parameter

Returns:

A PolyhedralSurface representing the 3D alpha wrapping of the geometry

function approximate#

approximate an Offset_polygon_2 (filter null segments)

auto algorithm::approximate (
    const Offset_polygon_2 & polygon,
    const int & n=0
)

function approximate#

approximate an Offset

auto algorithm::approximate (
    const Offset_polygon_with_holes_2 & polygon,
    const int & n=0
)

function approximateMedialAxis#

build an approximate medial axis for a Polygon __

auto algorithm::approximateMedialAxis (
    const Geometry & geom
)

Parameters:

geom input geometry

Precondition:

geom is a valid geometry

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function area#

Compute the 2D area for a Geometry.

auto algorithm::area (
    const Geometry & g,
    NoValidityCheck
)

Warning:

Z component is ignored, there is no 2D projection for 3D geometries

Precondition:

g is a valid geometry

Warning:

No actual validity check is done

function area#

Compute the 2D area for a Geometry.

auto algorithm::area (
    const Geometry & g
)

Warning:

Z component is ignored, there is no 2D projection for 3D geometries

Precondition:

g is a valid geometry

function area#

auto algorithm::area (
    const Triangle & g
)

Returns Compute the 2D area for a Triangle

function area#

auto algorithm::area (
    const Polygon & g
)

Returns Compute the 2D area for a Polygon

function area#

auto algorithm::area (
    const GeometryCollection & g
)

Returns the 2D area for a GeometryCollection

function area#

auto algorithm::area (
    const TriangulatedSurface & g
)

Returns the 2D area for a TriangulatedSurface

function area#

auto algorithm::area (
    const PolyhedralSurface & g
)

Returns the 2D area for a TriangulatedSurface

function area3D#

auto algorithm::area3D (
    const Geometry & g,
    NoValidityCheck
)

Returns 3D area for a Geometry

Warning:

Solid area is set to 0 (might be defined as the area of the surface)

Precondition:

g is a valid geometry

Warning:

No actual validity check is done

function area3D#

auto algorithm::area3D (
    const Geometry & g
)

Returns 3D area for a Geometry

Warning:

Solid area is set to 0 (might be defined as the area of the surface)

Precondition:

g is a valid geometry

function area3D#

auto algorithm::area3D (
    const Polygon & g
)

Returns 3D area for a Polygon

function area3D#

auto algorithm::area3D (
    const Triangle & g
)

Returns the 3D area for a Triangle

function area3D#

auto algorithm::area3D (
    const GeometryCollection & g
)

Returns the 3D area for a MultiPolygon

function area3D#

auto algorithm::area3D (
    const PolyhedralSurface & g
)

Returns the 3D area for a PolyhedralSurface

function area3D#

auto algorithm::area3D (
    const TriangulatedSurface & g
)

Returns the 3D area for a TriangulatedSurface

function boundingCircle#

auto algorithm::boundingCircle (
    const Geometry & geom
)

function boundingSphere#

auto algorithm::boundingSphere (
    const Geometry & geom
)

function centroid#

Returns the 2D centroid for a Geometry.

auto algorithm::centroid (
    const Geometry & g
)

The result is the weighted centroid of a geometry. The implementation follows PostGIS one (https://postgis.net/docs/ST_Centroid.html). The weigth is computed in the XY space.

Warning:

Z component is ignored, geometries must be valid when projected in the XY plane. Vertical geometries will generate an error.

Precondition:

g is a valid geometry in 2D

function centroid3D#

Returns the 3D centroid for a Geometry.

auto algorithm::centroid3D (
    const Geometry & g
)

The result is the weighted centroid of a geometry. The implementation follows PostGIS one (https://postgis.net/docs/ST_Centroid.html). The weigth is computed in the 3D space.

Precondition:

g is a valid geometry

function circleToPolygon#

helper to create a polygon from a circle

auto algorithm::circleToPolygon (
    const Kernel::Circle_2 & circle
)

function collect#

auto algorithm::collect (
    const Geometry & ga,
    const Geometry & gb
)

Returns an aggregate of ga and gb

function collect#

template<typename GeometryIterator>
std::unique_ptr< Geometry > algorithm::collect (
    GeometryIterator begin,
    GeometryIterator end
)

Returns an aggregate of a list of geometries

function collectionExtractPolygons#

auto algorithm::collectionExtractPolygons (
    std::unique_ptr< Geometry > coll
)

Given a geometry collection returns a MultiPolygon from triangles, polygons, polyhedral and polygons

Warning:

Ownership is taken from the parameter

function collectionHomogenize#

auto algorithm::collectionHomogenize (
    std::unique_ptr< Geometry > coll
)

Given a geometry collection, returns the "simplest" representation of the contents. Singletons will be returned as singletons. Collections that are homogeneous will be returned as the appropriate multi-type.

Warning:

Ownership is taken from the parameter

function collectionToMulti#

auto algorithm::collectionToMulti (
    std::unique_ptr< Geometry > coll
)

Given a geometry collection of triangles, TINs and polygons returns a MultiPolygon

Warning:

Ownership is taken from the parameter

function convexHull#

auto algorithm::convexHull (
    const Geometry & g
)

Compute the 2D convex hull for a geometry

function convexHull3D#

auto algorithm::convexHull3D (
    const Geometry & g
)

Compute the 3D convex hull for a geometry

Todo

improve to handle collinear points and coplanar points

function covers#

auto algorithm::covers (
    const Geometry & ga,
    const Geometry & gb
)

Cover test on 2D geometries. Checks if gA covers gB. Force projection to z=0 if needed

function covers#

template<int Dim>
bool algorithm::covers (
    const detail::GeometrySet < Dim > & a,
    const detail::GeometrySet < Dim > & b
)

function covers#

template<int Dim>
bool algorithm::covers (
    const detail::PrimitiveHandle < Dim > & a,
    const detail::PrimitiveHandle < Dim > & b
)

function covers3D#

auto algorithm::covers3D (
    const Geometry & ga,
    const Geometry & gb
)

Cover test on 3D geometries. Checks if gA covers gB. Assume z = 0 if needed

function difference#

auto algorithm::difference (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Diffrence on 2D geometries. No validity check variant

Precondition:

ga and gb are valid geometries

Warning:

No actual validity check is done.

function difference#

auto algorithm::difference (
    const Geometry & ga,
    const Geometry & gb
)

Difference on 2D geometries.

