Modules
	Algorithm implementation details

	IO implementation details

Namespaces
	SFCGAL::detail
	Implementation details namespace.

	SFCGAL::detail::algorithm
	Algorithm detail namespace.

	SFCGAL::detail::io
	Input/output detail namespace.

	SFCGAL::triangulate::detail
	Triangulate detail namespace.

Classes
class	SFCGAL::algorithm::BoundaryVisitor
	Compute the boundary for a Geometry. More...

class	SFCGAL::algorithm::WeightedCentroid
	Holds weighted data to compute the centroid for a Geometry. More...

class	SFCGAL::algorithm::SurfaceGraph
	Represents a polyhedral surface as a graph where faces are nodes and egde are graph edges. More...

class	SFCGAL::algorithm::ConsistentOrientationBuilder
	Make orientation consistent in a triangle set. More...

Functions
auto	SFCGAL::algorithm::signedArea (const Triangle &g)
	Compute the 2D signed area for a Triangle. More...

auto	SFCGAL::algorithm::signedArea (const LineString &g)
	Compute the 2D signed area for a closed LineString. More...

auto	SFCGAL::algorithm::area (const Triangle &g)
	Returns Compute the 2D area for a Triangle. More...

auto	SFCGAL::algorithm::area (const Polygon &g)
	Returns Compute the 2D area for a Polygon. More...

auto	SFCGAL::algorithm::area (const GeometryCollection &g)
	Returns the 2D area for a GeometryCollection. More...

auto	SFCGAL::algorithm::area (const TriangulatedSurface &g)
	Returns the 2D area for a TriangulatedSurface. More...

auto	SFCGAL::algorithm::area (const PolyhedralSurface &g)
	Returns the 2D area for a TriangulatedSurface. More...

auto	SFCGAL::algorithm::area3D (const Geometry &g, NoValidityCheck)
	Returns 3D area for a Geometry. More...

auto	SFCGAL::algorithm::area3D (const Polygon &g)
	Returns 3D area for a Polygon. More...

auto	SFCGAL::algorithm::area3D (const GeometryCollection &g)
	Returns the 3D area for a MultiPolygon. More...

auto	SFCGAL::algorithm::area3D (const PolyhedralSurface &g)
	Returns the 3D area for a PolyhedralSurface. More...

auto	SFCGAL::algorithm::area3D (const Triangle &g)
	Returns the 3D area for a Triangle. More...

auto	SFCGAL::algorithm::area3D (const TriangulatedSurface &g)
	Returns the 3D area for a TriangulatedSurface. More...

auto	SFCGAL::algorithm::weightedCentroid (const Geometry &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Geometry. More...

auto	SFCGAL::algorithm::weightedCentroid (const Triangle &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Triangle. More...

auto	SFCGAL::algorithm::weightedCentroid (const Point &a, const Point &b, const Point &c, bool enable3DComputation=false)
	Returns the weighted centroid for a Triangle. More...

auto	SFCGAL::algorithm::weightedCentroid (const LineString &g, bool enable3DComputation=false)
	Returns the weighted centroid for a LineString. More...

auto	SFCGAL::algorithm::weightedCentroid (const Polygon &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Polygon. More...

auto	SFCGAL::algorithm::weightedCentroid (const GeometryCollection &g, bool enable3DComputation=false)
	Returns the weighted centroid for a GeometryCollection. More...

auto	SFCGAL::algorithm::weightedCentroid (const TriangulatedSurface &g, bool enable3DComputation=false)
	Returns the weighted centroid for a TriangulatedSurface. More...

auto	SFCGAL::algorithm::weightedCentroid (const PolyhedralSurface &g, bool enable3DComputation=false)
	Returns the weighted centroid for a PolyhedralSurface. More...

auto	SFCGAL::algorithm::weightedCentroid (const Solid &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Solid. More...

template<typename GeometryIterator >
std::unique_ptr< Geometry >	SFCGAL::algorithm::collect (GeometryIterator begin, GeometryIterator end)
	Returns an aggregate of a list of geometries. More...

auto	SFCGAL::algorithm::isConnected (const SurfaceGraph &graph)
	test if a surface is connected, the graph should be build beforehand More...

auto	SFCGAL::algorithm::isClosed (const SurfaceGraph &graph)
	test if a surface is closed, the graph should be build beforehand More...

