namespace geometry

Geometry namespace hides geometry specific implementation details from the rest of the library.

Summary

Members	Descriptions
classDiscreteFrechet
classRDPSimplifier
classTriangleMesh
public template<int I> inline float get(constpoint_type& p)	Gets the ith component from a point.
public template<int I> inline float get(constplanar_point& p)	Gets the ith component from a 2D point.
public inline float getx(constpoint_type& p)	Gets point x coordinate.
public inline float gety(constpoint_type& p)	gets pòint y coordinate
public inline float getz(constpoint_type& p)	Gets point z coordinate.
public inline float get(constpoint_type& p,int coord)	Gets the ith component from a point.
public template<int I> planar_pointplanar_projection(constpoint_type& p)	Removes the ith component from P.
publicplanar_pointplanar_projection(constpoint_type& p,int i)	Dynamic planar projection.
public float distance(constpoint_type& a,constpoint_type& b)	Euclidean distance between a and b.
publicpoint_typevectorFromTo(constpoint_type& from,constpoint_type& to)	Vector with origin in from and end in to.
public void traslate(point_type& p,constpoint_type& v)	Adds v to p.
public void scale(point_type& p,float scale,constpoint_type& ref)	Modifies the point p scaling it by scale wrt ref so its norm is multiplied by scale.
public void scale(point_type& p,float rx,float ry,float rz)	Modifies the point p scaling it by (rx,ry,rz)
public void scale(point_type& p,float scale)	Modifies p multiplying its norm by scale.
publicpoint_typecross_product(constpoint_type& p,constpoint_type& q)	Computes the 3D cross product p ^ q.
public float norm(constpoint_type& p)	Returns de 2-norm of p as vector.
public inline bool equal(constpoint_type& a,constpoint_type& b)	Checks whether two point a and b are equal.
public inline bool equal(constplanar_point& a,constplanar_point& b)	Checks whether two point a and b are equal.
public std::array<point_type, 3 > get_basis(constpoint_type& vx,constpoint_type& up)	Retunrs a orthonormal right-oriented basis where vx is the first vector.
public float segment_segment_distance(constpoint_type& p0,constpoint_type& p1,constpoint_type& q0,constpoint_type& q1)	Computes the distance between two line-segments p and q.
public Eigen::Quaternionf align_vectors(constpoint_type& v,constpoint_type& u,constpoint_typeup)	Returns the quaternion to transform v into u (both unitary)
public bool segment_box_intersection(constbox_type& b,constsegment_type& s,point_type& inter)	Computes the box-segment intersection of b and s.
public template<typename G1,typename G2> inline bool covered_by(const G1 & g1,const G2 & g2)	Checks if first geometry is covered by the second.
public template<int I,typename Point> inline bool segment_cross_plane(constsegment_type& s,const Point & v,Point & inter)	Segment-axis plane intersection.
public template<int I,typename Point> inline void min_component(const Point & p,Point & res)	Set the ith component in res to the minimim betweeen the ith components in p and res.
public template<int I,typename Point> inline void max_component(const Point & p,Point & res)	Set the ith component in res to the maximum betweeen the ith components in p and res.
public template<typename Point> inline void max_by_component(const Point & p,Point & res)	Computes the component-wise maximum between p and res and stores it in res.
public template<typename Point> inline void min_by_component(const Point & p,Point & res)	Computes the component-wise minimum between p and res and stores it in res.
public template<Axisaxis> float axisLength(constbox_type& b)	Return box axis length.
public template<Axisaxis> void setAxis(box_type& b,float v)	Set box axis to given value.
publicpolygon_typeas_planar_polygon(const std::vector<point_type> & v)
public template<typename G> inline std::size_t num_points(const G & geom)	Number of points in the geometry.
public float polygon_area(constpolygon_type& p)	Computes the pclosed polygon area.
public template<typename Iter> inline float polygon_area(const Iter & begin,const Iter & end)	Computes the closed polygon area.
public void negate(point_type& p)	Multiplies every component by -1.
publicpoint_typebarycenter(const std::vector<point_type> & v)	Computes the barycenter of a pointset.
public void normalize(point_type& p)	Modifies p so its norm is equal to 1.
public float vector_vector_angle(constpoint_type& a,constpoint_type& b)	Computes the planar vector-vector shortest angle.
public bool box_box_intersection(constbox_type& a,constbox_type& b)	Checks if box a intersects with box b (axis aligned)
public std::vector<point_type> box_corners(constbox_type& b)	Returns 8 corner points in a axis-aligned box.
public float lineseg_dist(const std::vector<point_type> & u,const std::vector<point_type> & v)	Euclidean distance between two line-segments.
publicbox_typebounding_box(const std::vector<point_type> & v)	Computes the bounding box of a node set.
public float vector_vector_directed_angle(constpoint_type& a,constpoint_type& b,constpoint_typeup)	Computes the planar angle from a to b.
public std::pair< float, float > local_orientation(constpoint_type& p,const std::array<point_type, 3 > & basis)	Computes the local orientation (Azimuth and elevation) of p wrt basis.
public bool in_triangle_border(consttriangle_type& t,constpoint_type& p)	Verifies if p is in the border of the triangle t.
public bool is_triangle_vertex(consttriangle_type& t,constpoint_type& p)	Verifies if P is one of the vertices of T.
public bool within_triangle(consttriangle_type& t,constpoint_type& p)	Verifies if p is inside the triangle t.
public bool triangle_ray_intersection(consttriangle_type& t,constpoint_type& ray_o,constpoint_type& ray_v,point_type& intersection)	Computes Triangle-ray intersection with the moller-trumbore algorithm.
public float tetrahedron_volume(constpoint_type& p0,constpoint_type& p1,constpoint_type& p2,constpoint_type& p3)	Returns the volume of the tetrahedron.
public float triangle_area(consttriangle_type& t)	Compute the triangle area.

