Aleph::Point Class Reference

Represents a point with rectangular coordinates in a 2D plane. More...

#include <point.H>

Inheritance diagram for Aleph::Point:

Collaboration diagram for Aleph::Point:

Public Member Functions
	Point ()
	Default constructor.
	Point (const Geom_Number &x, const Geom_Number &y)
	Constructs a point from Cartesian coordinates.
	Point (const Polar_Point &pp)
	Constructs a point from polar coordinates.
bool	operator== (const Point &point) const noexcept
	Checks for exact equality between two points.
bool	operator!= (const Point &point) const noexcept
	Checks for inequality between two points.
bool	operator< (const Point &point) const noexcept
	Defines a strict lexicographical ordering for points.
Point	operator+ (const Point &p) const
	Vector addition.
Point &	operator+= (const Point &p)
	Vector addition and assignment.
Point	operator- (const Point &p) const
	Vector subtraction.
Point &	operator-= (const Point &p)
	Vector subtraction and assignment.
Point	operator- () const
	Unary negation (vector inversion).
Point	operator* (const Geom_Number &s) const
	Scalar multiplication.
Point	operator/ (const Geom_Number &s) const
	Scalar division.
Geom_Number	dot (const Point &p) const
	Dot product.
Geom_Number	cross (const Point &p) const
	2D cross-product (z-component of the 3D cross-product).
Geom_Number	norm_squared () const
	Squared Euclidean norm.
Geom_Number	norm () const
	Euclidean norm (vector magnitude).
Point	normalize () const
	Returns a normalized copy of this vector (magnitude 1).
Point	rotate (const Geom_Number &angle) const
	Rotates the point around the origin by a given angle.
Point	lerp (const Point &other, const Geom_Number &t) const
	Linear interpolation between this point and another.
Point	midpoint (const Point &other) const
	Calculates the midpoint between this point and another.
const Geom_Number &	get_x () const noexcept
	Gets the x-coordinate value.
const Geom_Number &	get_y () const noexcept
	Gets the y-coordinate value.
bool	is_colinear_with (const Point &p1, const Point &p2) const
	Checks if this point is collinear with two other points.
bool	is_colinear_with (const Segment &s) const
	Checks if this point is collinear with a segment.
bool	is_left_of (const Point &p1, const Point &p2) const
	Checks if this point is to the left of the directed line from p1 to p2.
bool	is_to_left_from (const Point &p1, const Point &p2) const
bool	is_to_right_from (const Point &p1, const Point &p2) const
	Checks if this point is to the right of the directed line from p1 to p2.
bool	is_to_left_on_from (const Point &p1, const Point &p2) const
	Checks if this point is to the left of or on the line from p1 to p2.
bool	is_right_on_of (const Point &p1, const Point &p2) const
	Checks if this point is to the right of or on the line from p1 to p2.
bool	is_to_right_on_from (const Point &p1, const Point &p2) const
bool	is_clockwise_with (const Point &p1, const Point &p2) const
	Determines if the sequence of three points (this, p1, p2) makes a clockwise turn.
bool	is_left_of (const Segment &s) const
	Checks if this point is to the left of a directed segment.
bool	is_right_of (const Segment &s) const
	Checks if this point is to the right of a directed segment.
bool	is_to_left_from (const Segment &s) const
bool	is_to_right_from (const Segment &s) const
bool	is_clockwise_with (const Segment &s) const
	Determines if the sequence (this, s.src, s.tgt) makes a clockwise turn.
bool	is_between (const Point &p1, const Point &p2) const
	Checks if this point is on the bounding box of p1 and p2 and is collinear with them.
const Point &	nearest_point (const Point &p1, const Point &p2) const
	Returns which of the two points, p1 or p2, is nearer to this point.
bool	is_inside (const Segment &s) const
	Checks if this point is contained within a segment.
bool	is_inside (const Ellipse &e) const
	Checks if this point is contained within an ellipse.
bool	intersects_with (const Ellipse &e) const
	Checks if this point lies exactly on the boundary of an ellipse.
std::string	to_string () const
	Returns a string representation of the point as "(x,y)".
	operator std::string () const
	Cast operator to std::string.
Geom_Number	distance_squared_to (const Point &that) const
	Calculates the squared Euclidean distance to another point.
Geom_Number	distance_to (const Point &p) const
	Calculates the Euclidean distance to another point.
Geom_Number	distance_with (const Point &p) const
const Point &	highest_point () const
	Returns the highest point (largest y-coordinate).
const Point &	lowest_point () const
	Returns the lowest point (smallest y-coordinate).
const Point &	leftmost_point () const
	Returns the leftmost point (smallest x-coordinate).
const Point &	rightmost_point () const
	Returns the rightmost point (largest x-coordinate).
Public Member Functions inherited from Aleph::Geom_Object
	Geom_Object ()=default
virtual	~Geom_Object ()=default

Private Attributes
Geom_Number	x_
Geom_Number	y_

Friends
class	Segment
class	Triangle
class	Polar_Point

Detailed Description

Represents a point with rectangular coordinates in a 2D plane.