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

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

auto	SFCGAL::algorithm::distancePointGeometry (const Point &gA, const Geometry &gB)
	dispatch distance from Point to Geometry More...

auto	SFCGAL::algorithm::distancePointPoint (const Point &gA, const Point &gB)
	distance between two Points More...

auto	SFCGAL::algorithm::distancePointLineString (const Point &gA, const LineString &gB)
	distance between a Point and a LineString More...

auto	SFCGAL::algorithm::distancePointPolygon (const Point &gA, const Polygon &gB)
	distance between a Point and a Polygon More...

auto	SFCGAL::algorithm::distancePointTriangle (const Point &gA, const Triangle &gB)
	distance between a Point and a Triangle More...

auto	SFCGAL::algorithm::distanceLineStringGeometry (const LineString &gA, const Geometry &gB)
	dispatch distance from LineString to Geometry More...

auto	SFCGAL::algorithm::distanceLineStringLineString (const LineString &gA, const LineString &gB)
	distance between two LineStrings More...

auto	SFCGAL::algorithm::distanceLineStringPolygon (const LineString &gA, const Polygon &gB)
	distance between a LineString and a Polygon More...

auto	SFCGAL::algorithm::distanceLineStringTriangle (const LineString &gA, const Triangle &gB)
	distance between a LineString and a Triangle More...

auto	SFCGAL::algorithm::distancePolygonGeometry (const Polygon &gA, const Geometry &gB)
	dispatch distance from Polygon to Geometry More...

auto	SFCGAL::algorithm::distancePolygonPolygon (const Polygon &gA, const Polygon &gB)
	distance between two Polygons More...

auto	SFCGAL::algorithm::distancePolygonTriangle (const Polygon &gA, const Triangle &gB)
	distance between a Polygon and a Triangle More...

auto	SFCGAL::algorithm::distanceTriangleGeometry (const Triangle &gA, const Geometry &gB)
	dispatch distance from a Triangle to a Geometry More...

auto	SFCGAL::algorithm::distanceGeometryCollectionToGeometry (const Geometry &gA, const Geometry &gB)
	dispatch distance from a collection of geometry (gA) to a Geometry (gB) More...

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

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

auto	SFCGAL::algorithm::distancePointGeometry3D (const Point &gA, const Geometry &gB)
	dispatch distance from Point to Geometry More...

auto	SFCGAL::algorithm::distancePointPoint3D (const Point &gA, const Point &gB)
	distance between two Points More...

auto	SFCGAL::algorithm::distancePointLineString3D (const Point &gA, const LineString &gB)
	distance between a Point and a LineString More...

auto	SFCGAL::algorithm::distancePointTriangle3D (const Point &gA, const Triangle &gB)
	distance between a Point and a Triangle More...

auto	SFCGAL::algorithm::distancePointPolygon3D (const Point &gA, const Polygon &gB)
	distance between a Point and a Triangle More...

auto	SFCGAL::algorithm::distancePointPolyhedralSurface3D (const Point &pointA, const PolyhedralSurface &polySurfaceB) -> double
	distance between a Point and a PolyhedralSurface More...

auto	SFCGAL::algorithm::distancePointTriangulatedSurface3D (const Point &pointA, const TriangulatedSurface &triangulatedSurfaceB) -> double
	distance between a Point and a TriangulatedSurface More...

auto	SFCGAL::algorithm::distancePointSolid3D (const Point &gA, const Solid &gB)
	distance between a Point and a Solid More...

auto	SFCGAL::algorithm::distanceLineStringGeometry3D (const LineString &gA, const Geometry &gB)
	dispatch distance between a LineString and a Geometry More...

auto	SFCGAL::algorithm::distanceLineStringLineString3D (const LineString &gA, const LineString &gB)
	distance between two LineStrings More...

auto	SFCGAL::algorithm::distanceLineStringTriangle3D (const LineString &gA, const Triangle &gB)
	distance between a LineString and a Triangle More...