Members

public template<int I>
inline float get(constpoint_type& p)

Gets the ith component from a point.

Parameters

• p Point

Returns

Ith component (float)

---

public template<int I>
inline float get(constplanar_point& p)

Gets the ith component from a 2D point.

Parameters

• p 2D Point

Returns

I-th component (float)

---

public inline float getx(constpoint_type& p)

Gets point x coordinate.

Parameters

• p

Returns

---

public inline float gety(constpoint_type& p)

gets pòint y coordinate

Parameters

• p

Returns

---

public inline float getz(constpoint_type& p)

Gets point z coordinate.

Parameters

• p

Returns

---

public inline float get(constpoint_type& p,int coord)

Gets the ith component from a point.

Parameters

• p Point

• coord coordinate

Returns

Ith component (float)

---

public template<int I>
planar_pointplanar_projection(constpoint_type& p)

Removes the ith component from P.

Parameters

• p Point to project

Returns

projected point

---

publicplanar_pointplanar_projection(constpoint_type& p,int i)

Dynamic planar projection.

Parameters

• p Point to project

Returns

projected point

---

public float distance(constpoint_type& a,constpoint_type& b)

Euclidean distance between a and b.

Parameters

• a First point

• b Second point

Returns

Eculidean distance (Float)

---

publicpoint_typevectorFromTo(constpoint_type& from,constpoint_type& to)

Vector with origin in from and end in to.

Parameters

• from Vector origin

• to Vector end

Returns

Vector (point type)

---

public void traslate(point_type& p,constpoint_type& v)

Adds v to p.

Parameters

• p point to be modified

• v traslation vector

---

public void scale(point_type& p,float scale,constpoint_type& ref)

Modifies the point p scaling it by scale wrt ref so its norm is multiplied by scale.

Parameters

• p Point to be modified

• scale Scale

• ref Referecne point

---

public void scale(point_type& p,float rx,float ry,float rz)

Modifies the point p scaling it by (rx,ry,rz)

Parameters

• p Point to be modified

• rx X scale

• ry Y Scale

• rz Z scale

---

public void scale(point_type& p,float scale)

Modifies p multiplying its norm by scale.

Parameters

• p Point to be modified

• scale Scale factor

---

publicpoint_typecross_product(constpoint_type& p,constpoint_type& q)

Computes the 3D cross product p ^ q.

Parameters

• p First 3D vector

• q Second 3D Vector

Returns

Cross product p^q

---

public float norm(constpoint_type& p)

Returns de 2-norm of p as vector.

Parameters

• p 3D Vector

Returns

P 2-Norm

---

public inline bool equal(constpoint_type& a,constpoint_type& b)

Checks whether two point a and b are equal.

Parameters

• a First point

• b Second point

Returns

True if every component in a is equal to b

---

public inline bool equal(constplanar_point& a,constplanar_point& b)

Checks whether two point a and b are equal.

Parameters

• a First point

• b Second point

Returns

True if every component in a is equal to b

---

public std::array<point_type, 3 > get_basis(constpoint_type& vx,constpoint_type& up)

Retunrs a orthonormal right-oriented basis where vx is the first vector.