Fundamental class defining a point in a Cartesian coordinate plane. It provides vector operations, transformations, and geometric predicates. Uses the Geom_Number type for exact-precision arithmetic.

Definition at line 220 of file point.H.

Constructor & Destructor Documentation

Point() [1/3]

Aleph::Point::Point ( )

inline

Default constructor.

Note

Initializes the point at the origin (0, 0).

Definition at line 234 of file point.H.

Point() [2/3]

Aleph::Point::Point ( const Geom_Number &  x, const Geom_Number &  y  )

inline

Constructs a point from Cartesian coordinates.

Parameters

x	The x-coordinate.
y	The y-coordinate.

Definition at line 243 of file point.H.

Point() [3/3]

Point::Point ( const Polar_Point &  pp )

inline

Constructs a point from polar coordinates.

Parameters

pp	The point in polar coordinates (Polar_Point) to be converted.

Definition at line 822 of file point.H.

Member Function Documentation

cross()

Geom_Number Aleph::Point::cross ( const Point &  p ) const

inline

2D cross-product (z-component of the 3D cross-product).

Parameters

p	The other vector (point).

Returns

The scalar x1*y2 - y1*x2. Its sign indicates orientation.

Definition at line 374 of file point.H.

References x_, and y_.

Referenced by Aleph::Segment::intersection_with().

distance_squared_to()

Geom_Number Point::distance_squared_to ( const Point &  that ) const

inline

Calculates the squared Euclidean distance to another point.

Parameters

that	The other point.

Returns

The squared distance.

Definition at line 1490 of file point.H.

References x_, and y_.

Referenced by Aleph::MinimumEnclosingCircle::Circle::contains(), Aleph::ClosestPairDivideAndConquer::dist2(), dist2(), Aleph::MinimumEnclosingCircle::from_three_points(), Aleph::MinimumEnclosingCircle::from_two_points(), Aleph::Segment::intersection_with(), Aleph::RotatingCalipersConvexPolygon::make_diameter(), K2Tree< T >::nearest(), nearest_point(), Aleph::GiftWrappingConvexHull::operator()(), Aleph::AlphaShape::operator()(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

distance_to()

Geom_Number Point::distance_to ( const Point &  p ) const

inline

Calculates the Euclidean distance to another point.

Parameters

p	The other point.

Returns

The Euclidean distance.

Definition at line 1498 of file point.H.

References Aleph::euclidean_distance(), x_, and y_.

Referenced by Aleph::Segment::distance_to(), distance_with(), Aleph::Euclidian_Graph< __Euclidian_Node, __Euclidian_Arc >::get_distance(), Aleph::Triangle::incenter(), and Aleph::Triangle::perimeter().

distance_with()

Geom_Number Aleph::Point::distance_with ( const Point &  p ) const

inline

Deprecated:

Use distance_to() instead.

Definition at line 670 of file point.H.

References distance_to().

dot()

Geom_Number Aleph::Point::dot ( const Point &  p ) const

inline

Dot product.

Parameters

p	The other vector (point).

Returns

The scalar result of the dot product (x1*x2 + y1*y2).

Definition at line 364 of file point.H.

References x_, and y_.

Referenced by Aleph::Segment::get_perpendicular(), and Aleph::Segment::project().

get_x()

const Geom_Number & Aleph::Point::get_x ( ) const

inlinenoexcept

Gets the x-coordinate value.

Returns

A const reference to the x-coordinate.

Definition at line 448 of file point.H.

References x_.