Precondition:

ga and gb are valid geometries

function difference3D#

auto algorithm::difference3D (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Difference on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

Warning:

@ No actual validity check is done

function difference3D#

auto algorithm::difference3D (
    const Geometry & ga,
    const Geometry & gb
)

Difference on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

function distance#

auto algorithm::distance (
    const Geometry & gA,
    const Geometry & gB,
    NoValidityCheck
)

Compute the distance between two Geometries

Precondition:

gA is a valid geometry

Precondition:

gB is a valid geometry

Warning:

No actual validity check is done

function distance#

auto algorithm::distance (
    const Geometry & gA,
    const Geometry & gB
)

Compute the distance between two Geometries

Precondition:

gA is a valid geometry

Precondition:

gB is a valid geometry

function distance3D#

auto algorithm::distance3D (
    const Geometry & gA,
    const Geometry & gB,
    NoValidityCheck
)

Compute distance between two 3D Geometries

Precondition:

gA is a valid geometry

Precondition:

gB is a valid geometry

Warning:

No actual validity check is done

function distance3D#

auto algorithm::distance3D (
    const Geometry & gA,
    const Geometry & gB
)

dispatch distance between two Geometries

Todo

complete with solid Compute distance between two 3D Geometries

Precondition:

gA is a valid geometry

Precondition:

gB is a valid geometry

function distanceGeometryCollectionToGeometry#

auto algorithm::distanceGeometryCollectionToGeometry (
    const Geometry & gA,
    const Geometry & gB
)

dispatch distance from a collection of geometry (gA) to a Geometry (gB)

function distanceGeometryCollectionToGeometry3D#

auto algorithm::distanceGeometryCollectionToGeometry3D (
    const Geometry & gA,
    const Geometry & gB
)

dispatch distance from a collection of geometry (gA) to a Geometry (gB)

function distanceLineStringGeometry#

auto algorithm::distanceLineStringGeometry (
    const LineString & gA,
    const Geometry & gB
)

dispatch distance from LineString to Geometry

function distanceLineStringGeometry3D#

auto algorithm::distanceLineStringGeometry3D (
    const LineString & gA,
    const Geometry & gB
)

dispatch distance between a LineString and a Geometry

function distanceLineStringLineString#

auto algorithm::distanceLineStringLineString (
    const LineString & gA,
    const LineString & gB
)

distance between two LineStrings

function distanceLineStringLineString3D#

auto algorithm::distanceLineStringLineString3D (
    const LineString & gA,
    const LineString & gB
)

distance between two LineStrings

function distanceLineStringPolygon#

auto algorithm::distanceLineStringPolygon (
    const LineString & gA,
    const Polygon & gB
)

distance between a LineString and a Polygon

function distanceLineStringPolygon3D#

auto algorithm::distanceLineStringPolygon3D (
    const LineString & gA,
    const Polygon & gB
)

distance between a LineString and a Polygon

Todo

same method than distancePointPolygon3D (unify if triangulate is available)

function distanceLineStringPolyhedralSurface3D#

auto algorithm::distanceLineStringPolyhedralSurface3D (
    const LineString & lineA,
    const PolyhedralSurface & polySurfaceB
)

distance between a LineString and a PolyhedralSurface

function distanceLineStringSolid3D#

auto algorithm::distanceLineStringSolid3D (
    const LineString & gA,
    const Solid & gB
)

distance between a LineString and a Solid

function distanceLineStringTriangle#

auto algorithm::distanceLineStringTriangle (
    const LineString & gA,
    const Triangle & gB
)

distance between a LineString and a Triangle

function distanceLineStringTriangle3D#

auto algorithm::distanceLineStringTriangle3D (
    const LineString & gA,
    const Triangle & gB
)

distance between a LineString and a Triangle

function distanceLineStringTriangulatedSurface3D#

auto algorithm::distanceLineStringTriangulatedSurface3D (
    const LineString & lineA,
    const TriangulatedSurface & triangulatedSurfaceB
)

distance between a LineString and a TriangulatedSurface

function distancePointGeometry#

auto algorithm::distancePointGeometry (
    const Point & gA,
    const Geometry & gB
)

dispatch distance from Point to Geometry

function distancePointGeometry3D#

auto algorithm::distancePointGeometry3D (
    const Point & gA,
    const Geometry & gB
)

dispatch distance from Point to Geometry

function distancePointLineString#

auto algorithm::distancePointLineString (
    const Point & gA,
    const LineString & gB
)

distance between a Point and a LineString

function distancePointLineString3D#

auto algorithm::distancePointLineString3D (
    const Point & gA,
    const LineString & gB
)

distance between a Point and a LineString

function distancePointPoint#

auto algorithm::distancePointPoint (
    const Point & gA,
    const Point & gB
)

distance between two Points

function distancePointPoint3D#

auto algorithm::distancePointPoint3D (
    const Point & gA,
    const Point & gB
)

distance between two Points

function distancePointPolygon#

auto algorithm::distancePointPolygon (
    const Point & gA,
    const Polygon & gB
)

distance between a Point and a Polygon

function distancePointPolygon3D#

auto algorithm::distancePointPolygon3D (
    const Point & gA,
    const Polygon & gB
)

distance between a Point and a Triangle

function distancePointPolyhedralSurface3D#

auto algorithm::distancePointPolyhedralSurface3D (
    const Point & pointA,
    const PolyhedralSurface & polySurfaceB
)

distance between a Point and a PolyhedralSurface

function distancePointSegment#

auto algorithm::distancePointSegment (
    const Point & p,
    const Point & a,
    const Point & b
)

function distancePointSegment3D#

auto algorithm::distancePointSegment3D (
    const Point & p,
    const Point & a,
    const Point & b
)