Parameters

• vx First vector in the basis

• up Up reference position (to be z)

---

public float segment_segment_distance(constpoint_type& p0,constpoint_type& p1,constpoint_type& q0,constpoint_type& q1)

Computes the distance between two line-segments p and q.

Parameters

• p0 P start point

• p1 P end point

• q0 Q start point

• q1 Q end point

Returns

Distance between p and q

---

public Eigen::Quaternionf align_vectors(constpoint_type& v,constpoint_type& u,constpoint_typeup)

Returns the quaternion to transform v into u (both unitary)

Parameters

• v Unitary vector

• u Unitary vector

• up Reference vector to determine sign in 3D angles

Returns

Quaternion

---

public bool segment_box_intersection(constbox_type& b,constsegment_type& s,point_type& inter)

Computes the box-segment intersection of b and s.

Parameters

• b Box

• s Segment

• inter (Return) Intersection point

Returns

True if b intersects with s

---

public template<typename G1,typename G2>
inline bool covered_by(const G1 & g1,const G2 & g2)

Checks if first geometry is covered by the second.

Parameters

• g1 First geometry

• g2 Second geometry

Returns

True if g1 is covered by g2

---

public template<int I,typename Point>
inline bool segment_cross_plane(constsegment_type& s,const Point & v,Point & inter)

Segment-axis plane intersection.

Parameters

• s Segment

• v Point that marks the Ith plane position

• inter Intersection point

Returns

True if they intersect

---

public template<int I,typename Point>
inline void min_component(const Point & p,Point & res)

Set the ith component in res to the minimim betweeen the ith components in p and res.

Parameters

• p Base point. unmodified

• res Point to be modified

---

public template<int I,typename Point>
inline void max_component(const Point & p,Point & res)

Set the ith component in res to the maximum betweeen the ith components in p and res.

Parameters

• p Base point. unmodified

• res Point to be modified

---

public template<typename Point>
inline void max_by_component(const Point & p,Point & res)

Computes the component-wise maximum between p and res and stores it in res.

Parameters

• p Base point

• res Return point

---

public template<typename Point>
inline void min_by_component(const Point & p,Point & res)

Computes the component-wise minimum between p and res and stores it in res.

Parameters

• p Base point

• res Return point

---

public template<Axisaxis>
float axisLength(constbox_type& b)

Return box axis length.

Parameters

• box

Returns

Axis length (value)

---

public template<Axisaxis>
void setAxis(box_type& b,float v)

Set box axis to given value.

Parameters

• b Box

• v Value

---

publicpolygon_typeas_planar_polygon(const std::vector<point_type> & v)

---

public template<typename G>
inline std::size_t num_points(const G & geom)

Number of points in the geometry.

Parameters

• geom Geoemtry object

Returns

Number of point

---

public float polygon_area(constpolygon_type& p)

Computes the pclosed polygon area.

Parameters

• p Polygon object

Returns

Area

---

public template<typename Iter>
inline float polygon_area(const Iter & begin,const Iter & end)

Computes the closed polygon area.

Parameters

• begin

• end

Returns

Area

---

public void negate(point_type& p)

Multiplies every component by -1.

Parameters

• p Point to negate

---

publicpoint_typebarycenter(const std::vector<point_type> & v)

Computes the barycenter of a pointset.

Parameters

• v Vector of points

Returns

Barycenter

---

public void normalize(point_type& p)

Modifies p so its norm is equal to 1.

Parameters

• p Point to normalize

---

public float vector_vector_angle(constpoint_type& a,constpoint_type& b)

Computes the planar vector-vector shortest angle.

Parameters

• a First vector

• b Second vector

Returns

Angle between a and b [0,pi]

---

public bool box_box_intersection(constbox_type& a,constbox_type& b)

Checks if box a intersects with box b (axis aligned)

Parameters

• a

• b

Returns

True if they intersect

---

public std::vector<point_type> box_corners(constbox_type& b)

Returns 8 corner points in a axis-aligned box.

Parameters

• a

Returns

Corner points

---

public float lineseg_dist(const std::vector<point_type> & u,const std::vector<point_type> & v)

Euclidean distance between two line-segments.

Parameters

• u

• v

Returns

euclidean distance

---

publicbox_typebounding_box(const std::vector<point_type> & v)

Computes the bounding box of a node set.

Parameters

• v node set

Returns

box

---

public float vector_vector_directed_angle(constpoint_type& a,constpoint_type& b,constpoint_typeup)

Computes the planar angle from a to b.

Parameters

• a First vector

• b Second vector

• up Reference vector to determine sign in 3D angles

Returns

Angle from a to b [0,wpi)

---

public std::pair< float, float > local_orientation(constpoint_type& p,const std::array<point_type, 3 > & basis)

Computes the local orientation (Azimuth and elevation) of p wrt basis.

