codac2_geometry.h File Reference

#include "codac2_BoolInterval.h"
#include "codac2_IntervalVector.h"

Include dependency graph for codac2_geometry.h:

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Enumerations
enum class	codac2::OrientationInterval { }
	Enumeration representing feasible orientations. Can be used to assess an oriented angle, or the alignement of three points. More...

Functions
std::ostream &	codac2::operator<< (std::ostream &os, const OrientationInterval &x)
	Streams out a OrientationInterval.
OrientationInterval	codac2::orientation (const IntervalVector &p1, const IntervalVector &p2, const IntervalVector &p3)
	Computes the orientation of an ordered triplet of 2D points.
BoolInterval	codac2::aligned (const IntervalVector &p1, const IntervalVector &p2, const IntervalVector &p3)
	Checks whether three 2D points are aligned (colinear).
std::vector< IntervalVector >	codac2::convex_hull (std::vector< IntervalVector > pts)
	Computes the convex hull of a set of 2d points.

Detailed Description

Date

2024

Author

Simon Rohou

Copyright

Copyright 2024 Codac Team

License: GNU Lesser General Public License (LGPL)

Enumeration Type Documentation

OrientationInterval

enum class codac2::OrientationInterval

strong

Enumeration representing feasible orientations. Can be used to assess an oriented angle, or the alignement of three points.

The logical operator | can be used to combine OrientationInterval values.

Enumerator
UNKNOWN	UNKNOWN: the orientation can be either clockwise, counter-clockwise, or aligned.

  {
    COLINEAR = 0x01,
    CLOCKWISE = 0x02,
    COUNTERCLOCKWISE = 0x04,
    EMPTY = 0x00,
    UNKNOWN = 0x01 | 0x02 | 0x04
  };

Function Documentation

operator<<()

std::ostream & codac2::operator<< ( std::ostream & os, const OrientationInterval & x )

inline

Streams out a OrientationInterval.

Parameters

os	The stream to be updated
x	The orientation interval to stream out

Returns

A Reference to the updated stream

  {
    if(x == OrientationInterval::EMPTY)
      os << "[ empty ]";
    else if(x == OrientationInterval::COLINEAR)
      os << "[ col ]";
    else if(x == OrientationInterval::CLOCKWISE)
      os << "[ cw ]";
    else if(x == OrientationInterval::COUNTERCLOCKWISE)
      os << "[ ccw ]";
    else if(x == (OrientationInterval::COLINEAR | OrientationInterval::CLOCKWISE))
      os << "[ col, cw ]";
    else if(x == (OrientationInterval::COLINEAR | OrientationInterval::COUNTERCLOCKWISE))
      os << "[ col, ccw ]";
    else if(x == OrientationInterval::UNKNOWN)
      os << "[ col, cw, ccw ]";
    return os;
  }

orientation()

OrientationInterval codac2::orientation	(	const IntervalVector &	p1,
		const IntervalVector &	p2,
		const IntervalVector &	p3 )

Computes the orientation of an ordered triplet of 2D points.

Determines whether the oriented angle \(\widehat{p_1 p_2 p_3}\) is positive (counterclockwise), negative (clockwise), or if the points are colinear (flat or 0 angle). Depending on floating point uncertainties, the test may not be able to conclude (a UNKNOWN value would then be returned).

Parameters

p1	First point (2d IntervalVector) of the triplet.
p2	Second point (2d IntervalVector) of the triplet (vertex of the angle).
p3	Third point (2d IntervalVector) of the triplet.

Returns

An orientation of type OrientationInterval

aligned()

BoolInterval codac2::aligned	(	const IntervalVector &	p1,
		const IntervalVector &	p2,
		const IntervalVector &	p3 )

Checks whether three 2D points are aligned (colinear).

Determines if the points lie on the same straight line using an orientation test (cross product). Depending on floating point uncertainties, the test may not be able to conclude (a UNKNOWN value would then be returned).

Parameters

p1	First point (2d IntervalVector) of the triplet.
p2	Second point (2d IntervalVector) of the triplet.
p3	Third point (2d IntervalVector) of the triplet.

Returns

A BooleanInterval

convex_hull()

std::vector< IntervalVector > codac2::convex_hull

(

std::vector< IntervalVector >

pts

)

Computes the convex hull of a set of 2d points.

Given a set of 2d points enclosed in tiny boxes, the function computes their convex hull. The method is based on a Graham scan algorithm. The output list of the algorithm is a subset of the input list, with same uncertainties and a possible different order.

Parameters

pts	2d points in any order

Returns

Points on the convex hull in counterclockwise order.