SFCGAL::algorithm Namespace Reference

Main algorithm namespace. More...

Classes
class	BoundaryVisitor
	Compute the boundary for a Geometry. More...
class	Buffer3D
	Computes a 3D buffer around a Point or LineString. More...
struct	Circle
class	ConsistentOrientationBuilder
	Make orientation consistent in a triangle set. More...
struct	found_an_intersection
struct	intersects_cb
struct	LoopDetector
struct	NoValidityCheck
	Tag used for variants of algorithm that do not do validity check. More...
struct	Plane3DInexactUnsafe
struct	Sphere
class	SurfaceGraph
	Represents a polyhedral surface as a graph where faces are nodes and egde are graph edges. More...
class	WeightedCentroid
	Holds weighted data to compute the centroid for a Geometry. More...

Typedefs
using	InexactKernel = CGAL::Exact_predicates_inexact_constructions_kernel
using	Inexact_Point_3 = InexactKernel::Point_3
using	Mesh = CGAL::Surface_mesh< Inexact_Point_3 >
using	ExactMesh = CGAL::Surface_mesh< Kernel::Point_3 >
using	EK_to_IK = CGAL::Cartesian_converter< Kernel, InexactKernel >
using	IK_to_EK = CGAL::Cartesian_converter< InexactKernel, Kernel >
using	Straight_skeleton_2 = CGAL::Straight_skeleton_2< Kernel >
using	Arrangement_2 = CGAL::Arrangement_2< CGAL::Arr_segment_traits_2< Kernel >>
template<class T >
using	SHARED_PTR = boost::shared_ptr< T >

Enumerations
enum	PartitionAlgorithm { y_monotone, approx_convex, greene_approx_convex, optimal_convex }
	Partition algorithm available. More...