function distancePointSolid3D#

auto algorithm::distancePointSolid3D (
    const Point & gA,
    const Solid & gB
)

distance between a Point and a Solid

function distancePointTriangle#

auto algorithm::distancePointTriangle (
    const Point & gA,
    const Triangle & gB
)

distance between a Point and a Triangle

function distancePointTriangle3D#

auto algorithm::distancePointTriangle3D (
    const Point & gA,
    const Triangle & gB
)

distance between a Point and a Triangle

function distancePointTriangle3D#

auto algorithm::distancePointTriangle3D (
    const Point & p_,
    const Point & a_,
    const Point & b_,
    const Point & c_
)

function distancePointTriangulatedSurface3D#

auto algorithm::distancePointTriangulatedSurface3D (
    const Point & pointA,
    const TriangulatedSurface & triangulatedSurfaceB
)

distance between a Point and a TriangulatedSurface

function distancePolygonGeometry#

auto algorithm::distancePolygonGeometry (
    const Polygon & gA,
    const Geometry & gB
)

dispatch distance from Polygon to Geometry

function distancePolygonGeometry3D#

auto algorithm::distancePolygonGeometry3D (
    const Polygon & gA,
    const Geometry & gB
)

dispatch distance between a Polygon and a Geometry

function distancePolygonPolygon#

auto algorithm::distancePolygonPolygon (
    const Polygon & gA,
    const Polygon & gB
)

distance between two Polygons

function distancePolygonTriangle#

auto algorithm::distancePolygonTriangle (
    const Polygon & gA,
    const Triangle & gB
)

distance between a Polygon and a Triangle

function distancePolyhedralSurfaceGeometry3D#

auto algorithm::distancePolyhedralSurfaceGeometry3D (
    const PolyhedralSurface & polySurfaceA,
    const Geometry & geomB
)

dispatch distance between a PolyhedralSurface and a Geometry

function distanceSegmentSegment#

auto algorithm::distanceSegmentSegment (
    const Point & a,
    const Point & b,
    const Point & c,
    const Point & d
)

function distanceSegmentSegment3D#

auto algorithm::distanceSegmentSegment3D (
    const Point & a,
    const Point & b,
    const Point & c,
    const Point & d
)

function distanceSegmentTriangle3D#

auto algorithm::distanceSegmentTriangle3D (
    const Point & sA_,
    const Point & sB_,
    const Point & tA_,
    const Point & tB_,
    const Point & tC_
)

function distanceSolidGeometry3D#

auto algorithm::distanceSolidGeometry3D (
    const Solid & gA,
    const Geometry & gB
)

dispatch distance between a Solid and a Geometry

function distanceSolidSolid3D#

auto algorithm::distanceSolidSolid3D (
    const Solid & gA,
    const Solid & gB
)

distance between two Solids

function distanceTriangleGeometry#

auto algorithm::distanceTriangleGeometry (
    const Triangle & gA,
    const Geometry & gB
)

dispatch distance from a Triangle to a Geometry

function distanceTriangleGeometry3D#

auto algorithm::distanceTriangleGeometry3D (
    const Triangle & gA,
    const Geometry & gB
)

dispatch distance between a Triangle and a Geometry

function distanceTrianglePolyhedralSurface3D#

auto algorithm::distanceTrianglePolyhedralSurface3D (
    const Triangle & triangleA,
    const PolyhedralSurface & polySurfaceB
)

distance between a Triangle and a PolyhedralSurface

function distanceTriangleSolid3D#

auto algorithm::distanceTriangleSolid3D (
    const Triangle & gA,
    const Solid & gB
)

distance between a Triangle and a Solid

function distanceTriangleTriangle3D#

auto algorithm::distanceTriangleTriangle3D (
    const Triangle & gA,
    const Triangle & gB
)

distance between two Triangles

function distanceTriangleTriangulatedSurface3D#

auto algorithm::distanceTriangleTriangulatedSurface3D (
    const Triangle & triangleA,
    const TriangulatedSurface & triangulatedSurfaceB
)

function distanceTriangulatedSurfaceGeometry3D#

auto algorithm::distanceTriangulatedSurfaceGeometry3D (
    const TriangulatedSurface & triangulatedSurfaceA,
    const Geometry & geomB
)

dispatch distance between a TriangulatedSurface and a Geometry

function extrude#

Returns a Geometry equal to the specified Geometry, extruded by the specified displacement vector.

auto algorithm::extrude (
    const Geometry & g,
    const Kernel::Vector_3 & v
)

Parameters:

g The specified Geometry.
v The specified displacement vector.

Returns:

A Geometry equal to g extruded by the displacement vector v.

Precondition:

g must be a valid geometry.

Note:

If g is such that g.isMeasured() is true, then, since there is no common expectation of the values of the measures on the returned Geometry, all measures from the result are removed.

Todo

Improve extrude for 3D surfaces - Extrude only faces whose scalar_product(v,normal) > 0 and use Polyhedron union to get output geometries with a clean topology.

function extrude#

auto algorithm::extrude (
    const Geometry & g,
    const Kernel::FT & dx,
    const Kernel::FT & dy,
    const Kernel::FT & dz,
    NoValidityCheck
)

function extrude#

Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.

auto algorithm::extrude (
    const Geometry & g,
    const Kernel::FT & dx,
    const Kernel::FT & dy,
    const Kernel::FT & dz
)

Parameters:

g The specified Geometry.
dx The component of the specified displacement in the x-direction.
dy The component of the specified displacement in the y-direction.
dz The component of the specified displacement in the z-direction.

Returns:

A Geometry equal to g extruded by the displacement vector {dx, dy, dz}.

Precondition:

g must be a valid geometry.

Precondition:

dx, dy and dz must all be finite.

Note:

If g is such that g.isMeasured() is true, then, since there is no common expectation of the values of the measures on the returned Geometry, all measures from the result are removed.

function extrude#

Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.

SFCGAL_API auto algorithm::extrude (
    const Geometry & g,
    const double & dx,
    const double & dy,
    const double & dz
)

Parameters:

g The specified Geometry.
dx The component of the specified displacement in the x-direction.
dy The component of the specified displacement in the y-direction.
dz The component of the specified displacement in the z-direction.