auto	SFCGAL::algorithm::distanceLineStringPolygon3D (const LineString &gA, const Polygon &gB)
	distance between a LineString and a Polygon More...

auto	SFCGAL::algorithm::distanceLineStringPolyhedralSurface3D (const LineString &lineA, const PolyhedralSurface &polySurfaceB) -> double
	distance between a LineString and a PolyhedralSurface More...

auto	SFCGAL::algorithm::distanceLineStringTriangulatedSurface3D (const LineString &lineA, const TriangulatedSurface &triangulatedSurfaceB) -> double
	distance between a LineString and a TriangulatedSurface More...

auto	SFCGAL::algorithm::distanceLineStringSolid3D (const LineString &gA, const Solid &gB)
	distance between a LineString and a Solid More...

auto	SFCGAL::algorithm::distanceTriangleGeometry3D (const Triangle &gA, const Geometry &gB)
	dispatch distance between a Triangle and a Geometry More...

auto	SFCGAL::algorithm::distanceTrianglePolyhedralSurface3D (const Triangle &triangleA, const PolyhedralSurface &polySurfaceB)
	distance between a Triangle and a PolyhedralSurface More...

auto	SFCGAL::algorithm::distanceTriangleSolid3D (const Triangle &gA, const Solid &gB)
	distance between a Triangle and a Solid More...

auto	SFCGAL::algorithm::distancePolygonGeometry3D (const Polygon &gA, const Geometry &gB)
	dispatch distance between a Polygon and a Geometry More...

auto	SFCGAL::algorithm::distancePolyhedralSurfaceGeometry3D (const PolyhedralSurface &polySurfaceA, const Geometry &geomB) -> double
	dispatch distance between a PolyhedralSurface and a Geometry More...

auto	SFCGAL::algorithm::distanceTriangulatedSurfaceGeometry3D (const TriangulatedSurface &triangulatedSurfaceA, const Geometry &geomB) -> double
	dispatch distance between a TriangulatedSurface and a Geometry More...

auto	SFCGAL::algorithm::distanceSolidGeometry3D (const Solid &gA, const Geometry &gB)
	dispatch distance between a Solid and a Geometry More...

auto	SFCGAL::algorithm::distanceSolidSolid3D (const Solid &gA, const Solid &gB)
	distance between two Solids More...

auto	SFCGAL::algorithm::distanceGeometryCollectionToGeometry3D (const Geometry &gA, const Geometry &gB)
	dispatch distance from a collection of geometry (gA) to a Geometry (gB) More...

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

auto	SFCGAL::algorithm::distancePointTriangle3D (const Point &p, const Point &a, const Point &b, const Point &c)

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

auto	SFCGAL::algorithm::distanceSegmentTriangle3D (const Point &sA, const Point &sB, const Point &tA, const Point &tB, const Point &tC)

auto	SFCGAL::algorithm::distanceTriangleTriangle3D (const Triangle &gA, const Triangle &gB)
	distance between two Triangles More...

SFCGAL_API auto	SFCGAL::algorithm::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. More...

auto	SFCGAL::algorithm::extrude (const Geometry &g, const Kernel::Vector_3 &v)
	Returns a Geometry equal to the specified Geometry, extruded by the specified displacement vector. More...

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

auto	SFCGAL::algorithm::intersects (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection test on 2D geometries. More...

auto	SFCGAL::algorithm::intersects3D (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection test on 3D geometries. More...

template<int Dim>
bool	SFCGAL::algorithm::intersects (const detail::GeometrySet< Dim > &a, const detail::GeometrySet< Dim > &b)
	Intersection test on GeometrySet. More...

template<int Dim>
bool	SFCGAL::algorithm::intersects (const detail::PrimitiveHandle< Dim > &a, const detail::PrimitiveHandle< Dim > &b)
	Intersection test on a PrimitiveHandle. More...

auto	SFCGAL::algorithm::selfIntersects (const LineString &l)
	Self intersection test for 2D LineString (false if only endpoint touch) More...

auto	SFCGAL::algorithm::selfIntersects3D (const LineString &l)
	Self intersection test for 3D LineString (false if only endpoints touch) More...