Functions
auto	optimal_alpha_shapes (const Geometry &g, bool allow_holes=false, size_t nb_components=1) -> std::unique_ptr< Geometry >
	Compute the optimal 2D alpha shapes for a geometry https://doc.cgal.org/latest/Alpha_shapes_2/index.html#Chapter_2D_Alpha_Shapes. More...
auto	alphaShapes (const Geometry &g, double alpha=1, bool allow_holes=false) -> std::unique_ptr< Geometry >
	Compute the 2D alpha shapes for a geometry https://doc.cgal.org/latest/Alpha_shapes_2/index.html#Chapter_2D_Alpha_Shapes. More...
auto	alphaWrapping3D (const Geometry &geom, size_t relativeAlpha, size_t relativeOffset) -> std::unique_ptr< PolyhedralSurface >
	end of private section More...
auto	area (const Geometry &g, NoValidityCheck)
	Compute the 2D area for a Geometry. More...
auto	area (const Geometry &g)
	Compute the 2D area for a Geometry. More...
auto	signedArea (const Triangle &g)
	Compute the 2D signed area for a Triangle. More...
auto	signedArea (const LineString &g)
	Compute the 2D signed area for a closed LineString. More...
auto	area (const Triangle &g)
	Returns Compute the 2D area for a Triangle. More...
auto	area (const Polygon &g)
	Returns Compute the 2D area for a Polygon. More...
auto	area (const GeometryCollection &g)
	Returns the 2D area for a GeometryCollection. More...
auto	area (const TriangulatedSurface &g)
	Returns the 2D area for a TriangulatedSurface. More...
auto	area (const PolyhedralSurface &g)
	Returns the 2D area for a TriangulatedSurface. More...
auto	area3D (const Geometry &g, NoValidityCheck)
	Returns 3D area for a Geometry. More...
auto	area3D (const Geometry &g)
	Returns 3D area for a Geometry. More...
auto	area3D (const Polygon &g)
	Returns 3D area for a Polygon. More...
auto	area3D (const Triangle &g)
	Returns the 3D area for a Triangle. More...
auto	area3D (const GeometryCollection &g)
	Returns the 3D area for a MultiPolygon. More...
auto	area3D (const PolyhedralSurface &g)
	Returns the 3D area for a PolyhedralSurface. More...
auto	area3D (const TriangulatedSurface &g)
	Returns the 3D area for a TriangulatedSurface. More...
auto	centroid (const Geometry &g)
	Returns the 2D centroid for a Geometry. More...
auto	centroid3D (const Geometry &g)
	Returns the 3D centroid for a Geometry. More...
auto	weightedCentroid (const Geometry &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Geometry. More...
auto	weightedCentroid (const Triangle &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Triangle. More...
auto	weightedCentroid (const Point &a, const Point &b, const Point &c, bool enable3DComputation=false)
	Returns the weighted centroid for a Triangle. More...
auto	weightedCentroid (const LineString &g, bool enable3DComputation=false)
	Returns the weighted centroid for a LineString. More...
auto	weightedCentroid (const Polygon &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Polygon. More...
auto	weightedCentroid (const GeometryCollection &g, bool enable3DComputation=false)
	Returns the weighted centroid for a GeometryCollection. More...
auto	weightedCentroid (const TriangulatedSurface &g, bool enable3DComputation=false)
	Returns the weighted centroid for a TriangulatedSurface. More...
auto	weightedCentroid (const PolyhedralSurface &g, bool enable3DComputation=false)
	Returns the weighted centroid for a PolyhedralSurface. More...
auto	weightedCentroid (const Solid &g, bool enable3DComputation=false)
	Returns the weighted centroid for a Solid. More...
auto	collect (const Geometry &ga, const Geometry &gb)
	Returns an aggregate of ga and gb. More...
template<typename GeometryIterator >
std::unique_ptr< Geometry >	collect (GeometryIterator begin, GeometryIterator end)
	Returns an aggregate of a list of geometries. More...
auto	collectionExtractPolygons (std::unique_ptr< Geometry > coll)
	Given a geometry collection returns a MultiPolygon from triangles, polygons, polyhedral and polygons. More...
auto	collectionHomogenize (std::unique_ptr< Geometry > coll)
	Given a geometry collection, returns the "simplest" representation of the contents. More...
auto	collectionToMulti (std::unique_ptr< Geometry > coll)
	Given a geometry collection of triangles, TINs and polygons returns a MultiPolygon. More...
auto	isConnected (const SurfaceGraph &graph)
	test if a surface is connected, the graph should be build beforehand More...
auto	isClosed (const SurfaceGraph &graph)
	test if a surface is closed, the graph should be build beforehand More...
auto	convexHull (const Geometry &g)
	Compute the 2D convex hull for a geometry. More...
auto	convexHull3D (const Geometry &g)
	Compute the 3D convex hull for a geometry. More...
auto	covers (const Geometry &ga, const Geometry &gb)
	Cover test on 2D geometries. More...
auto	covers3D (const Geometry &ga, const Geometry &gb)
	Cover test on 3D geometries. More...
template<int Dim>
bool	covers (const detail::GeometrySet< Dim > &a, const detail::GeometrySet< Dim > &b)
template<int Dim>
bool	covers (const detail::PrimitiveHandle< Dim > &a, const detail::PrimitiveHandle< Dim > &b)
auto	difference (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Diffrence on 2D geometries. More...
auto	difference (const Geometry &ga, const Geometry &gb)
	Difference on 2D geometries. More...
auto	difference3D (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Difference on 3D geometries. More...
auto	difference3D (const Geometry &ga, const Geometry &gb)
	Difference on 3D geometries. More...
auto	distance (const Geometry &gA, const Geometry &gB, NoValidityCheck)
	Compute the distance between two Geometries. More...
auto	distance (const Geometry &gA, const Geometry &gB)
	Compute the distance between two Geometries. More...
auto	distancePointGeometry (const Point &gA, const Geometry &gB)
	dispatch distance from Point to Geometry More...
auto	distancePointPoint (const Point &gA, const Point &gB)
	distance between two Points More...
auto	distancePointLineString (const Point &gA, const LineString &gB)
	distance between a Point and a LineString More...
auto	distancePointPolygon (const Point &gA, const Polygon &gB)
	distance between a Point and a Polygon More...
auto	distancePointTriangle (const Point &gA, const Triangle &gB)
	distance between a Point and a Triangle More...
auto	distanceLineStringGeometry (const LineString &gA, const Geometry &gB)
	dispatch distance from LineString to Geometry More...
auto	distanceLineStringLineString (const LineString &gA, const LineString &gB)
	distance between two LineStrings More...
auto	distanceLineStringPolygon (const LineString &gA, const Polygon &gB)
	distance between a LineString and a Polygon More...
auto	distanceLineStringTriangle (const LineString &gA, const Triangle &gB)
	distance between a LineString and a Triangle More...
auto	distancePolygonGeometry (const Polygon &gA, const Geometry &gB)
	dispatch distance from Polygon to Geometry More...
auto	distancePolygonPolygon (const Polygon &gA, const Polygon &gB)
	distance between two Polygons More...
auto	distancePolygonTriangle (const Polygon &gA, const Triangle &gB)
	distance between a Polygon and a Triangle More...
auto	distanceTriangleGeometry (const Triangle &gA, const Geometry &gB)
	dispatch distance from a Triangle to a Geometry More...
auto	boundingCircle (const Geometry &geom) -> const Circle
auto	distanceGeometryCollectionToGeometry (const Geometry &gA, const Geometry &gB)
	dispatch distance from a collection of geometry (gA) to a Geometry (gB) More...
auto	distancePointSegment (const Point &p, const Point &a, const Point &b)
auto	distanceSegmentSegment (const Point &a, const Point &b, const Point &c, const Point &d)
auto	distance3D (const Geometry &gA, const Geometry &gB, NoValidityCheck)
	Compute distance between two 3D Geometries. More...
auto	distance3D (const Geometry &gA, const Geometry &gB)
	dispatch distance between two Geometries More...
auto	distancePointGeometry3D (const Point &gA, const Geometry &gB)
	dispatch distance from Point to Geometry More...
auto	distancePointPoint3D (const Point &gA, const Point &gB)
	distance between two Points More...
auto	distancePointLineString3D (const Point &gA, const LineString &gB)
	distance between a Point and a LineString More...
auto	distancePointTriangle3D (const Point &gA, const Triangle &gB)
	distance between a Point and a Triangle More...
auto	distancePointPolygon3D (const Point &gA, const Polygon &gB)
	distance between a Point and a Triangle More...
auto	distancePointPolyhedralSurface3D (const Point &pointA, const PolyhedralSurface &polySurfaceB) -> double
	distance between a Point and a PolyhedralSurface More...
auto	distancePointTriangulatedSurface3D (const Point &pointA, const TriangulatedSurface &triangulatedSurfaceB) -> double
	distance between a Point and a TriangulatedSurface More...
auto	distancePointSolid3D (const Point &gA, const Solid &gB)
	distance between a Point and a Solid More...
auto	distanceLineStringGeometry3D (const LineString &gA, const Geometry &gB)
	dispatch distance between a LineString and a Geometry More...
auto	distanceLineStringLineString3D (const LineString &gA, const LineString &gB)
	distance between two LineStrings More...
auto	distanceLineStringTriangle3D (const LineString &gA, const Triangle &gB)
	distance between a LineString and a Triangle More...
auto	distanceLineStringPolygon3D (const LineString &gA, const Polygon &gB)
	distance between a LineString and a Polygon More...
auto	distanceLineStringPolyhedralSurface3D (const LineString &lineA, const PolyhedralSurface &polySurfaceB) -> double
	distance between a LineString and a PolyhedralSurface More...
auto	distanceLineStringTriangulatedSurface3D (const LineString &lineA, const TriangulatedSurface &triangulatedSurfaceB) -> double
	distance between a LineString and a TriangulatedSurface More...
auto	distanceLineStringSolid3D (const LineString &gA, const Solid &gB)
	distance between a LineString and a Solid More...
auto	distanceTriangleGeometry3D (const Triangle &gA, const Geometry &gB)
	dispatch distance between a Triangle and a Geometry More...
auto	distanceTrianglePolyhedralSurface3D (const Triangle &triangleA, const PolyhedralSurface &polySurfaceB)
	distance between a Triangle and a PolyhedralSurface More...
auto	distanceTriangleTriangulatedSurface3D (const Triangle &triangleA, const TriangulatedSurface &triangulatedSurfaceB) -> double
auto	distanceTriangleSolid3D (const Triangle &gA, const Solid &gB)
	distance between a Triangle and a Solid More...
auto	distancePolygonGeometry3D (const Polygon &gA, const Geometry &gB)
	dispatch distance between a Polygon and a Geometry More...
auto	distancePolyhedralSurfaceGeometry3D (const PolyhedralSurface &polySurfaceA, const Geometry &geomB) -> double
	dispatch distance between a PolyhedralSurface and a Geometry More...
auto	distanceTriangulatedSurfaceGeometry3D (const TriangulatedSurface &triangulatedSurfaceA, const Geometry &geomB) -> double
	dispatch distance between a TriangulatedSurface and a Geometry More...
auto	distanceSolidGeometry3D (const Solid &gA, const Geometry &gB)
	dispatch distance between a Solid and a Geometry More...
auto	distanceSolidSolid3D (const Solid &gA, const Solid &gB)
	distance between two Solids More...
auto	boundingSphere (const Geometry &geom) -> const Sphere
auto	distanceGeometryCollectionToGeometry3D (const Geometry &gA, const Geometry &gB)
	dispatch distance from a collection of geometry (gA) to a Geometry (gB) More...
auto	distancePointSegment3D (const Point &p, const Point &a, const Point &b)
auto	squaredDistancePointTriangle3D (const Point_3 &p, const Triangle_3 &abc) -> squared_distance_t
auto	distancePointTriangle3D (const Point &p, const Point &a, const Point &b, const Point &c)
auto	distanceSegmentSegment3D (const Point &a, const Point &b, const Point &c, const Point &d)
auto	squaredDistanceSegmentTriangle3D (const Segment_3 &sAB, const Triangle_3 &tABC) -> squared_distance_t
auto	distanceSegmentTriangle3D (const Point &sA, const Point &sB, const Point &tA, const Point &tB, const Point &tC)
auto	squaredDistanceTriangleTriangle3D (const Triangle_3 &triangleA, const Triangle_3 &triangleB) -> squared_distance_t
auto	distanceTriangleTriangle3D (const Triangle &gA, const Triangle &gB)
	distance between two Triangles More...
auto	extrude (const Geometry &g, const Kernel::Vector_3 &v)
	Returns a Geometry equal to the specified Geometry, extruded by the specified displacement vector. More...
auto	extrude (const Geometry &g, const Kernel::FT &dx, const Kernel::FT &dy, const Kernel::FT &dz, NoValidityCheck) -> std::unique_ptr< Geometry >
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. More...
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. More...
SFCGAL_API auto	extrude (const Polygon &g, const double &height) -> std::unique_ptr< Geometry >
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. More...
void	force2D (Geometry &g)
	force a geometry to be 2D (project on O,x,y) More...
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) More...
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) More...
template<int Dim>
void	intersection (const detail::GeometrySet< Dim > &a, const detail::GeometrySet< Dim > &b, detail::GeometrySet< Dim > &)
auto	intersection (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection on 2D geometries. More...
auto	intersection (const Geometry &ga, const Geometry &gb)
	Intersection on 2D geometries. More...
auto	intersection3D (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection on 3D geometries. More...
auto	intersection3D (const Geometry &ga, const Geometry &gb)
	Intersection on 3D geometries. More...
template<int Dim>
auto	intersects (const PrimitiveHandle< Dim > &pa, const PrimitiveHandle< Dim > &pb) -> bool
	Intersection test on a PrimitiveHandle. More...
template<int Dim>
auto	intersects (const GeometrySet< Dim > &a, const GeometrySet< Dim > &b) -> bool
	Intersection test on GeometrySet. More...