Returns:

A Geometry equal to g extruded by the displacement vector {dx, dy, dz}.

Precondition:

g must be a valid geometry.

Precondition:

dx, dy and dz must all be finite.

Note:

If g is such that g.isMeasured() is true, then, since there is no common expectation of the values of the measures on the returned Geometry, all measures from the result are removed.

Warning:

No actual validity check is conducted.

function extrude#

SFCGAL_API auto algorithm::extrude (
    const Polygon & g,
    const double & height
)

function extrude#

Returns a Geometry equal to the specified Geometry, extruded by the specified displacement.

SFCGAL_API std::unique_ptr< Geometry > algorithm::extrude (
    const Geometry & g,
    const Kernel::FT & dx,
    const Kernel::FT & dy,
    const Kernel::FT & dz,
    NoValidityCheck & nvc
)

Parameters:

g The specified Geometry.
dx The component of the specified displacement in the x-direction.
dy The component of the specified displacement in the y-direction.
dz The component of the specified displacement in the z-direction.
nvc A NoValidityCheck object.

Returns:

A Geometry equal to g extruded by the displacement vector {dx, dy, dz}.

Precondition:

g must be a valid geometry.

Precondition:

dx, dy and dz must all be finite.

Note:

If g is such that g.isMeasured() is true, then, since there is no common expectation of the values of the measures on the returned Geometry, all measures from the result are removed.

Warning:

No actual validity check is conducted.

function extrudeStraightSkeleton#

auto algorithm::extrudeStraightSkeleton (
    const Polygon & geom,
    double height
)

function extrudeStraightSkeleton#

auto algorithm::extrudeStraightSkeleton (
    const Geometry & geom,
    double height
)

function extrudeStraightSkeleton#

auto algorithm::extrudeStraightSkeleton (
    const Geometry & geom,
    double building_height,
    double roof_height
)

function extrudedStraightSkeleton#

build a 3D straight skeleton extruded for a Polygon __

SFCGAL_API auto algorithm::extrudedStraightSkeleton (
    const Polygon & geom,
    double height
)

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function force2D#

force a geometry to be 2D (project on O,x,y)

void algorithm::force2D (
    Geometry & g
)

Warning:

ignore empty geometries

function force3D#

force a 2D geometry to be 3D (replace undefined Z by defaultZ, existing Z values remains unchanged)

void algorithm::force3D (
    Geometry & g,
    const Kernel::FT & defaultZ=0
)

Warning:

ignore empty geometries

function forceMeasured#

force a 2D or M geometry to be M (replace undefined M by defaultM, existing M values remains unchanged)

void algorithm::forceMeasured (
    Geometry & geometry,
    const double & defaultM=0
)

Warning:

ignore empty geometries

function hasConsistentOrientation3D#

auto algorithm::hasConsistentOrientation3D (
    const TriangulatedSurface & g
)

Test if a Geometry has a consistent orientation

function hasConsistentOrientation3D#

auto algorithm::hasConsistentOrientation3D (
    const PolyhedralSurface & g
)

Test if a PolyhedralSurface has a consistent orientation

function hasPlane3D#

Test if a 3D plane can be extracted from a Polygon .

template<typename Kernel>
bool algorithm::hasPlane3D (
    const Polygon & polygon,
    CGAL::Point_3< Kernel > & a,
    CGAL::Point_3< Kernel > & b,
    CGAL::Point_3< Kernel > & c
)

function hasPlane3D#

template<typename Kernel>
bool algorithm::hasPlane3D (
    const Polygon & polygon
)

Test if a 3D plane can be extracted from a Polygon

function intersection#

auto algorithm::intersection (
    const CGAL::Triangle_3< Kernel > & a,
    const CGAL::Triangle_3< Kernel > & b
)

function intersection#

template<int Dim>
void algorithm::intersection (
    const GeometrySet < Dim > & a,
    const GeometrySet < Dim > & b,
    GeometrySet < Dim > & output
)

function intersection#

auto algorithm::intersection (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Intersection on 2D geometries. No validity check variant

Precondition:

ga and gb are valid geometries

Warning:

No actual validity check is done.

function intersection#

auto algorithm::intersection (
    const Geometry & ga,
    const Geometry & gb
)

Intersection on 2D geometries.

Precondition:

ga and gb are valid geometries

function intersection3D#

auto algorithm::intersection3D (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Intersection on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

Warning:

@ No actual validity check is done

function intersection3D#

auto algorithm::intersection3D (
    const Geometry & ga,
    const Geometry & gb
)

Intersection on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

function intersects#

template<int Dim>
auto algorithm::intersects (
    const detail::PrimitiveHandle < Dim > & a,
    const detail::PrimitiveHandle < Dim > & b
)

Intersection test on a PrimitiveHandle

function intersects#

template<int Dim>
auto algorithm::intersects (
    const detail::GeometrySet < Dim > & a,
    const detail::GeometrySet < Dim > & b
)

Intersection test on GeometrySet

function intersects#

auto algorithm::intersects (
    const Geometry & ga,
    const Geometry & gb
)

Robust intersection test on 2D geometries. Force projection to z=0 if needed

Precondition:

ga and gb are valid geometries

function intersects#

auto algorithm::intersects (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Intersection test on 2D geometries. Force projection to z=0 if needed

Precondition:

ga and gb are valid geometries

Warning:

the validity is assumed, no actual check is done

function intersects#

template<int Dim>
bool algorithm::intersects (
    const detail::GeometrySet < Dim > & a,
    const detail::GeometrySet < Dim > & b
)

Intersection test on GeometrySet

function intersects#

template<int Dim>
bool algorithm::intersects (
    const detail::PrimitiveHandle < Dim > & a,
    const detail::PrimitiveHandle < Dim > & b
)

Intersection test on a PrimitiveHandle

function intersects3D#

auto algorithm::intersects3D (
    const Geometry & ga,
    const Geometry & gb
)