Referenced by Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::Abstract_Euclidian_Plane(), Aleph::Polar_Point::Polar_Point(), Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::add_point(), Aleph::Polygon::add_vertex(), Aleph::VisibilityPolygon::angle_less(), Aleph::area_of_parallelogram(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::VoronoiDiagramFromDelaunay::bisector_halfplane_for_site(), Aleph::AABBTree::box_contains_point(), K2Tree< T >::bu_insert(), K2Tree< T >::build(), Aleph::RangeTree2D::build(), K2Tree< T >::build_balanced(), Aleph::MonotonePolygonTriangulation::build_faces_from_diagonals(), build_poly_graph(), Aleph::SweepLineSegmentIntersection::canonicalize(), Aleph::Polygon::centroid(), Aleph::Triangle::circumcenter(), Aleph::VoronoiDiagramFromDelaunay::circumcenter(), Aleph::ConvexPolygonDistanceGJK::closest_from_simplex(), Aleph::BruteForceConvexHull::CmpSegment::cmp_point(), Aleph::SegmentSegmentIntersection::collinear_overlap(), Eepic_Plane::compute_extreme_points(), Eepic_Plane::compute_geom_plane(), Aleph::Ellipse::compute_radius(), Aleph::Segment::compute_slope(), Aleph::Segment::compute_tgt_point(), Aleph::TrapezoidalMapPointLocation::Result::contains(), Aleph::BezierCurve::control_bbox(), Aleph::Segment::counterclockwise_angle_with(), Aleph::MinkowskiSumConvex::cross(), Aleph::ShortestPathInPolygon::cross(), Aleph::BezierCurve::cubic(), Aleph::KDTreePointSearch::debug_snapshot(), demo_convex_hull_cities(), demo_coverage_area(), Eepic_Triangle::draw(), Eepic_Plane::draw_cartesian_axis(), Eepic_Plane::draw_ellipse(), Eepic_Plane::draw_point(), Eepic_Plane::draw_point_text(), Aleph::Tikz_Plane::draw_rotated_ellipse(), Eepic_Plane::draw_text(), Eepic_Plane::draw_vertex_numbers_in_polygon(), Aleph::HalfPlaneIntersection::HalfPlane::dx(), Aleph::MonotonePolygonTriangulation::edge_x_at_y(), Aleph::VoronoiDiagramFortune::enqueue_circle_event(), Aleph::SweepLineSegmentIntersection::event_less(), export_csv(), Aleph::RotatedEllipse::extremal_points(), Aleph::Point3D::from_2d(), Aleph::Point3D::from_2d(), Aleph::MinimumEnclosingCircle::from_three_points(), Aleph::GiftWrappingConvexHull::get_lowest_point(), Aleph::Polar_Point::get_quadrant(), Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::get_width(), Aleph::Ellipse::highest_point(), hull_signature(), Aleph::in_circle_determinant(), Aleph::Ellipse::intersection_with(), Aleph::Ellipse::intersects_with(), Aleph::MonotonePolygonTriangulation::is_above(), is_between(), Aleph::MonotonePolygonTriangulation::EdgeStatusTree::left_edge_of_point(), Aleph::Triangle::leftmost_point(), Aleph::Ellipse::leftmost_point(), Aleph::Segment::leftmost_point(), Aleph::Segment::length(), Aleph::ConvexPolygonDistanceGJK::lerp_point(), Aleph::RegularTriangulationBowyerWatson::lex_less(), Aleph::KDTreePointSearch::lexicographic_less(), Aleph::DelaunayTriangulationBowyerWatson::lexicographic_less(), Aleph::ConstrainedDelaunayTriangulation::lexicographic_less(), Aleph::ConvexPolygonOffset::line_intersect(), Aleph::HalfPlaneIntersection::line_intersection(), Aleph::ConvexPolygonIntersectionBasic::line_intersection(), Aleph::Ellipse::lowest_point(), K2Tree< T >::lr_insert(), main(), main(), Aleph::Tikz_Plane::map_point(), Aleph::Segment::mid_perpendicular(), Aleph::Segment::mid_point(), objective(), Aleph::HalfPlaneIntersection::HalfPlane::offset(), Aleph::ConvexPolygonOffset::offset_edge(), std::hash< Aleph::Point >::operator()(), Aleph::SweepLineSegmentIntersection::operator()(), Aleph::SegmentArrangement::operator()(), Aleph::DelaunayTriangulationRandomizedIncremental::operator()(), Aleph::ClosestPairDivideAndConquer::LexicographicCmp::operator()(), Aleph::ClosestPairDivideAndConquer::ByYCmp::operator()(), Aleph::AndrewMonotonicChainConvexHull::LexicographicCmp::operator()(), Aleph::GrahamScanConvexHull::LexicographicCmp::operator()(), Aleph::VisibilityPolygon::operator()(), Aleph::operator<<(), Aleph::LineEq::perpendicular_through(), Aleph::RegularTriangulationBowyerWatson::point_in_power_circle(), Aleph::SegmentSegmentIntersection::point_less_on_axis(), Eepic_Plane::point_string(), points_equal(), polygon_area(), Aleph::PowerDiagram::power_center(), print_point(), print_point(), print_point(), print_polygon(), print_polygon(), print_triangle(), Aleph::SegmentArrangement::pt_less(), Aleph::put_trapezoidal_map_result(), Aleph::BezierCurve::quadratic(), Aleph::VisibilityPolygon::ray_edge_hit(), Aleph::ray_endpoint(), Aleph::VisibilityPolygon::ray_param(), Aleph::ClosestPairDivideAndConquer::recurse(), Aleph::Polygon::remove_vertex(), Aleph::Triangle::rightmost_point(), Aleph::Ellipse::rightmost_point(), Aleph::Segment::rightmost_point(), Aleph::Ellipse::sample(), scenario_exact_intersection(), Aleph::QuickHull::search_extremes(), Aleph::Segment::sense(), Aleph::Polygon::signed_area(), Aleph::GeomPolygonUtils::signed_double_area(), Aleph::Segment::slope_exact(), Aleph::SweepLineSegmentIntersection::slope_less(), sorted_hull_vertices(), Aleph::BezierCurve::split_cubic(), Aleph::detail::spp_cross(), Aleph::PolygonOffset::sq_dist(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_geojson(), Aleph::RotatedEllipse::to_local(), Aleph::GeomSerializer::to_wkt(), Aleph::GeomSerializer::to_wkt(), Aleph::GeomSerializer::to_wkt(), Aleph::RotatedEllipse::to_world(), triangle_area(), Aleph::Polygon::update_extreme_points(), write_polygon_wkt(), write_polygon_wkt(), write_polygon_wkt(), K2Tree< T >::Node::x(), and Aleph::SweepLineSegmentIntersection::y_at_x().