auto	intersects (const Geometry &ga, const Geometry &gb)
	Robust intersection test on 2D geometries. More...
auto	intersects3D (const Geometry &ga, const Geometry &gb)
	Robust intersection test on 3D geometries. More...
auto	intersects (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection test on 2D geometries. More...
auto	intersects3D (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Intersection test on 3D geometries. More...
auto	selfIntersects (const LineString &l)
	Self intersection test for 2D LineString (false if only endpoint touch) More...
auto	selfIntersects3D (const LineString &l)
	Self intersection test for 3D LineString (false if only endpoints touch) More...
auto	selfIntersects (const PolyhedralSurface &s, const SurfaceGraph &g)
	Self intersection test for 2D PolyhedralSurface (false if only point touch) More...
auto	selfIntersects3D (const PolyhedralSurface &s, const SurfaceGraph &g)
	Self intersection test for 3D PolyhedralSurface (false if only point touch) More...
auto	selfIntersects (const TriangulatedSurface &s, const SurfaceGraph &g)
	Self intersection test for 2D TriangulatedSurface (false if only point touch) More...
auto	selfIntersects3D (const TriangulatedSurface &s, const SurfaceGraph &g)
	Self intersection test for 3D TriangulatedSurface (false if only point touch) More...
template<int Dim>
bool	intersects (const detail::GeometrySet< Dim > &a, const detail::GeometrySet< Dim > &b)
	Intersection test on GeometrySet. More...
template<int Dim>
bool	intersects (const detail::PrimitiveHandle< Dim > &a, const detail::PrimitiveHandle< Dim > &b)
	Intersection test on a PrimitiveHandle. More...
auto	isSimple (const Geometry &g, const double &toleranceAbs=1e-9)
	Check simplicity of a geometry. More...
auto	isValid (const Point &p) -> const Validity
auto	isValid (const LineString &l, const double &toleranceAbs) -> const Validity
auto	isValid (const Polygon &p, const double &toleranceAbs) -> const Validity
auto	isValid (const Triangle &t, const double &toleranceAbs) -> const Validity
auto	isValid (const MultiLineString &ml, const double &toleranceAbs) -> const Validity
auto	isValid (const MultiPolygon &mp, const double &toleranceAbs) -> const Validity
auto	isValid (const GeometryCollection &gc, const double &toleranceAbs) -> const Validity
auto	isValid (const TriangulatedSurface &tin, const SurfaceGraph &graph, const double &toleranceAbs) -> const Validity
auto	isValid (const TriangulatedSurface &tin, const double &toleranceAbs) -> const Validity
auto	isValid (const PolyhedralSurface &s, const SurfaceGraph &graph, const double &toleranceAbs) -> const Validity
auto	isValid (const PolyhedralSurface &s, const double &toleranceAbs) -> const Validity
auto	isValid (const Solid &solid, const double &toleranceAbs) -> const Validity
auto	isValid (const MultiSolid &ms, const double &toleranceAbs) -> const Validity
auto	isValid (const Geometry &g, const double &toleranceAbs=1e-9)
	Check validity of a geometry. More...
void	propagateValidityFlag (Geometry &g, bool valid)
	Sets the geometry flag on a geometry and propagate to every internal geometries. More...
auto	length (const LineString &g)
	Compute the 2D length for a LineString. More...
auto	length (const GeometryCollection &g)
	Compute the 2D length for a GeometryCollection. More...
auto	length (const Geometry &g)
	Compute the 2D length for a Geometry (0 for incompatible types) More...
auto	length3D (const LineString &g)
	Compute the 3D length for a LineString. More...
auto	length3D (const GeometryCollection &g)
	Compute the 3D length for a GeometryCollection. More...
auto	length3D (const Geometry &g)
	Compute the 2D length for a geometry. More...
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 specified LineString. More...
auto	minkowskiSum (const Geometry &gA, const Polygon &gB, NoValidityCheck)
	2D minkowski sum (p+q) More...
auto	minkowskiSum (const Geometry &gA, const Polygon &gB)
	2D minkowski sum (p+q) More...
auto	minkowskiSum3D (const Geometry &gA, const Geometry &gB, NoValidityCheck)
	3D Minkowski sum (p+q) More...
auto	minkowskiSum3D (const Geometry &gA, const Geometry &gB)
	3D Minkowski sum (p+q) More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	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. More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	normal3D (const LineString &ls, bool exact=true)
	Returns the 3D normal to a ring (supposed to be planar and closed). More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	normal3D (const Polygon &polygon, bool exact=true)
	Returns the 3D normal to a polygon (supposed to be planar). More...
void	offset (const Geometry &g, const double &radius, Offset_polygon_set_2 &polygonSet)
	dispatch a geometry More...
void	offset (const Point &g, const double &radius, Offset_polygon_set_2 &polygonSet)
	offset for a Point More...
void	offset (const LineString &g, const double &radius, Offset_polygon_set_2 &polygonSet)
	offset for a LineString More...
void	offset (const Polygon &g, const double &radius, Offset_polygon_set_2 &polygonSet)
	offset for a Polygon More...
void	offsetCollection (const Geometry &g, const double &radius, Offset_polygon_set_2 &polygonSet)
	offset for MultiPoint, MultiLineString, MultiPolygon, TriangulatedSurface, PolyhedralSurface More...
auto	approximate (const Offset_polygon_2 &polygon, const int &n=0) -> Polygon_2
	approximate an Offset_polygon_2 (filter null segments) More...
auto	approximate (const Offset_polygon_with_holes_2 &polygon, const int &n=0) -> Polygon_with_holes_2
	approximate an Offset More...
auto	polygonSetToMultiPolygon (const Offset_polygon_set_2 &polygonSet, const int &n) -> std::unique_ptr< MultiPolygon >
	convert Offset_polygon_set_2 to MultiPolygon More...
auto	circleToPolygon (const Kernel::Circle_2 &circle) -> Offset_polygon_2
	helper to create a polygon from a circle More...
auto	offset (const Geometry &g, const double &r, NoValidityCheck)
	[experimental]compute polygon offset More...
auto	offset (const Geometry &g, const double &r)
	[experimental]compute polygon offset More...
void	makeValidOrientation (CGAL::Polygon_2< Kernel > &polygon)
	Make valid 2D orientation. More...
void	makeValidOrientation (CGAL::Polygon_with_holes_2< Kernel > &polygon)
	Make valid 2D orientation. More...
void	makeValidOrientation (Polygon &polygon)
	Make valid 2D orientation. More...
auto	hasConsistentOrientation3D (const TriangulatedSurface &g)
	Test if a Geometry has a consistent orientation. More...
auto	hasConsistentOrientation3D (const PolyhedralSurface &g)
	Test if a PolyhedralSurface has a consistent orientation. More...
void	makeConsistentOrientation3D (TriangulatedSurface &g)
	Try to make consistent orientation in a TriangulatedSurface. More...
auto	isCounterClockWiseOriented (const LineString &)
	Test if a 2D surface is oriented counter clockwise. More...
auto	isCounterClockWiseOriented (const Triangle &)
	Test if a 2D surface is oriented counter clockwise. More...
auto	isCounterClockWiseOriented (const Polygon &)
	Test if a 2D surface is oriented counter clockwise. More...
auto	partition_2 (const Geometry &g, PartitionAlgorithm alg, NoValidityCheck) -> std::unique_ptr< Geometry >
	Compute the partition of a 2D polygon https://doc.cgal.org/latest/Partition_2/index.html#Chapter_2D_Polygon_Partitioning. More...
auto	partition_2 (const Geometry &g, PartitionAlgorithm alg=y_monotone) -> std::unique_ptr< Geometry >
	Compute the partition of a 2D polygon https://doc.cgal.org/latest/Partition_2/index.html#Chapter_2D_Polygon_Partitioning. More...
template<typename Kernel >
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. More...
template<typename Kernel >
bool	hasPlane3D (const Polygon &polygon)
	Test if a 3D plane can be extracted from a Polygon. More...
template<typename Kernel >
void	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. More...
template<typename Kernel >
CGAL::Plane_3< Kernel >	plane3D (const Polygon &polygon)
	Returns the oriented 3D plane of a polygon (supposed to be planar). More...
template<typename Kernel >
CGAL::Plane_3< Kernel >	plane3D (const Polygon &polygon, const Plane3DInexactUnsafe &)
	Returns the oriented 3D plane of a polygon (supposed to be planar) - inexact version. More...
template<typename Kernel >
CGAL::Plane_3< Kernel >	plane3D (const Polygon &polygon, bool exact)
	Returns the oriented 3D plane of a polygon (supposed to be planar). More...
template<typename Kernel >
bool	isPlane3D (const Geometry &geom, const double &toleranceAbs)
	Test if all points of a geometry lie in the same plane. More...
void	rotate (Geometry &g, const Kernel::FT &angle)
	Rotate a geometry in 2D around the origin (0,0) More...
void	rotate (Geometry &g, const Kernel::FT &angle, const Point &origin)
	Rotate a geometry in 2D around a specified point. More...
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. More...
void	rotateX (Geometry &g, const Kernel::FT &angle)
	Rotate a geometry around the X axis. More...
void	rotateY (Geometry &g, const Kernel::FT &angle)
	Rotate a geometry around the Y axis. More...
void	rotateZ (Geometry &g, const Kernel::FT &angle)
	Rotate a geometry around the Z axis. More...
void	scale (Geometry &g, double s)
	Scale a geometry by a given factor. More...
void	scale (Geometry &g, double sx, double sy, double sz=0.0)
	Scale a geometry by different factors for each dimension. More...
void	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. More...
auto	simplify (const Geometry &geometry, double threshold, bool preserveTopology) -> std::unique_ptr< Geometry >
	Main entry point for geometry simplification. More...
auto	simplify (const Geometry &geometry, double threshold, bool preserveTopology, NoValidityCheck) -> std::unique_ptr< Geometry >
	Simplifies a geometry using the CGAL algorithm https://doc.cgal.org/latest/Polyline_simplification_2/index.html. More...
auto	straightSkeleton (const Geometry &geom, bool autoOrientation, NoValidityCheck, bool innerOnly=false, bool outputDistanceInM=false, const double &toleranceAbs=EPSILON) -> std::unique_ptr< MultiLineString >
	build a 2D straight skeleton for a Polygon More...
auto	straightSkeleton (const Geometry &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	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	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...
auto	approximateMedialAxis (const Geometry &geom) -> std::unique_ptr< MultiLineString >
	build an approximate medial axis for a Polygon More...
auto	extrudeStraightSkeleton (const Polygon &geom, double height) -> std::unique_ptr< PolyhedralSurface >
auto	extrudeStraightSkeleton (const Geometry &geom, double height) -> std::unique_ptr< PolyhedralSurface >
auto	extrudeStraightSkeleton (const Geometry &geom, double building_height, double roof_height) -> std::unique_ptr< PolyhedralSurface >
auto	straightSkeletonPartition (const Geometry &geom, bool autoOrientation=true) -> std::unique_ptr< PolyhedralSurface >
	Build a 2D straight skeleton partition for a Geometry. More...
auto	straightSkeletonPartition (const MultiPolygon &geom, bool autoOrientation=true) -> std::unique_ptr< PolyhedralSurface >
	Build a 2D straight skeleton partition for a MultiPolygon. More...
auto	straightSkeletonPartition (const Polygon &geom, bool autoOrientation=true) -> std::unique_ptr< PolyhedralSurface >
	Build a 2D straight skeleton partition for a Polygon. More...
SFCGAL_API auto	extrudedStraightSkeleton (const Polygon &geom, double height) -> std::unique_ptr< PolyhedralSurface >
	build a 3D straight skeleton extruded for a Polygon More...
auto	tesselate (const Geometry &, NoValidityCheck)
	Tesselate a geometry: this will triangulate surfaces (including polyhedral and solid's surfaces) and keep untouched points, lines, etc. More...
auto	tesselate (const Geometry &)
	Tesselate a geometry: this will triangulate surfaces (including polyhedral and solid's surfaces) and keep untouched points, lines, etc. More...
void	translate (Geometry &g, const Kernel::Vector_3 &v)
	translate a geometry from a given vector More...
void	translate (Geometry &g, const Kernel::Vector_2 &v)
	translate a geometry from a given vector More...
void	translate (Geometry &g, const Kernel::FT &dx, const Kernel::FT &dy, const Kernel::FT &dz)
	translate a geometry from a given vector More...
void	translate (Geometry &g, const double &dx, const double &dy, const double &dz)
	translate a geometry from double-coordinates More...
auto	union3D (const Geometry &ga, const Geometry &gb, NoValidityCheck)
	Union on 3D geometries. More...
auto	union3D (const Geometry &ga, const Geometry &gb)
	Union on 3D geometries. More...
template<int Dim>
void	union_ (const detail::GeometrySet< Dim > &a, const detail::GeometrySet< Dim > &b, detail::GeometrySet< Dim > &)
template<int Dim>
void	union_ (const detail::PrimitiveHandle< Dim > &a, const detail::PrimitiveHandle< Dim > &b, detail::GeometrySet< Dim > &)
auto	visibility (const Geometry &polygon, const Geometry &point) -> std::unique_ptr< Polygon >
	build the visibility polygon of a Point inside a Polygon More...
auto	visibility (const Geometry &polygon, const Geometry &point, NoValidityCheck) -> std::unique_ptr< Polygon >
	build the visibility polygon of a Point inside a Polygon More...
auto	visibility (const Geometry &polygon, const Geometry &pointA, const Geometry &pointB) -> std::unique_ptr< Polygon >
	build the visibility polygon of the segment [pointA ; pointB] on a Polygon More...
auto	visibility (const Geometry &polygon, const Geometry &pointA, const Geometry &pointB, NoValidityCheck) -> std::unique_ptr< Polygon >
	build the visibility polygon of a Point inside a Polygon More...
auto	volume (const Solid &g, NoValidityCheck)
	Computes the volume of a Solid. More...
auto	volume (const Geometry &g)
	Computes the volume of a geometry. More...