Robust intersection test on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

function intersects3D#

auto algorithm::intersects3D (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Intersection test on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

Warning:

the validity is assumed, no actual check is done

function isClosed#

auto algorithm::isClosed (
    const SurfaceGraph & graph
)

test if a surface is closed, the graph should be build beforehand

Note:

the surface may not be connected, eg. two spheres will yield a true result

function isConnected#

auto algorithm::isConnected (
    const SurfaceGraph & graph
)

test if a surface is connected, the graph should be build beforehand

function isCounterClockWiseOriented#

auto algorithm::isCounterClockWiseOriented (
    const LineString & ls
)

Test if a 2D surface is oriented counter clockwise

function isCounterClockWiseOriented#

auto algorithm::isCounterClockWiseOriented (
    const Triangle & tri
)

Test if a 2D surface is oriented counter clockwise

function isCounterClockWiseOriented#

auto algorithm::isCounterClockWiseOriented (
    const Polygon & poly
)

Test if a 2D surface is oriented counter clockwise

function isPlane3D#

template<typename Kernel>
bool algorithm::isPlane3D (
    const Geometry & geom,
    const double & toleranceAbs
)

Test if all points of a geometry lie in the same plane

function isSimple#

auto algorithm::isSimple (
    const Geometry & g,
    const double & toleranceAbs=1e-9
)

Check simplicity of a geometry

function isValid#

auto algorithm::isValid (
    const Point & p
)

Note:

empty geometries are valid, but the test is only performed in the interface function in individual functions for implementation, an assertion !empty is present for this reason

function isValid#

auto algorithm::isValid (
    const LineString & l,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const Polygon & p,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const Triangle & t,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const MultiLineString & ml,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const MultiPolygon & mp,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const GeometryCollection & gc,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const TriangulatedSurface & tin,
    const SurfaceGraph & graph,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const TriangulatedSurface & tin,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const PolyhedralSurface & s,
    const SurfaceGraph & graph,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const PolyhedralSurface & s,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const Solid & solid,
    const double & toleranceAbs
)

function isValid#

auto algorithm::isValid (
    const MultiSolid & ms,
    const double & toleranceAbs
)

function isValid#

Check validity of a geometry.

auto algorithm::isValid (
    const Geometry & g,
    const double & toleranceAbs
)

function length#

Compute the 2D length for a LineString .

auto algorithm::length (
    const LineString & g
)

function length#

Compute the 2D length for a GeometryCollection .

auto algorithm::length (
    const GeometryCollection & g
)

function length#

Compute the 2D length for a Geometry (0 for incompatible types)

auto algorithm::length (
    const Geometry & g
)

function length3D#

Compute the 3D length for a LineString .

auto algorithm::length3D (
    const LineString & g
)

function length3D#

Compute the 3D length for a GeometryCollection .

auto algorithm::length3D (
    const GeometryCollection & g
)

function length3D#

Compute the 2D length for a geometry.

auto algorithm::length3D (
    const Geometry & g
)

Returns:

the length of the Geometry, 0 for incompatible types

function lineSubstring#

Retrieve a substring of a specified LineString , between the specified fractional distances from the start of the specifiedLineString .

auto algorithm::lineSubstring (
    const LineString & ls,
    double start,
    double end
)

Parameters:

ls The specified LineString.
start The fraction along the specified LineString defining the start of the desired substring.
end The fraction along the specified LineString defining the end of the desired substring.

Note:

Negative values of and/or will be interpreted as a fractional distance taken from the end of the specified LineString. +/-0 will always be interpreted as the start of .

Note:

For open lines, a negative length range will result in a line substring terminating at the specified points, but with an orientation reversed relative to . For closed lines the a negative range corresponds to the complentary section of with an orientation equal to that of it.

Returns:

The specified line substring.

Exception:

If either or have an absolute value greater than 1.

function makeConsistentOrientation3D#

void algorithm::makeConsistentOrientation3D (
    TriangulatedSurface & g
)

Try to make consistent orientation in a TriangulatedSurface

function makeValidOrientation#

void algorithm::makeValidOrientation (
    CGAL::Polygon_2< Kernel > & polygon
)

Make valid 2D orientation

function makeValidOrientation#

void algorithm::makeValidOrientation (
    CGAL::Polygon_with_holes_2< Kernel > & polygon
)

Make valid 2D orientation

function makeValidOrientation#

void algorithm::makeValidOrientation (
    Polygon & polygon
)

Make valid 2D orientation

function minkowskiSum#

2D minkowski sum (p+q)

auto algorithm::minkowskiSum (
    const Geometry & gA,
    const Polygon & gB,
    NoValidityCheck
)

Warning:

If gA is a polygon, its orientation is taken into account. A "reversed" polygon (with a clockwise-oriented exterior ring) will involve a minkowski difference rather than a sum.

Todo

missing cases (union)

Precondition:

gA and gB are valid geometries

Warning:

@ No actual validity check is done.

function minkowskiSum#

2D minkowski sum (p+q)

auto algorithm::minkowskiSum (
    const Geometry & gA,
    const Polygon & gB
)

Warning:

If gA is a polygon, its orientation is taken into account. A "reversed" polygon (with a clockwise-oriented exterior ring) will involve a minkowski difference rather than a sum.

Todo

missing cases (union)

Precondition:

gA and gB are valid geometries

function minkowskiSum3D#

3D Minkowski sum (p+q)

auto algorithm::minkowskiSum3D (
    const Geometry & gA,
    const Geometry & gB,
    NoValidityCheck
)

Precondition:

gA and gB are valid 3D geometries

Warning:

No actual validity check is done.

function minkowskiSum3D#

3D Minkowski sum (p+q)

auto algorithm::minkowskiSum3D (
    const Geometry & gA,
    const Geometry & gB
)

Precondition:

gA and gB are valid 3D geometries

function normal3D#

template<typename Kernel>
CGAL::Vector_3< Kernel > algorithm::normal3D (
    const CGAL::Point_3< Kernel > & a,
    const CGAL::Point_3< Kernel > & b,
    const CGAL::Point_3< Kernel > & c
)

Returns the 3D normal to 3 consecutive points.

function normal3D#

template<typename Kernel>
CGAL::Vector_3< Kernel > algorithm::normal3D (
    const LineString & ls,
    bool exact=true
)

Returns the 3D normal to a ring (supposed to be planar and closed).

