JGEOMETRY2D Namespace Reference

Auxiliary classes and methods for 2D geometrical objects and operations. More...

Classes
class	JAngle2D
	Data structure for angle in two dimensions. More...
class	JAxis2D
	Axis object. More...
class	JCircle2D
	Data structure for circle in two dimensions. More...
class	JDirection2D
	Data structure for direction in two dimensions. More...
struct	JEigenValues2D
	Eigen values in 2D. More...
class	JCenter2D
	Center. More...
class	JConvexHull2D
	Auxiliary class for convex hull determination in X-Y plane. More...
class	JSmallestDistance2D
	Auxiliary class for determination of smallest distance between pair of 2D points. More...
struct	JOmega2D_t
	Base class for direction set. More...
class	JOmega2D
	Direction set covering (part of) circle. More...
class	JPosition2D
	Data structure for position in two dimensions. More...
class	JRotation2D
	Rotation matrix. More...
class	JRotator2D
	Rotation set. More...
class	JSegment2D
	Line segment in two dimensions. More...
class	JVector2D
	Data structure for vector in two dimensions. More...
class	JVersor2D
	Data structure for normalised vector in two dimensions. More...

Typedefs
typedef std::vector< JRotation2D >	JRotator2D_t
	Type definition of rotation set. More...
typedef std::pair< JPosition2D, JPosition2D >	JSegment2D_t
	Type definition of line segment in two dimensions. More...
typedef std::pair< double, double >	JRangeX
	Type definition of range along x-axis. More...
typedef std::pair< double, double >	JRangeY
	Type definition of range along y-axis. More...

Functions
void	randomize (JPosition2D *p)
	Randomize position. More...
template<class T >
bool	getCCW (const T &a, const T &b, const T &c)
	Check sequence of three points in X-Y plane. More...
template<class T >
double	getArea2D (T __begin, T __end)
	Get area of a convex polygon. More...
template<class T >
bool	inside2D (T __begin, T __end, const JVector2D &pos)
	Check if given point is inside a convex polygon. More...
template<class T >
bool	inside2D (T __begin, T __end1, T __end2, const JVector2D &pos)
	Check if given point is inside a convex polygon. More...
bool	getCCW (const JVector2D &a, const JVector2D &b, const JVector2D &c)
	Check sequence of three points. More...

Variables
static const JConvexHull2D	getConvexHull2D
	Function object for convex hull determination. More...
static const JSmallestDistance2D	getSmallestDistance2D
	Function object for smallest distance determination. More...
static const JVersor2D	JVersor2X_t (1, 0)
	unit x-vector More...
static const JVersor2D	JVersor2Y_t (0, 1)
	unit y-vector More...

Detailed Description

Auxiliary classes and methods for 2D geometrical objects and operations.

Author

mdejong

Typedef Documentation

typedef std::vector<JRotation2D> JGEOMETRY2D::JRotator2D_t

Type definition of rotation set.

Definition at line 23 of file JRotator2D.hh.

typedef std::pair<JPosition2D, JPosition2D> JGEOMETRY2D::JSegment2D_t

Type definition of line segment in two dimensions.

Definition at line 29 of file JSegment2D.hh.

typedef std::pair<double, double> JGEOMETRY2D::JRangeX

Type definition of range along x-axis.

Definition at line 23 of file JVector2D.hh.

typedef std::pair<double, double> JGEOMETRY2D::JRangeY

Type definition of range along y-axis.

Definition at line 24 of file JVector2D.hh.

Function Documentation

void JGEOMETRY2D::randomize ( JPosition2D *  p )

inline

Randomize position.

Parameters

p	pointer to valid object

Definition at line 28 of file JGeometry2DTestkit.hh.

  {
    new (p) JPosition2D(getRandom<double>(-1.0, +1.0),
                        getRandom<double>(-1.0, +1.0));
  };

template<class T >

bool JGEOMETRY2D::getCCW ( const T &  a, const T &  b, const T &  c  )

inline

Check sequence of three points in X-Y plane.