Variables
template<typename T >
std::function< WeightedCentroid(const T &, bool)>	weightedCentroidLambda
using	Vb = CGAL::Alpha_shape_vertex_base_2< Kernel >
using	Fb = CGAL::Alpha_shape_face_base_2< Kernel >
using	Tds = CGAL::Triangulation_data_structure_2< Vb, Fb >
using	Triangulation_2 = CGAL::Delaunay_triangulation_2< Kernel, Tds >
using	Alpha_shape_2 = CGAL::Alpha_shape_2< Triangulation_2 >
using	Alpha_shape_edges_iterator = Alpha_shape_2::Alpha_shape_edges_iterator
using	Traits_2 = CGAL::Arr_non_caching_segment_basic_traits_2< Kernel >
using	Arrangement = CGAL::Arrangement_2< Traits_2 >
typedef detail::NoVolume	NoVolume
typedef detail::MarkedPolyhedron	MarkedPolyhedron
typedef CGAL::Box_intersection_d::Box_with_handle_d< double, 3, MarkedPolyhedron::Halfedge_around_facet_const_circulator >	FaceBboxBase
auto	intersection (const CGAL::Triangle_3< Kernel > &a, const CGAL::Triangle_3< Kernel > &b) -> CGAL::Object
using	Polyline_3 = std::vector< Kernel::Point_3 >
using	Nef_polyhedron_3 = CGAL::Nef_polyhedron_3< Kernel >
using	Traits = CGAL::Partition_traits_2< Kernel >
using	TPoint_2 = Traits::Point_2
using	TPolygon_2 = Traits::Polygon_2
using	Face_handle = Arrangement_2::Face_handle
using	Face_const_handle = Arrangement_2::Face_const_handle
using	Halfedge_const_handle = Arrangement_2::Halfedge_const_handle
using	TEV = CGAL::Triangular_expansion_visibility_2< Arrangement_2, CGAL::Tag_true >