Warning:

exact allows to avoid double rounding at the end of the computation

function normal3D#

template<typename Kernel>
CGAL::Vector_3< Kernel > algorithm::normal3D (
    const Polygon & polygon,
    bool exact=true
)

Returns the 3D normal to a polygon (supposed to be planar).

Warning:

exact allows to avoid double rounding at the end of the computation

function offset#

dispatch a geometry

void algorithm::offset (
    const Geometry & g,
    const double & radius,
    Offset_polygon_set_2 & polygonSet
)

function offset#

offset for a Point __

void algorithm::offset (
    const Point & g,
    const double & radius,
    Offset_polygon_set_2 & polygonSet
)

build Point offset

function offset#

offset for a LineString __

void algorithm::offset (
    const LineString & g,
    const double & radius,
    Offset_polygon_set_2 & polygonSet
)

build LineString offset

function offset#

offset for a Polygon __

void algorithm::offset (
    const Polygon & g,
    const double & radius,
    Offset_polygon_set_2 & polygonSet
)

function offset#

[experimental]compute polygon offset

auto algorithm::offset (
    const Geometry & g,
    const double & r,
    NoValidityCheck
)

Warning:

test in order to compare with minkowski sum

Precondition:

g is a valid Geometry

Warning:

No actual validity check is done.

function offset#

[experimental]compute polygon offset

auto algorithm::offset (
    const Geometry & g,
    const double & r
)

Warning:

test in order to compare with minkowski sum

Precondition:

g is a valid Geometry

function offsetCollection#

offset for MultiPoint ,MultiLineString ,MultiPolygon ,TriangulatedSurface ,PolyhedralSurface __

void algorithm::offsetCollection (
    const Geometry & g,
    const double & radius,
    Offset_polygon_set_2 & polygonSet
)

function optimal_alpha_shapes#

auto algorithm::optimal_alpha_shapes (
    const Geometry & g,
    bool allow_holes=false,
    size_t nb_components=1
)

Compute the optimal 2D alpha shapes for a geometry https://doc.cgal.org/latest/Alpha_shapes_2/index.html#Chapter_2D_Alpha_Shapes

Since:

1.4.1

function partition_2#

auto algorithm::partition_2 (
    const Geometry & g,
    PartitionAlgorithm alg,
    NoValidityCheck
)

Compute the partition of a 2D polygon https://doc.cgal.org/latest/Partition_2/index.html#Chapter_2D_Polygon_Partitioning

Precondition:

g is a valid geometry

Warning:

No actual validity check is done

function partition_2#

auto algorithm::partition_2 (
    const Geometry & g,
    PartitionAlgorithm alg=y_monotone
)

Compute the partition of a 2D polygon https://doc.cgal.org/latest/Partition_2/index.html#Chapter_2D_Polygon_Partitioning

Since:

1.4.2

function plane3D#

template<typename Kernel>
void algorithm::plane3D (
    const Polygon & polygon,
    CGAL::Point_3< Kernel > & a,
    CGAL::Point_3< Kernel > & b,
    CGAL::Point_3< Kernel > & c
)

Get 3 non collinear points from a Polygon

function plane3D#

template<typename Kernel>
CGAL::Plane_3< Kernel > algorithm::plane3D (
    const Polygon & polygon
)

Returns the oriented 3D plane of a polygon (supposed to be planar). May return degenerate plane.

function plane3D#

template<typename Kernel>
CGAL::Plane_3< Kernel > algorithm::plane3D (
    const Polygon & polygon,
    const Plane3DInexactUnsafe &
)

Returns the oriented 3D plane of a polygon (supposed to be planar) - inexact version.

Warning:

Will divide by zero if polygon is degenerate.

Warning:

result is rounded to double (avoid huge expression tree).

function plane3D#

template<typename Kernel>
CGAL::Plane_3< Kernel > algorithm::plane3D (
    const Polygon & polygon,
    bool exact
)

Returns the oriented 3D plane of a polygon (supposed to be planar). This is legacy code for SFCGAL users and should be deprecated.

Warning:

result is rounded to double if exact is false (avoid huge expression tree).

Warning:

Will divide by zero if polygon is degenerate. This maintains the previous behaviour.

function polygonSetToMultiPolygon#

convert Offset_polygon_set_2 to MultiPolygon __

auto algorithm::polygonSetToMultiPolygon (
    const Offset_polygon_set_2 & polygonSet,
    const int & n
)

function propagateValidityFlag#

void algorithm::propagateValidityFlag (
    Geometry & g,
    bool valid
)

Sets the geometry flag on a geometry and propagate to every internal geometries

function rotate#

Rotate a geometry in 2D around the origin (0,0)

void algorithm::rotate (
    Geometry & g,
    const Kernel::FT & angle
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians

function rotate#

Rotate a geometry in 2D around a specified point.

void algorithm::rotate (
    Geometry & g,
    const Kernel::FT & angle,
    const Point & origin
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians
origin Point of origin for the rotation

function rotate#

Rotate a geometry in 3D around a specified axis and origin.

void algorithm::rotate (
    Geometry & g,
    const Kernel::FT & angle,
    const Kernel::Vector_3 & axis,
    const Point & origin=Point (0, 0, 0)
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians
axis The axis of rotation
origin Point of origin for the rotation

function rotateX#

Rotate a geometry around the X axis.

void algorithm::rotateX (
    Geometry & g,
    const Kernel::FT & angle
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians

function rotateY#

Rotate a geometry around the Y axis.

void algorithm::rotateY (
    Geometry & g,
    const Kernel::FT & angle
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians

function rotateZ#

Rotate a geometry around the Z axis.

void algorithm::rotateZ (
    Geometry & g,
    const Kernel::FT & angle
)

