Utils::Segment2D< Real > Class Template Reference

A class representing a 2D line segment defined by two endpoints. More...

#include <Utils_GG2D.hh>

Public Member Functions
	Segment2D ()=default
	Default constructor for the segment.
	Segment2D (Segment2D< Real > const &S)
	Copy constructor for the segment.
	Segment2D (Point2D< Real > const &A, Point2D< Real > const &B)
	Constructor to create a segment from two points.
void	setup (Point2D< Real > const &A, Point2D< Real > const &B)
	Setup the endpoints of the segment using Point2D objects.
void	setup (Real const A[], Real const B[])
	Setup the endpoints of the segment using arrays.
bool	projection (Point2D< Real > const &P, Real &s) const
	Projects a point onto the segment.
Point2D< Real >	projection (Point2D< Real > const &P, Real &s, Real &t) const
	Projects a point onto the segment and returns the projected point.
Point2D< Real >	eval (Real &s) const
	Evaluates the segment at a given parameter s.
Point2D< Real >	eval (Real &s, Real &t) const
	Evaluates the segment based on two parameters s and t.
Point2D< Real > const &	Pa () const
	Returns the first endpoint of the segment.
Point2D< Real > const &	Pb () const
	Returns the second endpoint of the segment.
void	bbox (Point2D< Real > &pmin, Point2D< Real > &pmax) const
	Computes the bounding box of the segment.
bool	intersect (Segment2D< Real > const &S, Real &s, Real &t) const
	Checks for intersection with another segment.

Detailed Description

template<typename Real>
class Utils::Segment2D< Real >

A class representing a 2D line segment defined by two endpoints.

The Segment2D class encapsulates a line segment in a two-dimensional space, defined by two points, \( P_a \) and \( P_b \). It provides methods for setting the endpoints, projecting points onto the segment, evaluating points on the segment, and checking for intersections with other segments.

Template Parameters

Real	The data type used for the coordinates of the segment's endpoints, typically a floating-point type (e.g., float, double).

Features

• Construction: Supports various constructors for initializing the segment.
• Setup: Methods to set or update the endpoints of the segment.
• Projection: Projects a point onto the segment and returns the corresponding scalar parameter.
• Evaluation: Computes points on the segment based on parameter values.
• Bounding Box: Computes the bounding box of the segment.
• Intersection: Checks for intersection with another segment and computes parameters.

Methods

• Segment2D():
  • Default constructor that initializes an empty segment.
• Segment2D(Segment2D<Real> const & S):
  • Copy constructor that initializes a segment as a copy of another segment.
• Segment2D(Point2D<Real> const & A, Point2D<Real> const & B):
  • Constructs a segment from two given points A and B.
• void setup(Point2D<Real> const & A, Point2D<Real> const & B):
  • Sets the endpoints of the segment to the given points A and B.
• void setup(Real const A[], Real const B[]):
  • Sets the endpoints of the segment using arrays representing the coordinates of A and B.
• bool projection(Point2D<Real> const & P, Real & s) const:
  • Projects the point P onto the segment and returns the corresponding parameter s.

  • Returns

    true if the projection is successful, false otherwise.

• Point2D<Real> projection(Point2D<Real> const & P, Real & s, Real & t) const:
  • Projects the point P onto the segment and returns the projected point.
  • Also returns the parameters s and t related to the projections on the segments.
• Point2D<Real> eval(Real & s) const:
  • Evaluates the segment at the parameter s and returns the corresponding point on the segment.
• Point2D<Real> eval(Real & s, Real & t) const:
  • Evaluates the segment based on parameters s and t and returns the corresponding point.
• Point2D<Real> const & Pa() const:
  • Returns the first endpoint \( P_a \) of the segment.
• Point2D<Real> const & Pb() const:
  • Returns the second endpoint \( P_b \) of the segment.
• void bbox(Point2D<Real> & pmin, Point2D<Real> & pmax) const:
  • Computes the bounding box of the segment and updates pmin and pmax with the minimum and maximum points.
• bool intersect(Segment2D<Real> const & S, Real & s, Real & t) const:
  • Checks if the current segment intersects with another segment S.
  • If they intersect, returns true and updates parameters s and t with the intersection information.

