point.H File Reference

2D point and geometric utilities. More...

#include <cmath>
#include <cstddef>
#include <limits>
#include <array>
#include <functional>
#include <iomanip>
#include <string>
#include <ahAssert.H>
#include <ahUtils.H>
#include <ah-errors.H>
#include <utility>
#include <gmpfrxx.h>

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Classes
struct	Aleph::Geom_Object
	Base class for all geometric objects. More...
class	Aleph::Point
	Represents a point with rectangular coordinates in a 2D plane. More...
class	Aleph::Polar_Point
	Polar representation of a 2D point. More...
class	Aleph::Segment
	Represents a line segment between two points. More...
class	Aleph::Triangle
	A non-degenerate triangle defined by three points. More...
class	Aleph::Rectangle
	An axis-aligned rectangle. More...
class	Aleph::Ellipse
	An axis-aligned ellipse. More...
class	Aleph::RotatedEllipse
	An ellipse with arbitrary rotation. More...
struct	Aleph::RotatedEllipse::ExtremalPoints
	Holds the four axis-extremal points of a rotated ellipse. More...
class	Aleph::Text
	Represents a text string positioned at a 2D point. More...
class	Aleph::Point3D
	Represents a point in 3D space with exact rational coordinates. More...
class	Aleph::Segment3D
	Represents a line segment in 3D space. More...
class	Aleph::Triangle3D
	Represents a triangle in 3D space defined by three points. More...
struct	Aleph::Triangle3D::BaryCoords
	Structure to hold barycentric coordinates. More...
class	Aleph::Tetrahedron
	Represents a tetrahedron in 3D space defined by four points. More...
struct	Aleph::Tetrahedron::Faces
	A struct holding the four faces of the tetrahedron. More...
struct	std::hash< Aleph::Point >
	Hash specialization for Aleph::Point. More...

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.
namespace	std
	STL namespace.

Typedefs
using	Aleph::Geom_Number = mpq_class
	Numeric type used by the geometry module.

Enumerations
enum class	Aleph::Orientation { Aleph::CCW , Aleph::CW , Aleph::COLLINEAR }
	Classification of three-point orientation. More...
enum class	Aleph::InCircleResult { Aleph::INSIDE , Aleph::ON_CIRCLE , Aleph::OUTSIDE , Aleph::DEGENERATE }
	Classification of a point with respect to a triangle circumcircle. More...

Functions
double	Aleph::geom_number_to_double (const Geom_Number &n)
	Converts a Geom_Number to its double precision representation.
const Geom_Number &	Aleph::geom_pi ()
	High-precision pi value for computations that require Geom_Number.
Geom_Number	Aleph::area_of_parallelogram (const Point &a, const Point &b, const Point &c)
	Compute the signed area of the parallelogram defined by vectors a->b and a->c.
Geom_Number	Aleph::euclidean_distance (const Geom_Number &x, const Geom_Number &y)
	Euclidean distance (hypotenuse) of the vector (x, y).
Geom_Number	Aleph::pitag (const Geom_Number &x, const Geom_Number &y)
Geom_Number	Aleph::arctan (const Geom_Number &m)
	Arc tangent of m (wrapper over mpfr).
Geom_Number	Aleph::arctan2 (const Geom_Number &m, const Geom_Number &n)
	Two-argument arc tangent (wrapper over mpfr).
Geom_Number	Aleph::sinus (const Geom_Number &x)
	Sine of x (wrapper over mpfr).
Geom_Number	Aleph::cosinus (const Geom_Number &x)
	Cosine of x (wrapper over mpfr).
Geom_Number	Aleph::square_root (const Geom_Number &x)
	Square root of x (wrapper over mpfr).
Point	Aleph::operator* (const Geom_Number &s, const Point &p)
	Scalar multiplication with commutative order.
size_t	Aleph::approximate_string_size (const std::string &str)
	Estimate the count of printable characters in a LaTeX string.
Orientation	Aleph::orientation (const Point &a, const Point &b, const Point &c)
	Return the orientation of the triple (a, b, c).
Geom_Number	Aleph::in_circle_determinant (const Point &a, const Point &b, const Point &c, const Point &p)
	Return the exact in-circle determinant for (a,b,c,p).
InCircleResult	Aleph::in_circle (const Point &a, const Point &b, const Point &c, const Point &p)
	Classify point p against circumcircle of triangle (a,b,c), exactly.
bool	Aleph::on_segment (const Segment &s, const Point &p)
	Return true if p lies on segment s (exact).
bool	Aleph::segments_intersect (const Segment &s1, const Segment &s2)
	Return true if segments s1 and s2 intersect (including endpoints).
bool	Aleph::segments_intersect (const Point &a, const Point &b, const Point &c, const Point &d)
	Return true if segments (a,b) and (c,d) intersect (including endpoints).
Point	Aleph::segment_intersection_point (const Segment &s1, const Segment &s2)
	Compute the exact intersection point of segments s1 and s2.
Geom_Number	Aleph::area_of_triangle (const Point &a, const Point &b, const Point &c)
	Return the (unsigned) area of triangle (a, b, c) as an exact rational.
Geom_Number	Aleph::scalar_triple_product (const Point3D &a, const Point3D &b, const Point3D &c)
	Scalar triple product: a · (b × c).
std::ostream &	Aleph::operator<< (std::ostream &o, const Point &p)
std::ostream &	Aleph::operator<< (std::ostream &o, const Segment &s)
std::ostream &	Aleph::operator<< (std::ostream &o, const Triangle &t)
std::ostream &	Aleph::operator<< (std::ostream &o, const Rectangle &r)
std::ostream &	Aleph::operator<< (std::ostream &o, const Ellipse &e)
std::ostream &	Aleph::operator<< (std::ostream &o, const RotatedEllipse &e)
std::ostream &	Aleph::operator<< (std::ostream &o, const Point3D &p)
std::ostream &	Aleph::operator<< (std::ostream &o, const Segment3D &s)
std::ostream &	Aleph::operator<< (std::ostream &o, const Triangle3D &t)
std::ostream &	Aleph::operator<< (std::ostream &o, const Tetrahedron &t)

Variables
constexpr double	Aleph::PI = 3.1415926535897932384626433832795028841971693993751
constexpr double	Aleph::PI_2 = PI / 2.0
constexpr double	Aleph::PI_4 = PI / 4.0

Detailed Description

2D point and geometric utilities.

This file provides classes for 2D points and geometric operations including distance calculations, vector operations, and coordinate transformations. Used by graph visualization and geometric algorithms.

Author

Leandro Rabindranath León

Definition in file point.H.