get_y()

const Geom_Number & Aleph::Point::get_y ( ) const

inlinenoexcept

Gets the y-coordinate value.

Returns

A const reference to the y-coordinate.

Definition at line 457 of file point.H.

References y_.

Referenced by Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::Abstract_Euclidian_Plane(), Aleph::Polar_Point::Polar_Point(), Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::add_point(), Aleph::Polygon::add_vertex(), Aleph::VisibilityPolygon::angle_less(), Aleph::area_of_parallelogram(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::Tikz_Plane::bbox_of(), Aleph::VoronoiDiagramFromDelaunay::bisector_halfplane_for_site(), Aleph::AABBTree::box_contains_point(), K2Tree< T >::bu_insert(), K2Tree< T >::build(), Aleph::RangeTree2D::build(), K2Tree< T >::build_balanced(), Aleph::MonotonePolygonTriangulation::build_faces_from_diagonals(), build_poly_graph(), Aleph::SweepLineSegmentIntersection::canonicalize(), Aleph::Polygon::centroid(), Aleph::Triangle::circumcenter(), Aleph::VoronoiDiagramFromDelaunay::circumcenter(), Aleph::ConvexPolygonDistanceGJK::closest_from_simplex(), Aleph::BruteForceConvexHull::CmpSegment::cmp_point(), Eepic_Plane::compute_extreme_points(), Eepic_Plane::compute_geom_plane(), Aleph::Ellipse::compute_radius(), Aleph::Segment::compute_slope(), Aleph::Segment::compute_tgt_point(), Aleph::TrapezoidalMapPointLocation::Result::contains(), Aleph::BezierCurve::control_bbox(), Aleph::Segment::counterclockwise_angle_with(), Aleph::MinkowskiSumConvex::cross(), Aleph::ShortestPathInPolygon::cross(), Aleph::BezierCurve::cubic(), Aleph::KDTreePointSearch::debug_snapshot(), demo_convex_hull_cities(), demo_coverage_area(), Eepic_Triangle::draw(), Eepic_Plane::draw_cartesian_axis(), Eepic_Plane::draw_ellipse(), Eepic_Plane::draw_point(), Eepic_Plane::draw_point_text(), Aleph::Tikz_Plane::draw_rotated_ellipse(), Eepic_Plane::draw_text(), Eepic_Plane::draw_vertex_numbers_in_polygon(), Aleph::HalfPlaneIntersection::HalfPlane::dy(), Aleph::MonotonePolygonTriangulation::edge_x_at_y(), Aleph::VoronoiDiagramFortune::enqueue_circle_event(), Aleph::SweepLineSegmentIntersection::event_less(), export_csv(), Aleph::RotatedEllipse::extremal_points(), Aleph::Point3D::from_2d(), Aleph::Point3D::from_2d(), Aleph::MinimumEnclosingCircle::from_three_points(), Aleph::Abstract_Euclidian_Plane< __Euclidian_Graph >::get_height(), Aleph::GiftWrappingConvexHull::get_lowest_point(), Aleph::Polar_Point::get_quadrant(), Aleph::Triangle::highest_point(), Aleph::Ellipse::highest_point(), Aleph::Segment::highest_point(), hull_signature(), Aleph::in_circle_determinant(), Aleph::Ellipse::intersection_with(), Aleph::Ellipse::intersects_with(), Aleph::MonotonePolygonTriangulation::is_above(), is_between(), Aleph::Ellipse::leftmost_point(), Aleph::Segment::length(), Aleph::ConvexPolygonDistanceGJK::lerp_point(), Aleph::RegularTriangulationBowyerWatson::lex_less(), Aleph::KDTreePointSearch::lexicographic_less(), Aleph::DelaunayTriangulationBowyerWatson::lexicographic_less(), Aleph::ConstrainedDelaunayTriangulation::lexicographic_less(), Aleph::ConvexPolygonOffset::line_intersect(), Aleph::HalfPlaneIntersection::line_intersection(), Aleph::ConvexPolygonIntersectionBasic::line_intersection(), Aleph::Polygon::locate_point(), Aleph::Triangle::lowest_point(), Aleph::Ellipse::lowest_point(), Aleph::Segment::lowest_point(), K2Tree< T >::lr_insert(), main(), main(), Aleph::Tikz_Plane::map_point(), Aleph::Segment::mid_perpendicular(), Aleph::Segment::mid_point(), objective(), Aleph::HalfPlaneIntersection::HalfPlane::offset(), Aleph::ConvexPolygonOffset::offset_edge(), std::hash< Aleph::Point >::operator()(), Aleph::SweepLineSegmentIntersection::operator()(), Aleph::DelaunayTriangulationRandomizedIncremental::operator()(), Aleph::ClosestPairDivideAndConquer::LexicographicCmp::operator()(), Aleph::ClosestPairDivideAndConquer::ByYCmp::operator()(), Aleph::AndrewMonotonicChainConvexHull::LexicographicCmp::operator()(), Aleph::GrahamScanConvexHull::LexicographicCmp::operator()(), Aleph::VisibilityPolygon::operator()(), Aleph::operator<<(), Aleph::LineEq::perpendicular_through(), Aleph::RegularTriangulationBowyerWatson::point_in_power_circle(), Aleph::BooleanPolygonOperations::point_inside_ccw(), Aleph::SegmentSegmentIntersection::point_less_on_axis(), Eepic_Plane::point_string(), points_equal(), polygon_area(), Aleph::PowerDiagram::power_center(), print_point(), print_point(), print_point(), print_polygon(), print_polygon(), print_triangle(), Aleph::SegmentArrangement::pt_less(), Aleph::put_trapezoidal_map_result(), Aleph::BezierCurve::quadratic(), Aleph::VisibilityPolygon::ray_edge_hit(), Aleph::ray_endpoint(), Aleph::VisibilityPolygon::ray_param(), Aleph::Polygon::remove_vertex(), Aleph::Ellipse::rightmost_point(), Aleph::Ellipse::sample(), scenario_exact_intersection(), Aleph::Segment::sense(), Aleph::Polygon::signed_area(), Aleph::GeomPolygonUtils::signed_double_area(), Aleph::Segment::slope_exact(), Aleph::SweepLineSegmentIntersection::slope_less(), sorted_hull_vertices(), Aleph::BezierCurve::split_cubic(), Aleph::detail::spp_cross(), Aleph::PolygonOffset::sq_dist(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_geojson(), Aleph::RotatedEllipse::to_local(), Aleph::GeomSerializer::to_wkt(), Aleph::GeomSerializer::to_wkt(), Aleph::GeomSerializer::to_wkt(), Aleph::RotatedEllipse::to_world(), triangle_area(), Aleph::Polygon::update_extreme_points(), write_polygon_wkt(), write_polygon_wkt(), write_polygon_wkt(), K2Tree< T >::Node::y(), and Aleph::SweepLineSegmentIntersection::y_at_x().

highest_point()

const Point & Aleph::Point::highest_point ( ) const

inline

Returns the highest point (largest y-coordinate).

For a Point, it's itself.

Returns

A const reference to itself.

Definition at line 679 of file point.H.

Referenced by TEST_F(), TEST_F(), TEST_F(), and TEST_F().

intersects_with()

bool Point::intersects_with ( const Ellipse &  e ) const

inline

Checks if this point lies exactly on the boundary of an ellipse.

Parameters

e	The ellipse to check against.

Returns

true if the point is on the boundary.

See also

Ellipse::intersects_with()

Definition at line 2436 of file point.H.

References Aleph::Ellipse::intersects_with().

is_between()

bool Aleph::Point::is_between ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is on the bounding box of p1 and p2 and is collinear with them.

Parameters

p1	First point of the segment.
p2	Second point of the segment.

Returns

true if this point lies on the segment joining p1 and p2.

Definition at line 588 of file point.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), get_x(), get_y(), and is_colinear_with().