auto	SFCGAL::algorithm::selfIntersects (const PolyhedralSurface &s, const SurfaceGraph &g)
	Self intersection test for 2D PolyhedralSurface (false if only point touch) More...

auto	SFCGAL::algorithm::selfIntersects3D (const PolyhedralSurface &s, const SurfaceGraph &g)
	Self intersection test for 3D PolyhedralSurface (false if only point touch) More...

auto	SFCGAL::algorithm::selfIntersects (const TriangulatedSurface &s, const SurfaceGraph &g)
	Self intersection test for 2D TriangulatedSurface (false if only point touch) More...

auto	SFCGAL::algorithm::selfIntersects3D (const TriangulatedSurface &s, const SurfaceGraph &g)
	Self intersection test for 3D TriangulatedSurface (false if only point touch) More...

template<typename Kernel >
bool	SFCGAL::algorithm::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. More...

template<typename Kernel >
CGAL::Plane_3< Kernel >	SFCGAL::algorithm::plane3D (const Polygon &polygon)
	Returns the oriented 3D plane of a polygon (supposed to be planar). More...

template<typename Kernel >
CGAL::Plane_3< Kernel >	SFCGAL::algorithm::plane3D (const Polygon &polygon, const Plane3DInexactUnsafe &)
	Returns the oriented 3D plane of a polygon (supposed to be planar) - inexact version. More...

template<typename Kernel >
bool	SFCGAL::algorithm::isPlane3D (const Geometry &geom, const double &toleranceAbs)
	Test if all points of a geometry lie in the same plane. More...

auto	SFCGAL::algorithm::straightSkeleton (const Polygon &geom, bool autoOrientation=true, bool innerOnly=false, bool outputDistanceInM=false, const double &toleranceAbs=EPSILON) -> std::unique_ptr< MultiLineString >
	build a 2D straight skeleton for a Polygon More...

auto	SFCGAL::algorithm::straightSkeleton (const MultiPolygon &geom, bool autoOrientation=true, bool innerOnly=false, bool outputDistanceInM=false, const double &toleranceAbs=EPSILON) -> std::unique_ptr< MultiLineString >
	build a 2D straight skeleton for a Polygon More...

SFCGAL_API auto	SFCGAL::algorithm::extrudedStraightSkeleton (const Polygon &geom, double height) -> std::unique_ptr< PolyhedralSurface >
	build a 3D straight skeleton extruded for a Polygon More...

auto	SFCGAL::algorithm::straightSkeletonPartition (const Polygon &geom, bool autoOrientation=true) -> std::unique_ptr< PolyhedralSurface >
	Build a 2D straight skeleton partition for a Polygon. More...

auto	SFCGAL::algorithm::straightSkeletonPartition (const MultiPolygon &geom, bool autoOrientation=true) -> std::unique_ptr< PolyhedralSurface >
	Build a 2D straight skeleton partition for a MultiPolygon. More...

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

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

auto	SFCGAL::detail::algorithm::coversPoints (const Geometry &ga, const Geometry &gb)
	Pseudo cover test on 2D geometries. More...

auto	SFCGAL::detail::algorithm::coversPoints3D (const Geometry &ga, const Geometry &gb)
	Pseudo cover test on 3D geometries. More...

void	SFCGAL::triangulate::triangulatePolygon3D (const Polygon &g, TriangulatedSurface &triangulatedSurface)
	Triangulate a 3D Polygon. More...

void	SFCGAL::triangulate::triangulatePolygon3D (const Triangle &g, TriangulatedSurface &triangulatedSurface)
	Triangulate a 3D Triangle (copy triangle) More...

void	SFCGAL::triangulate::triangulatePolygon3D (const TriangulatedSurface &g, TriangulatedSurface &triangulatedSurface)
	Triangulate a 3D TriangulatedSurface (copy triangles) More...