Parameters

a	1st point
b	2nd point
c	3rd point

Returns

true if points a, b, c are counter clockwise; else false

Definition at line 36 of file JGeometry2DToolkit.hh.

  {
    const double A = a.getX() - b.getX();
    const double B = a.getY() - b.getY();
    const double C = c.getX() - b.getX();
    const double D = c.getY() - b.getY();

    return A*D <= B*C;
  }

template<class T >

double JGEOMETRY2D::getArea2D ( T  __begin, T  __end  )

inline

Get area of a convex polygon.

Parameters

__begin	begin of data
__end	end of data

Returns

area

Definition at line 280 of file JGeometry2DToolkit.hh.

  {
    using namespace std;

    if (distance(__begin,__end) >= 3) {

      double A = 0.0;

      T i, j, k;
      
      i = j = k = __begin;
      
      for (++j, ++(++k); k != __end; ++i, ++j, ++k) {
        A += j->getX() * (k->getY()  -  i->getY());
      }
      
      k = __begin;
      
      A +=  j->getX() * (k->getY()  -  i->getY());
      
      ++i;
      j = k; 
      ++k;
      
      A +=  j->getX() * (k->getY()  -  i->getY());

      return 0.5 * fabs(A);

    } else {

      return 0.0;
    }
  }

template<class T >

bool JGEOMETRY2D::inside2D ( T  __begin, T  __end, const JVector2D &  pos  )

inline

Check if given point is inside a convex polygon.

Parameters

__begin	begin of data
__end	end of data
pos	position

Returns

true if inside; else false

Definition at line 324 of file JGeometry2DToolkit.hh.

  {
    using namespace std;

    if (distance(__begin,__end) >= 2) {

      T i = __begin, j = __begin;
      
      for (++j; j != __end; ++i, ++j) {

        if (!getCCW(*i, *j, pos)) {
          return false;
        }
      }

      j = __begin;

      return getCCW(*i, *j, pos);

    } else {

      return false;
    }
  }

template<class T >

bool JGEOMETRY2D::inside2D ( T  __begin, T  __end1, T  __end2, const JVector2D &  pos  )

inline

Check if given point is inside a convex polygon.

Parameters

__begin	begin of data
__end1	end of lower hull
__end2	end of upper hull
pos	position

Returns

true if inside; else false

Definition at line 360 of file JGeometry2DToolkit.hh.

  {
    using namespace std;

    if (distance(__begin,__end2) >= 3) {

      if (pos.getX() < __begin->getX()) {
        return false;
      }

      T i = lower_bound(__begin, __end1, pos, JConvexHull2D::sortUpperHull);

      if (i == __end1) {
        return false;
      }

      T j = i--;

      if (!getCCW(*i, *j, pos)) {
        return false;
      }

      i = lower_bound(__end1, __end2, pos, JConvexHull2D::sortLowerHull);
      j = i--;

      if (j == __end2) {
        j = __begin;
      }

      return getCCW(*i, *j, pos);

    } else {

      return false;
    }
  }

bool JGEOMETRY2D::getCCW ( const JVector2D &  a, const JVector2D &  b, const JVector2D &  c  )

inline

Check sequence of three points.

Parameters

a	1st point
b	2nd point
c	3rd point

Returns

true if points a, b, c are counter clockwise; else false

Definition at line 270 of file JVector2D.hh.

  {
    const double A = a.getX() - b.getX();
    const double B = a.getY() - b.getY();
    const double C = c.getX() - b.getX();
    const double D = c.getY() - b.getY();
    
    return A*D <= B*C;
  }

Variable Documentation

const JConvexHull2D JGEOMETRY2D::getConvexHull2D

static

Function object for convex hull determination.

Definition at line 269 of file JGeometry2DToolkit.hh.

const JSmallestDistance2D JGEOMETRY2D::getSmallestDistance2D

static

Function object for smallest distance determination.

Definition at line 660 of file JGeometry2DToolkit.hh.

const JVersor2D JGEOMETRY2D::JVersor2X_t(1, 0)

static

unit x-vector

const JVersor2D JGEOMETRY2D::JVersor2Y_t(0, 1)

static

unit y-vector