Detailed Description

Main algorithm namespace.

Typedef Documentation

using SFCGAL::algorithm::Alpha_shape_2 = typedef CGAL::Alpha_shape_2<Triangulation_2>

using SFCGAL::algorithm::Alpha_shape_edges_iterator = typedef Alpha_shape_2::Alpha_shape_edges_iterator

using SFCGAL::algorithm::Arrangement = typedef CGAL::Arrangement_2<Traits_2>

typedef CGAL::Arrangement_2< Traits_2 > SFCGAL::algorithm::Arrangement_2

using SFCGAL::algorithm::EK_to_IK = typedef CGAL::Cartesian_converter<Kernel, InexactKernel>

using SFCGAL::algorithm::ExactMesh = typedef CGAL::Surface_mesh<Kernel::Point_3>

using SFCGAL::algorithm::Face_const_handle = typedef Arrangement_2::Face_const_handle

using SFCGAL::algorithm::Face_handle = typedef Arrangement_2::Face_handle

typedef CGAL::Box_intersection_d::Box_with_handle_d< double, 3, MarkedPolyhedron::Halfedge_around_facet_const_circulator> SFCGAL::algorithm::FaceBboxBase

using SFCGAL::algorithm::Fb = typedef CGAL::Alpha_shape_face_base_2<Kernel>

using SFCGAL::algorithm::Halfedge_const_handle = typedef Arrangement_2::Halfedge_const_handle

using SFCGAL::algorithm::IK_to_EK = typedef CGAL::Cartesian_converter<InexactKernel, Kernel>

using SFCGAL::algorithm::Inexact_Point_3 = typedef InexactKernel::Point_3

using SFCGAL::algorithm::InexactKernel = typedef CGAL::Exact_predicates_inexact_constructions_kernel

typedef detail::MarkedPolyhedron SFCGAL::algorithm::MarkedPolyhedron

using SFCGAL::algorithm::Mesh = typedef CGAL::Surface_mesh<Inexact_Point_3>

using SFCGAL::algorithm::Nef_polyhedron_3 = typedef CGAL::Nef_polyhedron_3<Kernel>

