constructions/kernel_ftC2.h File Reference

#include <CGAL/determinant.h>

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Functions
template<class FT >
CGAL_BEGIN_NAMESPACE CGAL_KERNEL_INLINE void	midpointC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, FT &x, FT &y)
template<class FT >
CGAL_KERNEL_LARGE_INLINE void	circumcenter_translateC2 (const FT &dqx, const FT &dqy, const FT &drx, const FT &dry, FT &dcx, FT &dcy)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE void	circumcenterC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, FT &x, FT &y)
template<class FT >
void	line_from_pointsC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, FT &a, FT &b, FT &c)
template<class FT >
void	line_from_point_directionC2 (const FT &px, const FT &py, const FT &dx, const FT &dy, FT &a, FT &b, FT &c)
template<class FT >
CGAL_KERNEL_INLINE void	bisector_of_pointsC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, FT &a, FT &b, FT &c)
template<class FT >
FT	line_y_at_xC2 (const FT &a, const FT &b, const FT &c, const FT &x)
template<class FT >
void	line_get_pointC2 (const FT &a, const FT &b, const FT &c, int i, FT &x, FT &y)
template<class FT >
void	perpendicular_through_pointC2 (const FT &la, const FT &lb, const FT &px, const FT &py, FT &a, FT &b, FT &c)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE void	line_project_pointC2 (const FT &la, const FT &lb, const FT &lc, const FT &px, const FT &py, FT &x, FT &y)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE FT	squared_circumradiusC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, FT &x, FT &y)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE FT	squared_circumradiusC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry)
template<class FT >
CGAL_KERNEL_INLINE FT	squared_distanceC2 (const FT &px, const FT &py, const FT &qx, const FT &qy)
template<class FT >
CGAL_KERNEL_INLINE FT	scaled_distance_to_lineC2 (const FT &la, const FT &lb, const FT &lc, const FT &px, const FT &py)
template<class FT >
CGAL_KERNEL_INLINE FT	scaled_distance_to_directionC2 (const FT &la, const FT &lb, const FT &px, const FT &py)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE FT	scaled_distance_to_lineC2 (const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry)

Function Documentation

CGAL_KERNEL_INLINE void bisector_of_pointsC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		FT &	a,
		FT &	b,
		FT &	c
	)

Definition at line 134 of file constructions/kernel_ftC2.h.

References CGAL_NTS, and square().

{
  a = FT(2)*(px - qx);
  b = FT(2)*(py - qy);
  c = CGAL_NTS square(qx) + CGAL_NTS square(qy) -
      CGAL_NTS square(px) - CGAL_NTS square(py);
}

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CGAL_KERNEL_LARGE_INLINE void circumcenter_translateC2	(	const FT &	dqx,
		const FT &	dqy,
		const FT &	drx,
		const FT &	dry,
		FT &	dcx,
		FT &	dcy
	)

Definition at line 69 of file constructions/kernel_ftC2.h.

References CGAL_kernel_assertion, CGAL_NTS, den, det2x2_by_formula(), and square().

Referenced by circumcenterC2(), and squared_circumradiusC2().

{
  // Given 3 points P, Q, R, this function takes as input:
  // qx-px, qy-py, rx-px, ry-py.  And returns cx-px, cy-py,
  // where (cx, cy) are the coordinates of the circumcenter C.

  // What we do is intersect the bisectors.
  FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
  FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
  FT den = FT(2) * det2x2_by_formula(dqx, dqy, drx, dry);

  // The 3 points aren't collinear.
  // Hopefully, this is already checked at the upper level.
  CGAL_kernel_assertion ( den != FT(0) );

  // One possible optimization here is to precompute 1/den, to avoid one
  // division.  However, we loose precision, and it's maybe not worth it (?).
  dcx =   det2x2_by_formula (dry, dqy, r2, q2) / den;
  dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
}

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CGAL_KERNEL_MEDIUM_INLINE void circumcenterC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		const FT &	rx,
		const FT &	ry,
		FT &	x,
		FT &	y
	)

Definition at line 95 of file constructions/kernel_ftC2.h.

References circumcenter_translateC2().

{
  circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y);
  x += px;
  y += py;
}

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void line_from_point_directionC2 ( const FT &  px, const FT &  py, const FT &  dx, const FT &  dy, FT &  a, FT &  b, FT &  c  )

inline

Definition at line 122 of file constructions/kernel_ftC2.h.

References dx, and dy.

{
  a = - dy;
  b = dx;
  c = px*dy - py*dx;
}

void line_from_pointsC2 ( const FT &  px, const FT &  py, const FT &  qx, const FT &  qy, FT &  a, FT &  b, FT &  c  )

inline

Definition at line 108 of file constructions/kernel_ftC2.h.

{
  a = py - qy;
  b = qx - px;
  // Suggested by Serge Pashkov (psw@rt.kiam.ru) for better numeric stability.
  c = -px*a - py*b;
  // c = px*qy - py*qx;
}

void line_get_pointC2 ( const FT &  a, const FT &  b, const FT &  c, int  i, FT &  x, FT &  y  )

inline

Definition at line 155 of file constructions/kernel_ftC2.h.