Referenced by Aleph::between(), Aleph::Segment::contains(), and Aleph::intersect_improp().

is_clockwise_with() [1/2]

bool Aleph::Point::is_clockwise_with ( const Point &  p1, const Point &  p2  ) const

inline

Determines if the sequence of three points (this, p1, p2) makes a clockwise turn.

Parameters

p1	The second point in the sequence.
p2	The third point in the sequence.

Returns

true if the orientation is clockwise.

Definition at line 544 of file point.H.

References Aleph::area_of_parallelogram().

Referenced by is_clockwise_with().

is_clockwise_with() [2/2]

bool Point::is_clockwise_with ( const Segment &  s ) const

inline

Determines if the sequence (this, s.src, s.tgt) makes a clockwise turn.

Parameters

s	The segment.

Returns

true if the orientation is clockwise.

Definition at line 1484 of file point.H.

References is_clockwise_with(), Aleph::Segment::src_, and Aleph::Segment::tgt_.

is_colinear_with() [1/2]

bool Aleph::Point::is_colinear_with ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is collinear with two other points.

Parameters

p1	The first point.
p2	The second point.

Returns

true if all three points lie on the same line.

Definition at line 468 of file point.H.

References Aleph::area_of_parallelogram().

Referenced by Aleph::Polygon::add_vertex(), is_between(), Aleph::Segment::is_colinear_with(), is_colinear_with(), and TEST_F().

is_colinear_with() [2/2]

bool Point::is_colinear_with ( const Segment &  s ) const

inline

Checks if this point is collinear with a segment.

Parameters

s	The segment.

Returns

true if the point lies on the infinite line defined by the segment.

Definition at line 1466 of file point.H.

References is_colinear_with(), Aleph::Segment::src_, and Aleph::Segment::tgt_.

is_inside() [1/2]

bool Point::is_inside ( const Ellipse &  e ) const

inline

Checks if this point is contained within an ellipse.

Parameters

e	The ellipse to check against.

Returns

true if the point is inside or on the boundary of the ellipse.

See also

Ellipse::contains()

Definition at line 2430 of file point.H.

References Aleph::Ellipse::contains().

is_inside() [2/2]

bool Point::is_inside ( const Segment &  s ) const

inline

Checks if this point is contained within a segment.

Parameters

s	The segment to check against.

Returns

true if the point is on the segment.

See also

Segment::contains()

Definition at line 1460 of file point.H.

References Aleph::Segment::contains().

Referenced by Aleph::Polygon::add_vertex().

is_left_of() [1/2]

bool Aleph::Point::is_left_of ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is to the left of the directed line from p1 to p2.

Parameters

p1	The starting point of the line.
p2	The ending point of the line.

Returns

true if the point is to the left.

Definition at line 486 of file point.H.

References Aleph::area_of_parallelogram().

Referenced by Aleph::Triangle::contains(), Aleph::CuttingEarsTriangulation::in_cone(), is_left_of(), Aleph::Segment::is_right_of(), is_right_on_of(), is_to_left_from(), and is_to_left_from().

is_left_of() [2/2]

bool Point::is_left_of ( const Segment &  s ) const

inline

Checks if this point is to the left of a directed segment.

Parameters

s	The segment.

Returns

true if the point is to the left.

Definition at line 1472 of file point.H.

References is_left_of(), Aleph::Segment::src_, and Aleph::Segment::tgt_.

is_right_of()

bool Point::is_right_of ( const Segment &  s ) const

inline

Checks if this point is to the right of a directed segment.

Parameters

s	The segment.

Returns

true if the point is to the right.

Definition at line 1478 of file point.H.

References Aleph::area_of_parallelogram(), Aleph::Segment::src_, and Aleph::Segment::tgt_.

Referenced by Aleph::Segment::is_left_of(), and is_to_right_from().

is_right_on_of()

bool Aleph::Point::is_right_on_of ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is to the right of or on the line from p1 to p2.

Parameters

p1	The starting point of the line.
p2	The ending point of the line.

Returns

true if the point is not to the left.

Definition at line 526 of file point.H.

References Aleph::blossom_maximum_cardinality_matching(), and is_left_of().

Referenced by is_to_right_on_from().

is_to_left_from() [1/2]

bool Aleph::Point::is_to_left_from ( const Point &  p1, const Point &  p2  ) const

inline

Deprecated:

Use is_left_of() instead.

Definition at line 492 of file point.H.

References is_left_of().

is_to_left_from() [2/2]

bool Aleph::Point::is_to_left_from ( const Segment &  s ) const

inline

Deprecated:

Use is_left_of() instead.

Definition at line 564 of file point.H.

References is_left_of().

is_to_left_on_from()

bool Aleph::Point::is_to_left_on_from ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is to the left of or on the line from p1 to p2.

Parameters

p1	The starting point of the line.
p2	The ending point of the line.