typedef detail::NoVolume SFCGAL::algorithm::NoVolume

using SFCGAL::algorithm::Polyline_3 = typedef std::vector<Kernel::Point_3>

template<class T >

using SFCGAL::algorithm::SHARED_PTR = typedef boost::shared_ptr<T>

using SFCGAL::algorithm::Straight_skeleton_2 = typedef CGAL::Straight_skeleton_2<Kernel>

using SFCGAL::algorithm::Tds = typedef CGAL::Triangulation_data_structure_2<Vb, Fb>

using SFCGAL::algorithm::TEV = typedef CGAL::Triangular_expansion_visibility_2<Arrangement_2, CGAL::Tag_true>

using SFCGAL::algorithm::TPoint_2 = typedef Traits::Point_2

using SFCGAL::algorithm::TPolygon_2 = typedef Traits::Polygon_2

using SFCGAL::algorithm::Traits = typedef CGAL::Partition_traits_2<Kernel>

typedef CGAL::Arr_segment_traits_2< Kernel > SFCGAL::algorithm::Traits_2

using SFCGAL::algorithm::Triangulation_2 = typedef CGAL::Delaunay_triangulation_2<Kernel, Tds>

using SFCGAL::algorithm::Vb = typedef CGAL::Alpha_shape_vertex_base_2<Kernel>

Enumeration Type Documentation

enum SFCGAL::algorithm::PartitionAlgorithm

Partition algorithm available.

Since

1.4.2

Enumerator
y_monotone	Y Monotone Partition: https://doc.cgal.org/latest/Partition_2/index.html#secpartition_2_monotone
approx_convex	Simple approximation algorithm of Hertel and Mehlhorn https://doc.cgal.org/latest/Partition_2/index.html#secpartition_2_convex
greene_approx_convex	Sweep-line approximation algorithm of Greene https://doc.cgal.org/latest/Partition_2/index.html#secpartition_2_convex
optimal_convex	Optimal convex partition https://doc.cgal.org/latest/Partition_2/index.html#secpartition_2_convex

Function Documentation

SFCGAL_API auto SFCGAL::algorithm::alphaShapes	(	const Geometry &	g,
		double	alpha = 1,
		bool	allow_holes = false
	)		-> std::unique_ptr< Geometry >

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

SFCGAL_API std::unique_ptr< PolyhedralSurface > SFCGAL::algorithm::alphaWrapping3D	(	const Geometry &	geom,
		size_t	relativeAlpha,
		size_t	relativeOffset = 0
	)

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

auto SFCGAL::algorithm::approximate	(	const Offset_polygon_2 &	polygon,
		const int &	n = 0
	)		-> Polygon_2

approximate an Offset_polygon_2 (filter null segments)

auto SFCGAL::algorithm::approximate	(	const Offset_polygon_with_holes_2 &	polygon,
		const int &	n = 0
	)		-> Polygon_with_holes_2

approximate an Offset

SFCGAL_API auto SFCGAL::algorithm::approximateMedialAxis

(

const Geometry &

geom

)

-> std::unique_ptr< MultiLineString >

build an approximate medial axis for a Polygon

Parameters

geom	input geometry

Precondition

geom is a valid geometry

Exceptions

NotImplementedException

If geom is a Polygon with point touching rings.

SFCGAL_API double SFCGAL::algorithm::area	(	const Geometry &	g,
		NoValidityCheck
	)

Compute the 2D area for a Geometry.

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

SFCGAL_API double SFCGAL::algorithm::area

(

const Geometry &

g

)

Compute the 2D area for a Geometry.

Warning

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

Precondition

g is a valid geometry

SFCGAL_API double SFCGAL::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

auto SFCGAL::algorithm::boundingCircle

(

const Geometry &

geom

)

-> const Circle

auto SFCGAL::algorithm::boundingSphere

(

const Geometry &

geom

)

-> const Sphere

SFCGAL_API std::unique_ptr< Point > SFCGAL::algorithm::centroid

(

const Geometry &

g

)

Returns the 2D centroid for a Geometry.

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

SFCGAL_API std::unique_ptr< Point > SFCGAL::algorithm::centroid3D

(

const Geometry &

g

)

Returns the 3D centroid for a Geometry.

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

auto SFCGAL::algorithm::circleToPolygon

(

const Kernel::Circle_2 &

circle

)

-> Offset_polygon_2

helper to create a polygon from a circle

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::collect	(	const Geometry &	ga,
		const Geometry &	gb
	)		-> std::unique_ptr< Geometry >

Returns an aggregate of ga and gb.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

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

(

const Geometry &

g

)

-> std::unique_ptr< Geometry >

Compute the 2D convex hull for a geometry.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::convexHull3D

(

const Geometry &

g

)

Compute the 3D convex hull for a geometry.

Todo:

improve to handle collinear points and coplanar points

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::algorithm::covers3D	(	const Geometry &	ga,
		const Geometry &	gb
	)

Cover test on 3D geometries.

Checks if gA covers gB. Assume z = 0 if needed

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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::difference	(	const Geometry &	ga,
		const Geometry &	gb
	)

Difference on 2D geometries.

Precondition

ga and gb are valid geometries

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::difference3D	(	const Geometry &	ga,
		const Geometry &	gb
	)

Difference on 3D geometries.

Assume z = 0 if needed

Precondition

ga and gb are valid geometries

SFCGAL_API double SFCGAL::algorithm::distance	(	const Geometry &	gA,
		const Geometry &	gB,
		NoValidityCheck
	)

Compute the distance between two Geometries.

Precondition

gA is a valid geometry

gB is a valid geometry

Warning

No actual validity check is done

SFCGAL_API double SFCGAL::algorithm::distance	(	const Geometry &	gA,
		const Geometry &	gB
	)

Compute the distance between two Geometries.

Precondition

gA is a valid geometry

gB is a valid geometry

SFCGAL_API double SFCGAL::algorithm::distance3D	(	const Geometry &	gA,
		const Geometry &	gB,
		NoValidityCheck
	)

Compute distance between two 3D Geometries.

Precondition

gA is a valid geometry

gB is a valid geometry

Warning

No actual validity check is done

SFCGAL_API double SFCGAL::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

gB is a valid geometry

auto SFCGAL::algorithm::distanceTriangleTriangulatedSurface3D	(	const Triangle &	triangleA,
		const TriangulatedSurface &	triangulatedSurfaceB
	)		-> double

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

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.

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.

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

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

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.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::extrude	(	const Polygon &	g,
		const double &	height
	)		-> std::unique_ptr< Geometry >

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

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

SFCGAL_API auto SFCGAL::algorithm::extrudeStraightSkeleton	(	const Geometry &	geom,
		double	building_height,
		double	roof_height
	)		-> std::unique_ptr< PolyhedralSurface >

SFCGAL_API void SFCGAL::algorithm::force2D

(

Geometry &

g

)

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

Warning

ignore empty geometries

SFCGAL_API void SFCGAL::algorithm::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)

Warning

ignore empty geometries

SFCGAL_API void SFCGAL::algorithm::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)

Warning

ignore empty geometries

SFCGAL_API bool SFCGAL::algorithm::hasConsistentOrientation3D

(

const TriangulatedSurface &

g

)

-> bool

Test if a Geometry has a consistent orientation.