{
  if (b==FT(0))
    {
      x = (-b-c)/a + FT(i)*b;
      y = FT(1) - FT(i)*a;
    }
  else
    {
      x = FT(1) + FT(i)*b;
      y = -(a+c)/b - FT(i)*a;
    }
}

CGAL_KERNEL_MEDIUM_INLINE void line_project_pointC2	(	const FT &	la,
		const FT &	lb,
		const FT &	lc,
		const FT &	px,
		const FT &	py,
		FT &	x,
		FT &	y
	)

Definition at line 185 of file constructions/kernel_ftC2.h.

References CGAL_NTS, d, and square().

{
#if 1
  // Original old version
  if (la==FT(0)) // horizontal line
  {
    x = px;
    y = -lc/lb;
  }
  else if (lb==FT(0)) // vertical line
  {
    x = -lc/la;
    y = py;
  }
  else
  {
    FT ab = la/lb, ba = lb/la, ca = lc/la;
    y = ( -px + ab*py - ca ) / ( ba + ab );
    x = -ba * y - ca;
  }
#else
  // New version, with more multiplications, but less divisions and tests.
  // Let's compare the results of the 2, benchmark them, as well as check
  // the precision with the intervals.
  FT a2 = CGAL_NTS square(la);
  FT b2 = CGAL_NTS square(lb);
  FT d = a2 + b2;
  x = (la * (lb * py - lc) - px * b2) / d;
  y = (lb * (lc - la * px) + py * a2) / d;
#endif
}

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FT line_y_at_xC2 ( const FT &  a, const FT &  b, const FT &  c, const FT &  x  )

inline

Definition at line 147 of file constructions/kernel_ftC2.h.

{
  return (-a*x-c) / b;
}

CGAL_BEGIN_NAMESPACE CGAL_KERNEL_INLINE void midpointC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		FT &	x,
		FT &	y
	)

Definition at line 58 of file constructions/kernel_ftC2.h.

{
  x = (px+qx) / FT(2);
  y = (py+qy) / FT(2);
}

void perpendicular_through_pointC2 ( const FT &  la, const FT &  lb, const FT &  px, const FT &  py, FT &  a, FT &  b, FT &  c  )

inline

Definition at line 173 of file constructions/kernel_ftC2.h.

{
  a = -lb;
  b = la;
  c = lb * px - la * py;
}

CGAL_KERNEL_INLINE FT scaled_distance_to_directionC2	(	const FT &	la,
		const FT &	lb,
		const FT &	px,
		const FT &	py
	)

Definition at line 269 of file constructions/kernel_ftC2.h.

Referenced by cmp_signed_dist_to_directionC2().

{
  // scalar product with direction
  return la*px + lb*py;
}

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CGAL_KERNEL_INLINE FT scaled_distance_to_lineC2	(	const FT &	la,
		const FT &	lb,
		const FT &	lc,
		const FT &	px,
		const FT &	py
	)

Definition at line 258 of file constructions/kernel_ftC2.h.

Referenced by cmp_signed_dist_to_lineC2().

{
  // for comparisons, use distance_to_directionsC2 instead
  // since lc is irrelevant
  return la*px + lb*py + lc;
}

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CGAL_KERNEL_MEDIUM_INLINE FT scaled_distance_to_lineC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		const FT &	rx,
		const FT &	ry
	)

Definition at line 279 of file constructions/kernel_ftC2.h.

References det2x2_by_formula().

{
  return det2x2_by_formula(px-rx,py-ry,qx-rx,qy-ry);
}

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CGAL_KERNEL_MEDIUM_INLINE FT squared_circumradiusC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		const FT &	rx,
		const FT &	ry,
		FT &	x,
		FT &	y
	)

Definition at line 222 of file constructions/kernel_ftC2.h.

References CGAL_NTS, circumcenter_translateC2(), and square().

{
  circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y);
  FT r2 = CGAL_NTS square(x) + CGAL_NTS square(y);
  x += px;
  y += py;
  return r2;
}

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CGAL_KERNEL_MEDIUM_INLINE FT squared_circumradiusC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy,
		const FT &	rx,
		const FT &	ry
	)

Definition at line 237 of file constructions/kernel_ftC2.h.

References CGAL_NTS, circumcenter_translateC2(), square(), x, and y.

{
  FT x, y;
  circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y);
  return CGAL_NTS square(x) + CGAL_NTS square(y);
}

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CGAL_KERNEL_INLINE FT squared_distanceC2	(	const FT &	px,
		const FT &	py,
		const FT &	qx,
		const FT &	qy
	)

Definition at line 249 of file constructions/kernel_ftC2.h.

References CGAL_NTS, and square().

Referenced by cmp_dist_to_pointC2().

{
  return CGAL_NTS square(px-qx) + CGAL_NTS square(py-qy);
}

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