SFCGAL_API void	SFCGAL::triangulate::opentriangulatePolygon3D (const GeometryCollection &g, TriangulatedSurface &triangulatedSurface)
	Triangulate a 3D MultiPolygon. More...

void	SFCGAL::triangulate::triangulatePolygon3D (const PolyhedralSurface &polyhedralSurface, TriangulatedSurface &triangulatedSurface)
	Triangulate 3D polygons in a PolyhedralSurface. More...

void	SFCGAL::triangulate::triangulatePolygon3D (const Solid &g, TriangulatedSurface &triangulatedSurface)
	Triangulate a Solid. More...

Detailed Description

Function Documentation

SFCGAL_API double SFCGAL::algorithm::area ( const Triangle & g ) -> double

Returns Compute the 2D area for a Triangle.

SFCGAL_API double SFCGAL::algorithm::area ( const Polygon & g ) -> double

Returns Compute the 2D area for a Polygon.

SFCGAL_API double SFCGAL::algorithm::area ( const GeometryCollection & g ) -> double

Returns the 2D area for a GeometryCollection.

SFCGAL_API double SFCGAL::algorithm::area ( const TriangulatedSurface & g ) -> double

Returns the 2D area for a TriangulatedSurface.

SFCGAL_API double SFCGAL::algorithm::area ( const PolyhedralSurface & g ) -> double

Returns the 2D area for a TriangulatedSurface.

SFCGAL_API double SFCGAL::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

SFCGAL_API double SFCGAL::algorithm::area3D ( const Polygon & g ) -> double

Returns 3D area for a Polygon.

SFCGAL_API double SFCGAL::algorithm::area3D ( const Triangle & g ) -> double

Returns the 3D area for a Triangle.

SFCGAL_API double SFCGAL::algorithm::area3D ( const GeometryCollection & g ) -> double

Returns the 3D area for a MultiPolygon.

SFCGAL_API double SFCGAL::algorithm::area3D ( const PolyhedralSurface & g ) -> double

Returns the 3D area for a PolyhedralSurface.

SFCGAL_API double SFCGAL::algorithm::area3D ( const TriangulatedSurface & g ) -> double

Returns the 3D area for a TriangulatedSurface.

template<typename GeometryIterator >

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

Returns an aggregate of a list of geometries.

template<int Dim>

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

template<int Dim>

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

SFCGAL_API bool SFCGAL::detail::algorithm::coversPoints	(	const Geometry &	ga,
		const Geometry &	gb
	)

Pseudo cover test on 2D geometries.

Collect points of gb and tests if no points of gb is outside ga

SFCGAL_API bool SFCGAL::detail::algorithm::coversPoints3D	(	const Geometry &	ga,
		const Geometry &	gb
	)

Pseudo cover test on 3D geometries.

Collect points of gb and tests if no points of gb is outside ga

SFCGAL_API double SFCGAL::algorithm::distanceGeometryCollectionToGeometry	(	const Geometry &	gA,
		const Geometry &	gB
	)		-> double

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

SFCGAL_API double SFCGAL::algorithm::distanceGeometryCollectionToGeometry3D	(	const Geometry &	gA,
		const Geometry &	gB
	)		-> double

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

SFCGAL_API double SFCGAL::algorithm::distanceLineStringGeometry	(	const LineString &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance from LineString to Geometry

SFCGAL_API double SFCGAL::algorithm::distanceLineStringGeometry3D	(	const LineString &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance between a LineString and a Geometry

SFCGAL_API double SFCGAL::algorithm::distanceLineStringLineString	(	const LineString &	gA,
		const LineString &	gB
	)		-> double

distance between two LineStrings

SFCGAL_API double SFCGAL::algorithm::distanceLineStringLineString3D	(	const LineString &	gA,
		const LineString &	gB
	)		-> double

distance between two LineStrings

SFCGAL_API double SFCGAL::algorithm::distanceLineStringPolygon	(	const LineString &	gA,
		const Polygon &	gB
	)		-> double

distance between a LineString and a Polygon

SFCGAL_API double SFCGAL::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)