SFCGAL_API bool SFCGAL::algorithm::hasConsistentOrientation3D

(

const PolyhedralSurface &

g

)

-> bool

Test if a PolyhedralSurface has a consistent orientation.

template<typename Kernel >

bool SFCGAL::algorithm::hasPlane3D

(

const Polygon &

polygon

)

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

CGAL::Object SFCGAL::algorithm::intersection	(	const CGAL::Triangle_3< Kernel > &	a,
		const CGAL::Triangle_3< Kernel > &	b
	)		-> CGAL::Object

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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::intersection	(	const Geometry &	ga,
		const Geometry &	gb
	)

Intersection on 2D geometries.

Precondition

ga and gb are valid geometries

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::intersection3D	(	const Geometry &	ga,
		const Geometry &	gb
	)

Intersection on 3D geometries.

Assume z = 0 if needed

Precondition

ga and gb are valid geometries

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::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

SFCGAL_API bool SFCGAL::algorithm::isCounterClockWiseOriented

(

const LineString &

ls

)

-> bool

Test if a 2D surface is oriented counter clockwise.

SFCGAL_API bool SFCGAL::algorithm::isCounterClockWiseOriented

(

const Triangle &

tri

)

-> bool

Test if a 2D surface is oriented counter clockwise.

SFCGAL_API bool SFCGAL::algorithm::isCounterClockWiseOriented

(

const Polygon &

poly

)

-> bool

Test if a 2D surface is oriented counter clockwise.

SFCGAL_API const Simplicity SFCGAL::algorithm::isSimple	(	const Geometry &	g,
		const double &	toleranceAbs
	)		-> const Simplicity

Check simplicity of a geometry.

auto SFCGAL::algorithm::isValid

(

const Point &

p

)

-> const Validity

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

auto SFCGAL::algorithm::isValid	(	const LineString &	l,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const Polygon &	p,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const Triangle &	t,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const MultiLineString &	ml,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const MultiPolygon &	mp,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const GeometryCollection &	gc,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const TriangulatedSurface &	tin,
		const SurfaceGraph &	graph,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const TriangulatedSurface &	tin,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const PolyhedralSurface &	s,
		const SurfaceGraph &	graph,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const PolyhedralSurface &	s,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const Solid &	solid,
		const double &	toleranceAbs
	)		-> const Validity

auto SFCGAL::algorithm::isValid	(	const MultiSolid &	ms,
		const double &	toleranceAbs
	)		-> const Validity

SFCGAL_API const Validity SFCGAL::algorithm::isValid	(	const Geometry &	g,
		const double &	toleranceAbs
	)		-> const Validity

Check validity of a geometry.

SFCGAL_API double SFCGAL::algorithm::length

(

const LineString &

g

)

-> double

Compute the 2D length for a LineString.

SFCGAL_API double SFCGAL::algorithm::length

(

const GeometryCollection &

g

)

-> double

Compute the 2D length for a GeometryCollection.

SFCGAL_API double SFCGAL::algorithm::length

(

const Geometry &

g

)

-> double

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

SFCGAL_API double SFCGAL::algorithm::length3D

(

const LineString &

g

)

-> double

Compute the 3D length for a LineString.

SFCGAL_API double SFCGAL::algorithm::length3D

(

const GeometryCollection &

g

)

-> double

Compute the 3D length for a GeometryCollection.

SFCGAL_API double SFCGAL::algorithm::length3D

(

const Geometry &

g

)

Compute the 2D length for a geometry.

Returns

the length of the Geometry, 0 for incompatible types

SFCGAL_API std::unique_ptr< LineString > SFCGAL::algorithm::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 specified LineString.

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

start 

and/or

end 

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

ls 

.

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

ls 

. For closed lines the a negative range corresponds to the complentary section of

ls 

with an orientation equal to that of it.

Returns

The specified line substring.

Exceptions

If	either start or end have an absolute value greater than 1.

SFCGAL_API void SFCGAL::algorithm::makeConsistentOrientation3D

(

TriangulatedSurface &

g

)

Try to make consistent orientation in a TriangulatedSurface.

SFCGAL_API void SFCGAL::algorithm::makeValidOrientation

(

CGAL::Polygon_2< Kernel > &

polygon

)

Make valid 2D orientation.

SFCGAL_API void SFCGAL::algorithm::makeValidOrientation

(

CGAL::Polygon_with_holes_2< Kernel > &

polygon

)

Make valid 2D orientation.

SFCGAL_API void SFCGAL::algorithm::makeValidOrientation

(

Polygon &

polygon

)

Make valid 2D orientation.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::minkowskiSum	(	const Geometry &	gA,
		const Polygon &	gB,
		NoValidityCheck
	)

2D minkowski sum (p+q)

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.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::minkowskiSum	(	const Geometry &	gA,
		const Polygon &	gB
	)

2D minkowski sum (p+q)

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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::minkowskiSum3D	(	const Geometry &	gA,
		const Geometry &	gB,
		NoValidityCheck
	)

3D Minkowski sum (p+q)

Precondition

gA and gB are valid 3D geometries

Warning

No actual validity check is done.

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::minkowskiSum3D	(	const Geometry &	gA,
		const Geometry &	gB
	)

3D Minkowski sum (p+q)

Precondition

gA and gB are valid 3D geometries

template<typename Kernel >

CGAL::Vector_3<Kernel> SFCGAL::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.

template<typename Kernel >

CGAL::Vector_3<Kernel> SFCGAL::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

template<typename Kernel >

CGAL::Vector_3<Kernel> SFCGAL::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

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

dispatch a geometry

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

offset for a Point

build Point offset

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

offset for a LineString

build LineString offset

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

offset for a Polygon

SFCGAL_API std::unique_ptr< MultiPolygon > SFCGAL::algorithm::offset	(	const Geometry &	g,
		const double &	r,
		NoValidityCheck
	)

[experimental]compute polygon offset

Warning

test in order to compare with minkowski sum

Precondition

g is a valid Geometry

Warning

No actual validity check is done.