Parameters:

g The geometry to rotate
angle Rotation angle in radians

function scale#

void algorithm::scale (
    Geometry & g,
    double s
)

Scale a geometry by a given factor

Parameters:

g input geometry
s scale factor

function scale#

void algorithm::scale (
    Geometry & g,
    double sx,
    double sy,
    double sz=0.0
)

Scale a geometry by different factors for each dimension

Parameters:

g input geometry
sx scale factor for x dimension
sy scale factor for y dimension
sz scale factor for z dimension

function scale#

void algorithm::scale (
    Geometry & g,
    double sx,
    double sy,
    double sz,
    double cx,
    double cy,
    double cz
)

Scale a geometry by different factors for each dimension around a center point

Parameters:

g input geometry
sx scale factor for x dimension
sy scale factor for y dimension
sz scale factor for z dimension
cx x-coordinate of the center point
cy y-coordinate of the center point
cz z-coordinate of the center point

function selfIntersects#

auto algorithm::selfIntersects (
    const LineString & l
)

Self intersection test for 2D LineString (false if only endpoint touch)

function selfIntersects#

auto algorithm::selfIntersects (
    const PolyhedralSurface & s,
    const SurfaceGraph & g
)

Self intersection test for 2D PolyhedralSurface (false if only point touch)

function selfIntersects#

auto algorithm::selfIntersects (
    const TriangulatedSurface & s,
    const SurfaceGraph & g
)

Self intersection test for 2D TriangulatedSurface (false if only point touch)

function selfIntersects3D#

auto algorithm::selfIntersects3D (
    const LineString & l
)

Self intersection test for 3D LineString (false if only endpoints touch)

function selfIntersects3D#

auto algorithm::selfIntersects3D (
    const PolyhedralSurface & s,
    const SurfaceGraph & g
)

Self intersection test for 3D PolyhedralSurface (false if only point touch)

function selfIntersects3D#

auto algorithm::selfIntersects3D (
    const TriangulatedSurface & s,
    const SurfaceGraph & g
)

Self intersection test for 3D TriangulatedSurface (false if only point touch)

function signedArea#

Compute the 2D signed area for a Triangle .

auto algorithm::signedArea (
    const Triangle & g
)

function signedArea#

Compute the 2D signed area for a closed LineString .

auto algorithm::signedArea (
    const LineString & g
)

function simplify#

Main entry point for geometry simplification.

auto algorithm::simplify (
    const Geometry & geometry,
    double threshold,
    bool preserveTopology
)

Simplifies a geometry using the CGAL algorithm https://doc.cgal.org/latest/Polyline_simplification_2/index.html.

Parameters:

geometry The geometry to simplify
threshold The distance (in geometry unit) threshold for simplification
preserveTopology Whether to preserve topology during simplification

Returns:

A simplified copy of the input geometry

function squaredDistancePointTriangle3D#

auto algorithm::squaredDistancePointTriangle3D (
    const Point_3 & p,
    const Triangle_3 & abc
)

function squaredDistanceSegmentTriangle3D#

auto algorithm::squaredDistanceSegmentTriangle3D (
    const Segment_3 & sAB,
    const Triangle_3 & tABC
)

function squaredDistanceTriangleTriangle3D#

auto algorithm::squaredDistanceTriangleTriangle3D (
    const Triangle_3 & triangleA,
    const Triangle_3 & triangleB
)

function straightSkeleton#

build a 2D straight skeleton for a Polygon __

auto algorithm::straightSkeleton (
    const Geometry & geom,
    bool autoOrientation,
    NoValidityCheck,
    bool innerOnly=false,
    bool outputDistanceInM=false,
    const double & toleranceAbs=EPSILON
)

Parameters:

geom input geometry
autoOrientation check and fix polygon orientation
innerOnly Skip non-inner edges if requested
outputDistanceInM whether to output the distance to border as M
toleranceAbs Distance tolerance between returned points. A line must have a maximum distance of toleranceAbs.

Precondition:

geom is a valid geometry

Warning:

No actual validity check is done

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function straightSkeleton#

build a 2D straight skeleton for a Polygon __

auto algorithm::straightSkeleton (
    const Geometry & geom,
    bool autoOrientation=true,
    bool innerOnly=false,
    bool outputDistanceInM=false,
    const double & toleranceAbs=EPSILON
)

Todo

add supports for TriangulatedSurface and PolyhedralSurface

Parameters:

geom input geometry
autoOrientation check and fix polygon orientation
innerOnly Skip non-inner edges if requested
outputDistanceInM whether to output the distance to border as M
toleranceAbs Distance tolerance between returned points. A line must have a maximum distance of toleranceAbs.

Precondition:

geom is a valid geometry

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function straightSkeleton#

build a 2D straight skeleton for a Polygon __

auto algorithm::straightSkeleton (
    const Polygon & geom,
    bool autoOrientation=true,
    bool innerOnly=false,
    bool outputDistanceInM=false,
    const double & toleranceAbs=EPSILON
)

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function straightSkeleton#

build a 2D straight skeleton for a Polygon __

auto algorithm::straightSkeleton (
    const MultiPolygon & geom,
    bool autoOrientation=true,
    bool innerOnly=false,
    bool outputDistanceInM=false,
    const double & toleranceAbs=EPSILON
)

Exception:

NotImplementedException If geom is a Polygon with point touching rings.

function straightSkeletonPartition#

Build a 2D straight skeleton partition for a Geometry.

auto algorithm::straightSkeletonPartition (
    const Geometry & geom,
    bool autoOrientation=true
)

Parameters:

geom The input geometry
autoOrientation Check and fix polygon orientation

Returns:

A unique pointer to a MultiPolygon representing the partitioned geometry

Exception:

Exception If CGAL fails to create the straight skeleton

Note:

Only Triangle, Polygon, and MultiPolygon geometries are supported

This function creates a partition of the input geometry based on its straight skeleton. For unsupported geometry types, an empty MultiPolygon is returned.

function straightSkeletonPartition#

Build a 2D straight skeleton partition for a MultiPolygon .