SFCGAL_API auto SFCGAL::algorithm::distanceLineStringPolyhedralSurface3D	(	const LineString &	lineA,
		const PolyhedralSurface &	polySurfaceB
	)		-> double

distance between a LineString and a PolyhedralSurface

SFCGAL_API double SFCGAL::algorithm::distanceLineStringSolid3D	(	const LineString &	gA,
		const Solid &	gB
	)		-> double

distance between a LineString and a Solid

SFCGAL_API double SFCGAL::algorithm::distanceLineStringTriangle	(	const LineString &	gA,
		const Triangle &	gB
	)		-> double

distance between a LineString and a Triangle

SFCGAL_API double SFCGAL::algorithm::distanceLineStringTriangle3D	(	const LineString &	gA,
		const Triangle &	gB
	)		-> double

distance between a LineString and a Triangle

SFCGAL_API auto SFCGAL::algorithm::distanceLineStringTriangulatedSurface3D	(	const LineString &	lineA,
		const TriangulatedSurface &	triangulatedSurfaceB
	)		-> double

distance between a LineString and a TriangulatedSurface

SFCGAL_API double SFCGAL::algorithm::distancePointGeometry	(	const Point &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance from Point to Geometry

SFCGAL_API double SFCGAL::algorithm::distancePointGeometry3D	(	const Point &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance from Point to Geometry

SFCGAL_API double SFCGAL::algorithm::distancePointLineString	(	const Point &	gA,
		const LineString &	gB
	)		-> double

distance between a Point and a LineString

SFCGAL_API double SFCGAL::algorithm::distancePointLineString3D	(	const Point &	gA,
		const LineString &	gB
	)		-> double

distance between a Point and a LineString

SFCGAL_API double SFCGAL::algorithm::distancePointPoint	(	const Point &	gA,
		const Point &	gB
	)		-> double

distance between two Points

SFCGAL_API double SFCGAL::algorithm::distancePointPoint3D	(	const Point &	gA,
		const Point &	gB
	)		-> double

distance between two Points

SFCGAL_API double SFCGAL::algorithm::distancePointPolygon	(	const Point &	gA,
		const Polygon &	gB
	)		-> double

distance between a Point and a Polygon

SFCGAL_API double SFCGAL::algorithm::distancePointPolygon3D	(	const Point &	gA,
		const Polygon &	gB
	)		-> double

distance between a Point and a Triangle

SFCGAL_API auto SFCGAL::algorithm::distancePointPolyhedralSurface3D	(	const Point &	pointA,
		const PolyhedralSurface &	polySurfaceB
	)		-> double

distance between a Point and a PolyhedralSurface

SFCGAL_API double SFCGAL::algorithm::distancePointSegment	(	const Point &	p,
		const Point &	a,
		const Point &	b
	)		-> double

SFCGAL_API double SFCGAL::algorithm::distancePointSegment3D	(	const Point &	p,
		const Point &	a,
		const Point &	b
	)		-> double

SFCGAL_API double SFCGAL::algorithm::distancePointSolid3D	(	const Point &	gA,
		const Solid &	gB
	)		-> double

distance between a Point and a Solid

SFCGAL_API double SFCGAL::algorithm::distancePointTriangle	(	const Point &	gA,
		const Triangle &	gB
	)		-> double

distance between a Point and a Triangle

SFCGAL_API double SFCGAL::algorithm::distancePointTriangle3D	(	const Point &	gA,
		const Triangle &	gB
	)		-> double

distance between a Point and a Triangle

SFCGAL_API double SFCGAL::algorithm::distancePointTriangle3D	(	const Point &	p_,
		const Point &	a_,
		const Point &	b_,
		const Point &	c_
	)		-> double

SFCGAL_API auto SFCGAL::algorithm::distancePointTriangulatedSurface3D	(	const Point &	pointA,
		const TriangulatedSurface &	triangulatedSurfaceB
	)		-> double

distance between a Point and a TriangulatedSurface

SFCGAL_API double SFCGAL::algorithm::distancePolygonGeometry	(	const Polygon &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance from Polygon to Geometry

SFCGAL_API double SFCGAL::algorithm::distancePolygonGeometry3D	(	const Polygon &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance between a Polygon and a Geometry