Returns

true if the point is not to the right.

Definition at line 515 of file point.H.

References Aleph::blossom_maximum_cardinality_matching(), and is_to_right_from().

Referenced by Aleph::CuttingEarsTriangulation::in_cone().

is_to_right_from() [1/2]

bool Aleph::Point::is_to_right_from ( const Point &  p1, const Point &  p2  ) const

inline

Checks if this point is to the right of the directed line from p1 to p2.

Parameters

p1	The starting point of the line.
p2	The ending point of the line.

Returns

true if the point is to the right.

Definition at line 504 of file point.H.

References Aleph::area_of_parallelogram().

Referenced by Aleph::Triangle::contains(), and is_to_left_on_from().

is_to_right_from() [2/2]

bool Aleph::Point::is_to_right_from ( const Segment &  s ) const

inline

Deprecated:

Use is_right_of() instead.

Definition at line 570 of file point.H.

References is_right_of().

is_to_right_on_from()

bool Aleph::Point::is_to_right_on_from ( const Point &  p1, const Point &  p2  ) const

inline

Deprecated:

Use is_right_on_of() instead.

Definition at line 532 of file point.H.

References is_right_on_of().

leftmost_point()

const Point & Aleph::Point::leftmost_point ( ) const

inline

Returns the leftmost point (smallest x-coordinate).

For a Point, it's itself.

Returns

A const reference to itself.

Definition at line 697 of file point.H.

Referenced by TEST_F().

lerp()

Point Aleph::Point::lerp ( const Point &  other, const Geom_Number &  t  ) const

inline

Linear interpolation between this point and another.

Parameters

other	The other point for interpolation.
t	The interpolation parameter, typically in [0, 1].

Returns

this * (1-t) + other * t.

Definition at line 428 of file point.H.

References Aleph::blossom_maximum_cardinality_matching().

Referenced by Aleph::Segment::at(), Aleph::Segment::get_perpendicular(), and midpoint().

lowest_point()

const Point & Aleph::Point::lowest_point ( ) const

inline

Returns the lowest point (smallest y-coordinate).

For a Point, it's itself.

Returns

A const reference to itself.

Definition at line 688 of file point.H.

Referenced by TEST_F().

midpoint()

Point Aleph::Point::midpoint ( const Point &  other ) const

inline

Calculates the midpoint between this point and another.

Parameters

other

The other point.

Returns

The midpoint, equivalent to lerp(other, 0.5).

Definition at line 439 of file point.H.

References Aleph::blossom_maximum_cardinality_matching(), and lerp().

Referenced by Aleph::MinimumEnclosingCircle::from_two_points().

nearest_point()

const Point & Aleph::Point::nearest_point ( const Point &  p1, const Point &  p2  ) const

inline

Returns which of the two points, p1 or p2, is nearer to this point.

Parameters

p1	The first candidate point.
p2	The second candidate point.

Returns

A const reference to the nearest point (p1 or p2).

Definition at line 607 of file point.H.

References distance_squared_to().

Referenced by arc_segment(), arc_trigon(), Aleph::Segment::nearest_point(), and TEST_F().

norm()

Geom_Number Aleph::Point::norm ( ) const

inline

Euclidean norm (vector magnitude).

Returns

The square root of the sum of the squares of the coordinates.

Definition at line 393 of file point.H.

References Aleph::euclidean_distance(), x_, and y_.

Referenced by normalize().

norm_squared()

Geom_Number Aleph::Point::norm_squared ( ) const

inline

Squared Euclidean norm.

Returns

The sum of the squares of the coordinates (x*x + y*y).

Note

This is more efficient than norm() if only needed for magnitude comparisons.

Definition at line 384 of file point.H.

References x_, and y_.

normalize()

Point Aleph::Point::normalize ( ) const

inline

Returns a normalized copy of this vector (magnitude 1).

Returns

A new Point representing the unit vector.

Exceptions

std::domain_error

if normalizing the zero vector is attempted.

Definition at line 403 of file point.H.

References ah_domain_error_if, and norm().

Referenced by TEST_F().

operator std::string()

Aleph::Point::operator std::string ( ) const

inline

Cast operator to std::string.

Returns

The result of to_string().

Definition at line 650 of file point.H.

References to_string().

operator!=()

bool Aleph::Point::operator!= ( const Point &  point ) const

inlinenoexcept

Checks for inequality between two points.

Parameters

point

The other point to compare against.

Returns

true if either the x or y coordinate is different.

Definition at line 269 of file point.H.

References Aleph::blossom_maximum_cardinality_matching().

operator*()

Point Aleph::Point::operator* ( const Geom_Number &  s ) const

inline

Scalar multiplication.