Parameters

• p Point

• basis local basis

Returns

pair (azimuth, elevation)

---

public bool in_triangle_border(consttriangle_type& t,constpoint_type& p)

Verifies if p is in the border of the triangle t.

Parameters

• t Triangle

• p Point

Returns

True if p lies in the border of t

---

public bool is_triangle_vertex(consttriangle_type& t,constpoint_type& p)

Verifies if P is one of the vertices of T.

Parameters

• t Triangle

• p Point

Returns

True if p is a vertex of t

---

public bool within_triangle(consttriangle_type& t,constpoint_type& p)

Verifies if p is inside the triangle t.

Parameters

• t Triangle

• p Point

Returns

True if p is inside t

---

public bool triangle_ray_intersection(consttriangle_type& t,constpoint_type& ray_o,constpoint_type& ray_v,point_type& intersection)

Computes Triangle-ray intersection with the moller-trumbore algorithm.

Parameters

• t Triangle

• ray_o Ray origin

• ray_v Ray direction

• intersection Output: intersection point

Returns

True if the ray intersects the triangle

---

public float tetrahedron_volume(constpoint_type& p0,constpoint_type& p1,constpoint_type& p2,constpoint_type& p3)

Returns the volume of the tetrahedron.

Parameters

• p0 vertex

• p1 vertex

• p2 vertex

• p3 vertex

Returns

Tetrahedron voulme

---

public float triangle_area(consttriangle_type& t)

Compute the triangle area.

Returns

Triangle area

---

---

class DiscreteFrechet

Summary

Members	Descriptions
public inline DiscreteFrechet(IterA ini_a,IterA end_a,IterB ini_b,IterB end_b)	Base constructor.
public inline double value()	Computes de discrete frechet distance recursively.

Members

public inline DiscreteFrechet(IterA ini_a,IterA end_a,IterB ini_b,IterB end_b)

Base constructor.

Initializes the class with the tow line-segment

Parameters

• ini_a First branch line-segment begin iterator

• end_a First branch line-segment end iterator

• ini_b Second branch line-segment begin iterator

• end_b Secondbranch line-segment end iterator

Returns

DiscreteFrechet class

---

public inline double value()

Computes de discrete frechet distance recursively.

Returns

Discrete frechet distance

---

class RDPSimplifier

Summary

Members	Descriptions
public inline RDPSimplifier(float eps,std::vector< Node > & v)	Base constructor, sets toleracne and the line-segment.
public inline void simplify()	Applies the simplification to the line-segment.

Members

public inline RDPSimplifier(float eps,std::vector< Node > & v)

Base constructor, sets toleracne and the line-segment.

Parameters

• eps Tolerance

• v Node set (vector)

---

public inline void simplify()

Applies the simplification to the line-segment.

---

class TriangleMesh

Summary

Members	Descriptions
public TriangleMesh()	Creates an empty (no vertex no faces) mesh.
public TriangleMesh(constface_storage& faces)	Creates a mesh with given faces.
public ~TriangleMesh()	Default destructor.
public TriangleMesh(constTriangleMesh&) = delete
publicTriangleMesh& operator=(constTriangleMesh&) = delete
public TriangleMesh(TriangleMesh&&) = default
publicTriangleMesh& operator=(TriangleMesh&&) = default
publicvertex_iteratoradd(constpoint_type& p)	Adds a vertex to the mesh (if it doesnt exist already)
public template<typename Iter> inline void add(const Iter & b,const Iter & e)	Copies a range of vertices to the mesh.
public void remove(constvertex_iterator& it)	Removes the vertex and all its faces from the mesh.
public void remove(constvertex_iterator& b,constvertex_iterator& e)	Removes a range of vertices and their faces from the mesh.
public void clear()	Removes all vertices and faces.
publicvertex_iteratorbegin_vertex()	Creates an iterator to the first vertex in the mesh.
publicconst_vertex_iteratorbegin_vertex() const	Creates an iterator to the first vertex in the mesh.
publicvertex_iteratorend_vertex()	Creates an iterator to one-past position of the last vertex in the mesh.
publicconst_vertex_iteratorend_vertex() const	Creates an iterator to one-past position of the last vertex in the mesh.
public std::size_t vertex_count() const	Number of vertices in the mesh.
publicface_iteratoradd(constpoint_type& v0,constpoint_type& v1,constpoint_type& v2)	Adds a new triangular face to the mesh.
publicface_iteratoradd(consttriangle_type& t)	Adds a new triangular face to the mesh.
public void remove(constface_iterator& it)	Removes a face from the mesh.
public void remove(constface_iterator& b,constface_iterator& e)	Removes a set of faces from the mesh.
public void clear_faces()	Removes all faces (but not the vertices)
publicface_iteratorbegin_face()	Returns an iterator to the first face in the mesh.
publicconst_face_iteratorbegin_face() const	Returns an iterator to the first face in the mesh.
publicface_iteratorend_face()	Returns an iterator to one-past the last face in the mesh.
publicconst_face_iteratorend_face() const	Returns an iterator to one-past the last face in the mesh.
public std::size_t face_count() const	Number of faces in the mesh.
public bool point_inside(constpoint_type& p,constpoint_type& ray_direction) const	Using ray-tracing method computes if the point p is Inside the triangular mesh assuming that it is closed.
publicpoint_typeray_intersection(constpoint_type& p,constpoint_type& ray_direction) const