auto algorithm::straightSkeletonPartition (
    const MultiPolygon & geom,
    bool autoOrientation=true
)

Parameters:

geom The input multi-polygon
autoOrientation Check and fix polygon orientation

Returns:

A unique pointer to a MultiPolygon representing the partitioned multi-polygon

This function applies the straight skeleton partition to each polygon in the input multi-polygon and combines the results into a single MultiPolygon.

function straightSkeletonPartition#

Build a 2D straight skeleton partition for a Polygon .

auto algorithm::straightSkeletonPartition (
    const Polygon & geom,
    bool autoOrientation=true
)

Parameters:

geom The input polygon
autoOrientation Check and fix polygon orientation (not used in this implementation)

Returns:

A unique pointer to a MultiPolygon representing the partitioned polygon

Exception:

Exception If CGAL fails to create the straight skeleton

This function creates a partition of the input polygon based on its straight skeleton. It uses CGAL's Arrangement_2 to handle the intersection of skeleton and polygon edges.

function tesselate#

auto algorithm::tesselate (
    const Geometry & g,
    NoValidityCheck
)

Tesselate a geometry: this will triangulate surfaces (including polyhedral and solid's surfaces) and keep untouched points, lines, etc.

Precondition:

g is a valid geometry

Warning:

No actual validity check is done.

function tesselate#

auto algorithm::tesselate (
    const Geometry & g
)

Tesselate a geometry: this will triangulate surfaces (including polyhedral and solid's surfaces) and keep untouched points, lines, etc.

Precondition:

g is a valid geometry

function translate#

translate a geometry from a given vector

void algorithm::translate (
    Geometry & g,
    const Kernel::Vector_3 & v
)

function translate#

translate a geometry from a given vector

void algorithm::translate (
    Geometry & g,
    const Kernel::Vector_2 & v
)

function translate#

translate a geometry from a given vector

void algorithm::translate (
    Geometry & g,
    const Kernel::FT & dx,
    const Kernel::FT & dy,
    const Kernel::FT & dz
)

function translate#

translate a geometry from double-coordinates

void algorithm::translate (
    Geometry & g,
    const double & dx,
    const double & dy,
    const double & dz
)

function union3D#

auto algorithm::union3D (
    const Geometry & ga,
    const Geometry & gb,
    NoValidityCheck
)

Union on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

Warning:

@ No actual validity check is done

function union3D#

auto algorithm::union3D (
    const Geometry & ga,
    const Geometry & gb
)

Union on 3D geometries. Assume z = 0 if needed

Precondition:

ga and gb are valid geometries

function union_#

template<int Dim>
void algorithm::union_ (
    const detail::GeometrySet < Dim > & a,
    const detail::GeometrySet < Dim > & b,
    detail::GeometrySet < Dim > &
)

function union_#

template<int Dim>
void algorithm::union_ (
    const detail::PrimitiveHandle < Dim > & a,
    const detail::PrimitiveHandle < Dim > & b,
    detail::GeometrySet < Dim > &
)

function visibility#

build the visibility polygon of a Point inside aPolygon __

auto algorithm::visibility (
    const Geometry & polygon,
    const Geometry & point
)

Parameters:

polygon input geometry
point input geometry

Precondition:

polygon is a valid geometry

Precondition:

point must be inside polygon or on the boundary

function visibility#

build the visibility polygon of a Point inside aPolygon __

auto algorithm::visibility (
    const Geometry & polygon,
    const Geometry & point,
    NoValidityCheck
)

Parameters:

polygon input geometry
point input geometry

Precondition:

polygon is a valid geometry

Precondition:

point must be inside polygon or on the boundary

Warning:

No actual validity check is done

function visibility#

build the visibility polygon of the segment [pointA ; pointB] on a Polygon __

auto algorithm::visibility (
    const Geometry & polygon,
    const Geometry & pointA,
    const Geometry & pointB
)

Parameters:

polygon input geometry
pointA input geometry
pointB input geometry

Precondition:

polygon is a valid geometry

Precondition:

pointA and pointB must be vertices of poly, adjacents and respect the direction

function visibility#

build the visibility polygon of a Point inside aPolygon __

auto algorithm::visibility (
    const Geometry & polygon,
    const Geometry & pointA,
    const Geometry & pointB,
    NoValidityCheck
)

Parameters:

polygon input geometry
pointA input geometry
pointB input geometry

Precondition:

polygon is a valid geometry

Warning:

No actual validity check is done

Precondition:

pointA and pointB must be vertices of poly, adjacents and respect the direction

function volume#

auto algorithm::volume (
    const Solid & g,
    NoValidityCheck
)

Computes the volume of a Solid

Precondition:

(not checked) volume is closed and consistently oriented

function volume#

auto algorithm::volume (
    const Geometry & g
)

Computes the volume of a geometry

Precondition:

g is a valid Geometry

function weightedCentroid#

auto algorithm::weightedCentroid (
    const Geometry & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a Geometry

function weightedCentroid#

auto algorithm::weightedCentroid (
    const Triangle & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a Triangle

function weightedCentroid#

auto algorithm::weightedCentroid (
    const Point & a,
    const Point & b,
    const Point & c,
    bool enable3DComputation=false
)

Returns the weighted centroid for a Triangle

function weightedCentroid#

auto algorithm::weightedCentroid (
    const LineString & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a LineString

function weightedCentroid#

auto algorithm::weightedCentroid (
    const Polygon & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a Polygon

function weightedCentroid#

auto algorithm::weightedCentroid (
    const GeometryCollection & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a GeometryCollection

function weightedCentroid#

auto algorithm::weightedCentroid (
    const TriangulatedSurface & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a TriangulatedSurface

function weightedCentroid#

auto algorithm::weightedCentroid (
    const PolyhedralSurface & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a PolyhedralSurface

function weightedCentroid#

auto algorithm::weightedCentroid (
    const Solid & g,
    bool enable3DComputation=false
)

Returns the weighted centroid for a Solid

The documentation for this class was generated from the following file /builds/sfcgal/SFCGAL/src/algorithm/alphaShapes.cpp