SFCGAL_API std::unique_ptr< MultiPolygon > SFCGAL::algorithm::offset	(	const Geometry &	g,
		const double &	r
	)

[experimental]compute polygon offset

Warning

test in order to compare with minkowski sum

Precondition

g is a valid Geometry

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

offset for MultiPoint, MultiLineString, MultiPolygon, TriangulatedSurface, PolyhedralSurface

SFCGAL_API auto SFCGAL::algorithm::optimal_alpha_shapes	(	const Geometry &	g,
		bool	allow_holes = false,
		size_t	nb_components = 1
	)		-> std::unique_ptr< Geometry >

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

SFCGAL_API auto SFCGAL::algorithm::partition_2	(	const Geometry &	g,
		PartitionAlgorithm	alg,
		NoValidityCheck
	)		-> std::unique_ptr< Geometry >

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

SFCGAL_API auto SFCGAL::algorithm::partition_2	(	const Geometry &	g,
		PartitionAlgorithm	alg = y_monotone
	)		-> std::unique_ptr< Geometry >

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

Since

1.4.2

template<typename Kernel >

void SFCGAL::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.

template<typename Kernel >

CGAL::Plane_3<Kernel> SFCGAL::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).

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

auto SFCGAL::algorithm::polygonSetToMultiPolygon	(	const Offset_polygon_set_2 &	polygonSet,
		const int &	n
	)		-> std::unique_ptr<MultiPolygon>

convert Offset_polygon_set_2 to MultiPolygon

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

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

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

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

Parameters

g	The geometry to rotate
angle	Rotation angle in radians

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

Rotate a geometry in 2D around a specified point.

Parameters

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

SFCGAL_API void SFCGAL::algorithm::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.

Parameters

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

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

Rotate a geometry around the X axis.

Parameters

g	The geometry to rotate
angle	Rotation angle in radians

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

Rotate a geometry around the Y axis.

Parameters

g	The geometry to rotate
angle	Rotation angle in radians

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

Rotate a geometry around the Z axis.

Parameters

g	The geometry to rotate
angle	Rotation angle in radians

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

Scale a geometry by a given factor.

Parameters

g	input geometry
s	scale factor

SFCGAL_API void SFCGAL::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

SFCGAL_API void SFCGAL::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

SFCGAL_API auto SFCGAL::algorithm::simplify	(	const Geometry &	geometry,
		double	threshold,
		bool	preserveTopology
	)		-> std::unique_ptr< Geometry >

Main entry point for geometry simplification.

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

SFCGAL_API auto SFCGAL::algorithm::simplify	(	const Geometry &	geometry,
		double	threshold,
		bool	preserveTopology,
		NoValidityCheck
	)		-> std::unique_ptr< Geometry >

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

Warning

No actual validity check is done

auto SFCGAL::algorithm::squaredDistancePointTriangle3D	(	const Point_3 &	p,
		const Triangle_3 &	abc
	)		-> squared_distance_t

auto SFCGAL::algorithm::squaredDistanceSegmentTriangle3D	(	const Segment_3 &	sAB,
		const Triangle_3 &	tABC
	)		-> squared_distance_t

auto SFCGAL::algorithm::squaredDistanceTriangleTriangle3D	(	const Triangle_3 &	triangleA,
		const Triangle_3 &	triangleB
	)		-> squared_distance_t

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

build a 2D straight skeleton for a Polygon

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

Exceptions

NotImplementedException

If geom is a Polygon with point touching rings.

SFCGAL_API auto SFCGAL::algorithm::straightSkeleton	(	const Geometry &	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

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

Exceptions

NotImplementedException

If geom is a Polygon with point touching rings.

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

Build a 2D straight skeleton partition for a Geometry.

Parameters

[in]	geom	The input geometry
[in]	autoOrientation	Check and fix polygon orientation

Returns

A unique pointer to a MultiPolygon representing the partitioned geometry

Exceptions

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.

SFCGAL_API std::unique_ptr< SFCGAL::Geometry > SFCGAL::algorithm::tesselate	(	const Geometry &	,
		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.

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

(

const Geometry &

)

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

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

translate a geometry from a given vector

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

translate a geometry from a given vector

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

translate a geometry from a given vector

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

translate a geometry from double-coordinates

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::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

SFCGAL_API std::unique_ptr< Geometry > SFCGAL::algorithm::union3D	(	const Geometry &	ga,
		const Geometry &	gb
	)

Union on 3D geometries.

Assume z = 0 if needed

Precondition

ga and gb are valid geometries

SFCGAL_API auto SFCGAL::algorithm::visibility	(	const Geometry &	polygon,
		const Geometry &	point
	)		-> std::unique_ptr< Polygon >

build the visibility polygon of a Point inside a Polygon

Parameters

polygon	input geometry
point	input geometry

Precondition

polygon is a valid geometry

point must be inside polygon or on the boundary

SFCGAL_API auto SFCGAL::algorithm::visibility	(	const Geometry &	polygon,
		const Geometry &	point,
		NoValidityCheck
	)		-> std::unique_ptr< Polygon >

build the visibility polygon of a Point inside a Polygon

Parameters

polygon	input geometry
point	input geometry

Precondition

polygon is a valid geometry

point must be inside polygon or on the boundary

Warning

No actual validity check is done

SFCGAL_API auto SFCGAL::algorithm::visibility	(	const Geometry &	polygon,
		const Geometry &	pointA,
		const Geometry &	pointB
	)		-> std::unique_ptr< Polygon >

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

Parameters

polygon	input geometry
pointA	input geometry
pointB	input geometry

Precondition

polygon is a valid geometry

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

SFCGAL_API auto SFCGAL::algorithm::visibility	(	const Geometry &	polygon,
		const Geometry &	pointA,
		const Geometry &	pointB,
		NoValidityCheck
	)		-> std::unique_ptr< Polygon >

build the visibility polygon of a Point inside a Polygon

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

SFCGAL_API const Kernel::FT SFCGAL::algorithm::volume	(	const Solid &	g,
		NoValidityCheck
	)

Computes the volume of a Solid.

Precondition

(not checked) volume is closed and consistently oriented

SFCGAL_API const Kernel::FT SFCGAL::algorithm::volume

(

const Geometry &

g

)

Computes the volume of a geometry.

Precondition

g is a valid Geometry

Variable Documentation

template<typename T >

std::function<WeightedCentroid(const T &, bool)> SFCGAL::algorithm::weightedCentroidLambda

Initial value:

=
    [](const T &g, bool enable3DComputation) -> WeightedCentroid {
  SFCGAL::Kernel::FT totalArea = 0.0;
  SFCGAL::Kernel::FT totalM    = 0.0;
  Vector_3           totalWeightedCentroid;

  for (typename T::const_iterator ite = g.begin(); ite != g.end(); ite++) {
    
    WeightedCentroid wc = weightedCentroid(*ite, enable3DComputation);

    
    if (ite == g.begin())
      totalWeightedCentroid = wc.area * wc.centroid;
    else
      totalWeightedCentroid += wc.area * wc.centroid;
    totalM += wc.area * wc.m;
    totalArea += wc.area;
  }

  totalWeightedCentroid /= totalArea;
  totalM /= totalArea;

  return {totalArea, totalWeightedCentroid, totalM};
}