SFCGAL_API double SFCGAL::algorithm::distancePolygonPolygon	(	const Polygon &	gA,
		const Polygon &	gB
	)		-> double

distance between two Polygons

SFCGAL_API double SFCGAL::algorithm::distancePolygonTriangle	(	const Polygon &	gA,
		const Triangle &	gB
	)		-> double

distance between a Polygon and a Triangle

SFCGAL_API auto SFCGAL::algorithm::distancePolyhedralSurfaceGeometry3D	(	const PolyhedralSurface &	polySurfaceA,
		const Geometry &	geomB
	)		-> double

dispatch distance between a PolyhedralSurface and a Geometry

SFCGAL_API double SFCGAL::algorithm::distanceSegmentSegment	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		const Point &	d
	)		-> double

SFCGAL_API double SFCGAL::algorithm::distanceSegmentSegment3D	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		const Point &	d
	)		-> double

SFCGAL_API double SFCGAL::algorithm::distanceSegmentTriangle3D	(	const Point &	sA_,
		const Point &	sB_,
		const Point &	tA_,
		const Point &	tB_,
		const Point &	tC_
	)		-> double

SFCGAL_API double SFCGAL::algorithm::distanceSolidGeometry3D	(	const Solid &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance between a Solid and a Geometry

SFCGAL_API double SFCGAL::algorithm::distanceSolidSolid3D	(	const Solid &	gA,
		const Solid &	gB
	)		-> double

distance between two Solids

SFCGAL_API double SFCGAL::algorithm::distanceTriangleGeometry	(	const Triangle &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance from a Triangle to a Geometry

SFCGAL_API double SFCGAL::algorithm::distanceTriangleGeometry3D	(	const Triangle &	gA,
		const Geometry &	gB
	)		-> double

dispatch distance between a Triangle and a Geometry

SFCGAL_API double SFCGAL::algorithm::distanceTrianglePolyhedralSurface3D	(	const Triangle &	triangleA,
		const PolyhedralSurface &	polySurfaceB
	)		-> double

distance between a Triangle and a PolyhedralSurface

SFCGAL_API double SFCGAL::algorithm::distanceTriangleSolid3D	(	const Triangle &	gA,
		const Solid &	gB
	)		-> double

distance between a Triangle and a Solid

SFCGAL_API double SFCGAL::algorithm::distanceTriangleTriangle3D	(	const Triangle &	gA,
		const Triangle &	gB
	)		-> double

distance between two Triangles

SFCGAL_API auto SFCGAL::algorithm::distanceTriangulatedSurfaceGeometry3D	(	const TriangulatedSurface &	triangulatedSurfaceA,
		const Geometry &	geomB
	)		-> double

dispatch distance between a TriangulatedSurface and a Geometry

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::extrude	(	const Geometry &	g,
		const Kernel::Vector_3 &	v
	)

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

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.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::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.

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.; 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.

SFCGAL_API auto SFCGAL::algorithm::extrudedStraightSkeleton	(	const Polygon &	geom,
		double	height
	)		-> std::unique_ptr< PolyhedralSurface >

build a 3D straight skeleton extruded for a Polygon

Exceptions

NotImplementedException If geom is a Polygon with point touching rings.

template<typename Kernel >

bool SFCGAL::algorithm::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.

template<int Dim>

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

template<int Dim>

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

Intersection test on GeometrySet.

template<int Dim>

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

Intersection test on a PrimitiveHandle.

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::algorithm::isConnected ( const SurfaceGraph & graph ) -> bool

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

template<typename Kernel >

bool SFCGAL::algorithm::isPlane3D	(	const Geometry &	geom,
		const double &	toleranceAbs
	)

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

SFCGAL_API void SFCGAL::triangulate::opentriangulatePolygon3D	(	const GeometryCollection &	g,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate a 3D MultiPolygon.