Usage

#include "Point2D.h" // Assuming Point2D is defined elsewhere
 
// Create two points for the segment
Point2D<double> A, B;
A.to_eigen() << 1.0, 2.0; // Set coordinates for point A
B.to_eigen() << 3.0, 4.0; // Set coordinates for point B
 
// Create a Segment2D object
Segment2D<double> segment(A, B);
 
// Access endpoints
Point2D<double> start = segment.Pa(); // Get endpoint A
Point2D<double> end = segment.Pb(); // Get endpoint B
 
// Project a point onto the segment
Point2D<double> P;
P.to_eigen() << 2.0, 3.0;
Real param;
segment.projection(P, param); // Project P onto the segment
 
// Evaluate a point on the segment at parameter s
Real s = 0.5;
Point2D<double> eval_point = segment.eval(s); // Evaluate the midpoint of the segment

Constructor & Destructor Documentation

Segment2D() [1/3]

template<typename Real>

Utils::Segment2D< Real >::Segment2D ( )

default

Default constructor for the segment.

Initializes an empty segment with uninitialized endpoints.

Segment2D() [2/3]

template<typename Real>

Utils::Segment2D< Real >::Segment2D ( Segment2D< Real > const & S )

inline

Copy constructor for the segment.

Parameters

S	The segment to copy from.

Segment2D() [3/3]

template<typename Real>

Utils::Segment2D< Real >::Segment2D ( Point2D< Real > const & A, Point2D< Real > const & B )

inline

Constructor to create a segment from two points.

Parameters

A	The first endpoint of the segment.
B	The second endpoint of the segment.

Member Function Documentation

bbox()

template<typename Real>

void Utils::Segment2D< Real >::bbox	(	Point2D< Real > &	pmin,
		Point2D< Real > &	pmax ) const

Computes the bounding box of the segment.

Parameters

pmin	The minimum point of the bounding box.
pmax	The maximum point of the bounding box.

eval() [1/2]

template<typename Real>

Point2D< Real > Utils::Segment2D< Real >::eval

(

Real &

s

)

const

Evaluates the segment at a given parameter s.

Parameters

s	The parameter to evaluate on the segment.

Returns

The point on the segment corresponding to the parameter s.

eval() [2/2]

template<typename Real>

Point2D< Real > Utils::Segment2D< Real >::eval	(	Real &	s,
		Real &	t ) const

Evaluates the segment based on two parameters s and t.

Parameters

s	The first parameter to evaluate.
t	The second parameter to evaluate.

Returns

The point on the segment corresponding to the parameters s and t.

intersect()

template<typename Real>

bool Utils::Segment2D< Real >::intersect	(	Segment2D< Real > const &	S,
		Real &	s,
		Real &	t ) const

Checks for intersection with another segment.

Parameters

S	The other segment to check for intersection.
s	The parameter along the current segment at the intersection point.
t	The parameter along the other segment at the intersection point.

Returns

true if the segments intersect, false otherwise.

Pa()

template<typename Real>

Point2D< Real > const & Utils::Segment2D< Real >::Pa ( ) const

inline

Returns the first endpoint of the segment.

Returns

The first endpoint \( P_a \).

Pb()

template<typename Real>

Point2D< Real > const & Utils::Segment2D< Real >::Pb ( ) const

inline

Returns the second endpoint of the segment.

Returns

The second endpoint \( P_b \).

projection() [1/2]

template<typename Real>

bool Utils::Segment2D< Real >::projection	(	Point2D< Real > const &	P,
		Real &	s ) const

Projects a point onto the segment.

Parameters

P	The point to be projected onto the segment.
s	The parameter along the segment where the projection occurs.

Returns

true if the projection is successful, false otherwise.

projection() [2/2]

template<typename Real>

Point2D< Real > Utils::Segment2D< Real >::projection	(	Point2D< Real > const &	P,
		Real &	s,
		Real &	t ) const

Projects a point onto the segment and returns the projected point.

Parameters

P	The point to be projected onto the segment.
s	The parameter along the segment where the projection occurs.
t	The parameter along the other segment (if applicable).

Returns

The projected point on the segment.

setup() [1/2]

template<typename Real>

void Utils::Segment2D< Real >::setup ( Point2D< Real > const & A, Point2D< Real > const & B )

inline

Setup the endpoints of the segment using Point2D objects.

Parameters

A	The first endpoint of the segment.
B	The second endpoint of the segment.

setup() [2/2]

template<typename Real>

void Utils::Segment2D< Real >::setup ( Real const A[], Real const B[] )

inline

Setup the endpoints of the segment using arrays.

Parameters

A	Array containing the coordinates of the first endpoint.
B	Array containing the coordinates of the second endpoint.

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

• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_GG2D.hh
• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_GG2D.cc