Members

public TriangleMesh()

Creates an empty (no vertex no faces) mesh.

---

public TriangleMesh(constface_storage& faces)

Creates a mesh with given faces.

Vertices are added automatically

---

public ~TriangleMesh()

Default destructor.

Nothign special to do

---

public TriangleMesh(constTriangleMesh&) = delete

---

publicTriangleMesh& operator=(constTriangleMesh&) = delete

---

public TriangleMesh(TriangleMesh&&) = default

---

publicTriangleMesh& operator=(TriangleMesh&&) = default

---

publicvertex_iteratoradd(constpoint_type& p)

Adds a vertex to the mesh (if it doesnt exist already)

Parameters

• p Vertex to add.

---

public template<typename Iter>
inline void add(const Iter & b,const Iter & e)

Copies a range of vertices to the mesh.

Parameters

• b Range begin iterator

• e Range end iterator

---

public void remove(constvertex_iterator& it)

Removes the vertex and all its faces from the mesh.

Parameters

• it Vertex iterator

---

public void remove(constvertex_iterator& b,constvertex_iterator& e)

Removes a range of vertices and their faces from the mesh.

Parameters

• b Range begin

• e Range end

---

public void clear()

Removes all vertices and faces.

---

publicvertex_iteratorbegin_vertex()

Creates an iterator to the first vertex in the mesh.

Returns

Begin iterator

---

publicconst_vertex_iteratorbegin_vertex() const

Creates an iterator to the first vertex in the mesh.

Returns

Begin iterator

---

publicvertex_iteratorend_vertex()

Creates an iterator to one-past position of the last vertex in the mesh.

Returns

End iterator

---

publicconst_vertex_iteratorend_vertex() const

Creates an iterator to one-past position of the last vertex in the mesh.

Returns

End iterator

---

public std::size_t vertex_count() const

Number of vertices in the mesh.

---

publicface_iteratoradd(constpoint_type& v0,constpoint_type& v1,constpoint_type& v2)

Adds a new triangular face to the mesh.

Inserts the vertices if necessary

Parameters

• v0 First vertex

• v1 Second vertex

• v2 Third vertex

Returns

Iterator to the inserted face

---

publicface_iteratoradd(consttriangle_type& t)

Adds a new triangular face to the mesh.

Inserts the vertices if necessary

Parameters

• t face triangle

Returns

Iterator to the inserted face

---

public void remove(constface_iterator& it)

Removes a face from the mesh.

Parameters

• it Face iterator

---

public void remove(constface_iterator& b,constface_iterator& e)

Removes a set of faces from the mesh.

Parameters

• b Begin iterator

• e End iterator

---

public void clear_faces()

Removes all faces (but not the vertices)

---

publicface_iteratorbegin_face()

Returns an iterator to the first face in the mesh.

Returns

Begin iterator

---

publicconst_face_iteratorbegin_face() const

Returns an iterator to the first face in the mesh.

Returns

Begin iterator

---

publicface_iteratorend_face()

Returns an iterator to one-past the last face in the mesh.

Returns

End iterator

---

publicconst_face_iteratorend_face() const

Returns an iterator to one-past the last face in the mesh.

Returns

End iterator

---

public std::size_t face_count() const

Number of faces in the mesh.

---

public bool point_inside(constpoint_type& p,constpoint_type& ray_direction) const

Using ray-tracing method computes if the point p is Inside the triangular mesh assuming that it is closed.

Parameters

• p Point

Returns

True if the point is within the mesh

---

publicpoint_typeray_intersection(constpoint_type& p,constpoint_type& ray_direction) const

Parameters

• p

• ray_direction

Returns