Todo:: unittest

template<typename Kernel >

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

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

May return degenerate plane.

template<typename Kernel >

CGAL::Plane_3<Kernel> SFCGAL::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.; result is rounded to double (avoid huge expression tree).

bool SFCGAL::algorithm::selfIntersects ( const LineString & l ) -> bool

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

bool SFCGAL::algorithm::selfIntersects	(	const PolyhedralSurface &	s,
		const SurfaceGraph &	g
	)		-> bool

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

bool SFCGAL::algorithm::selfIntersects	(	const TriangulatedSurface &	tin,
		const SurfaceGraph &	g
	)		-> bool

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

bool SFCGAL::algorithm::selfIntersects3D ( const LineString & l ) -> bool

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

bool SFCGAL::algorithm::selfIntersects3D	(	const PolyhedralSurface &	s,
		const SurfaceGraph &	g
	)		-> bool

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

bool SFCGAL::algorithm::selfIntersects3D	(	const TriangulatedSurface &	tin,
		const SurfaceGraph &	g
	)		-> bool

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

SFCGAL_API Kernel::FT SFCGAL::algorithm::signedArea ( const Triangle & g ) -> Kernel::FT

Compute the 2D signed area for a Triangle.

SFCGAL_API Kernel::FT SFCGAL::algorithm::signedArea ( const LineString & g ) -> Kernel::FT

Compute the 2D signed area for a closed LineString.

SFCGAL_API auto SFCGAL::algorithm::straightSkeleton	(	const Polygon &	geom,
		bool	autoOrientation = `true`,
		bool	innerOnly = `false`,
		bool	outputDistanceInM = `false`,
		const double &	toleranceAbs = `EPSILON`
	)		-> std::unique_ptr< MultiLineString >

build a 2D straight skeleton for a Polygon

Exceptions

NotImplementedException If geom is a Polygon with point touching rings.

SFCGAL_API auto SFCGAL::algorithm::straightSkeleton	(	const MultiPolygon &	geom,
		bool	autoOrientation = `true`,
		bool	innerOnly = `false`,
		bool	outputDistanceInM = `false`,
		const double &	toleranceAbs = `EPSILON`
	)		-> std::unique_ptr< MultiLineString >

build a 2D straight skeleton for a Polygon

Exceptions

NotImplementedException If geom is a Polygon with point touching rings.

SFCGAL_API auto SFCGAL::algorithm::straightSkeletonPartition	(	const MultiPolygon &	geom,
		bool	autoOrientation = `true`
	)		-> std::unique_ptr< PolyhedralSurface >

Build a 2D straight skeleton partition for a MultiPolygon.

Parameters

[in]	geom	The input multi-polygon
[in]	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.

SFCGAL_API auto SFCGAL::algorithm::straightSkeletonPartition	(	const Polygon &	geom,
		bool	autoOrientation = `true`
	)		-> std::unique_ptr< PolyhedralSurface >

Build a 2D straight skeleton partition for a Polygon.

Parameters

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

Returns: A unique pointer to a MultiPolygon representing the partitioned polygon

Exceptions

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.

SFCGAL_API void SFCGAL::triangulate::triangulatePolygon3D	(	const Triangle &	g,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate a 3D Triangle (copy triangle)

Todo:: unittest

SFCGAL_API void SFCGAL::triangulate::triangulatePolygon3D	(	const TriangulatedSurface &	g,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate a 3D TriangulatedSurface (copy triangles)

Todo:: unittest

SFCGAL_API void SFCGAL::triangulate::triangulatePolygon3D	(	const Polygon &	g,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate a 3D Polygon.

Todo:: unittest

SFCGAL_API void SFCGAL::triangulate::triangulatePolygon3D	(	const PolyhedralSurface &	polyhedralSurface,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate 3D polygons in a PolyhedralSurface.

SFCGAL_API void SFCGAL::triangulate::triangulatePolygon3D	(	const Solid &	g,
		TriangulatedSurface &	triangulatedSurface
	)

Triangulate a Solid.

Todo:: unittest

template<int Dim>

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

template<int Dim>

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

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const Geometry &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a Geometry.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const Triangle &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a Triangle.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a Triangle.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const LineString &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a LineString.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const Polygon &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a Polygon.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const GeometryCollection &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a GeometryCollection.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const TriangulatedSurface &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a TriangulatedSurface.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const PolyhedralSurface &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a PolyhedralSurface.

SFCGAL_API WeightedCentroid SFCGAL::algorithm::weightedCentroid	(	const Solid &	g,
		bool	enable3DComputation
	)		-> WeightedCentroid

Returns the weighted centroid for a Solid.

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