Parameters

s	The scalar value to multiply by.

Returns

A new point with each coordinate multiplied by s.

Definition at line 344 of file point.H.

References x_, and y_.

operator+()

Point Aleph::Point::operator+ ( const Point &  p ) const

inline

Vector addition.

Parameters

p	The other point (vector) to add.

Returns

A new point representing the sum of the corresponding coordinates.

Definition at line 289 of file point.H.

References x_, and y_.

operator+=()

Point & Aleph::Point::operator+= ( const Point &  p )

inline

Vector addition and assignment.

Parameters

p	The other point (vector) to add.

Returns

A reference to this modified point.

Definition at line 299 of file point.H.

References x_, and y_.

operator-() [1/2]

Point Aleph::Point::operator- ( ) const

inline

Unary negation (vector inversion).

Returns

A new point with both coordinates negated.

Definition at line 334 of file point.H.

References x_, and y_.

operator-() [2/2]

Point Aleph::Point::operator- ( const Point &  p ) const

inline

Vector subtraction.

Parameters

p	The point (vector) to subtract.

Returns

A new point representing the difference of the coordinates.

Definition at line 312 of file point.H.

References x_, and y_.

operator-=()

Point & Aleph::Point::operator-= ( const Point &  p )

inline

Vector subtraction and assignment.

Parameters

p	The point (vector) to subtract.

Returns

A reference to this modified point.

Definition at line 322 of file point.H.

References x_, and y_.

operator/()

Point Aleph::Point::operator/ ( const Geom_Number &  s ) const

inline

Scalar division.

Parameters

s	The scalar value to divide by.

Returns

A new point with each coordinate divided by s.

Definition at line 354 of file point.H.

References x_, and y_.

operator<()

bool Aleph::Point::operator< ( const Point &  point ) const

inlinenoexcept

Defines a strict lexicographical ordering for points.

Parameters

point

The other point to compare against.

Returns

true if this point is less than point (first by x, then by y).

Definition at line 279 of file point.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), x_, and y_.

operator==()

bool Aleph::Point::operator== ( const Point &  point ) const

inlinenoexcept

Checks for exact equality between two points.

Parameters

point

The other point to compare against.

Returns

true if both x and y coordinates are identical, false otherwise.

Definition at line 259 of file point.H.

References Aleph::and, x_, and y_.

Referenced by TEST().

rightmost_point()

const Point & Aleph::Point::rightmost_point ( ) const

inline

Returns the rightmost point (largest x-coordinate).

For a Point, it's itself.

Returns

A const reference to itself.

Definition at line 706 of file point.H.

Referenced by TEST_F(), TEST_F(), TEST_F(), and TEST_F().

rotate()

Point Aleph::Point::rotate ( const Geom_Number &  angle ) const

inline

Rotates the point around the origin by a given angle.

Parameters

angle

The rotation angle in radians.

Returns

A new Point with the rotated coordinates.

Definition at line 415 of file point.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::cosinus(), Aleph::sinus(), x_, and y_.

Referenced by TEST_F(), and TEST_F().

to_string()

std::string Aleph::Point::to_string ( ) const

inline

Returns a string representation of the point as "(x,y)".

Returns

A std::string representing the point.

Definition at line 640 of file point.H.

References Aleph::geom_number_to_double(), x_, and y_.

Referenced by Eepic_Triangle::draw(), Eepic_Plane::draw(), Eepic_Plane::draw_ellipse(), Eepic_Plane::draw_point(), Eepic_Plane::draw_point_text(), Eepic_Plane::draw_text(), main(), make_random_polygon(), operator std::string(), Aleph::operator<<(), print_case(), scenario_exact_intersection(), Aleph::Segment::to_string(), Aleph::Ellipse::to_string(), Aleph::RotatedEllipse::to_string(), and write_tree().

Friends And Related Symbol Documentation

Polar_Point

friend class Polar_Point

friend

Definition at line 224 of file point.H.

Segment

friend class Segment

friend

Definition at line 222 of file point.H.

Triangle

friend class Triangle

friend

Definition at line 223 of file point.H.

Member Data Documentation

x_

Geom_Number Aleph::Point::x_

private

Definition at line 226 of file point.H.

Referenced by cross(), distance_squared_to(), distance_to(), dot(), get_x(), norm(), norm_squared(), operator*(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator<(), operator==(), rotate(), and to_string().

y_

Geom_Number Aleph::Point::y_

private

Definition at line 227 of file point.H.

Referenced by cross(), distance_squared_to(), distance_to(), dot(), get_y(), norm(), norm_squared(), operator*(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator<(), operator==(), rotate(), and to_string().

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The documentation for this class was generated from the following file:

• point.H