predicates/kernel_ftC3.h File Reference

#include <CGAL/predicates/sign_of_determinant.h>
#include <CGAL/predicates/kernel_ftC2.h>
#include <CGAL/constructions/kernel_ftC3.h>

Include dependency graph for predicates/kernel_ftC3.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Functions
template<class FT >
CGAL_BEGIN_NAMESPACE CGAL_KERNEL_MEDIUM_INLINE Comparison_result	compare_lexicographically_xyzC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	strict_dominanceC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	dominanceC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	collinearC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE Orientation	orientationC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz, const FT &sx, const FT &sy, const FT &sz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE Orientation	coplanar_orientationC3 (const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz, const FT &sx, const FT &sy, const FT &sz, const FT &px, const FT &py, const FT &pz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	collinear_are_ordered_along_lineC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	collinear_are_strictly_ordered_along_lineC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	equal_directionC3 (const FT &dx1, const FT &dy1, const FT &dz1, const FT &dx2, const FT &dy2, const FT &dz2)
template<class FT >
CGAL_KERNEL_LARGE_INLINE Oriented_side	side_of_oriented_planeC3 (const FT &a, const FT &b, const FT &c, const FT &d, const FT &px, const FT &py, const FT &pz)
template<class FT >
CGAL_KERNEL_LARGE_INLINE Oriented_side	side_of_oriented_sphereC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz, const FT &sx, const FT &sy, const FT &sz, const FT &tx, const FT &ty, const FT &tz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE Bounded_side	side_of_bounded_sphereC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz, const FT &sx, const FT &sy, const FT &sz, const FT &tx, const FT &ty, const FT &tz)
template<class FT >
CGAL_KERNEL_INLINE Comparison_result	cmp_dist_to_pointC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_larger_dist_to_pointC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_smaller_dist_to_pointC3 (const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz, const FT &rx, const FT &ry, const FT &rz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE Comparison_result	cmp_signed_dist_to_directionC3 (const FT &pa, const FT &pb, const FT &pc, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_larger_signed_dist_to_directionC3 (const FT &pa, const FT &pb, const FT &pc, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_smaller_signed_dist_to_directionC3 (const FT &pa, const FT &pb, const FT &pc, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE Comparison_result	cmp_signed_dist_to_planeC3 (const FT &ppx, const FT &ppy, const FT &ppz, const FT &pqx, const FT &pqy, const FT &pqz, const FT &prx, const FT &pry, const FT &prz, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_larger_signed_dist_to_planeC3 (const FT &ppx, const FT &ppy, const FT &ppz, const FT &pqx, const FT &pqy, const FT &pqz, const FT &prx, const FT &pry, const FT &prz, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)
template<class FT >
CGAL_KERNEL_MEDIUM_INLINE bool	has_smaller_signed_dist_to_planeC3 (const FT &ppx, const FT &ppy, const FT &ppz, const FT &pqx, const FT &pqy, const FT &pqz, const FT &prx, const FT &pry, const FT &prz, const FT &px, const FT &py, const FT &pz, const FT &qx, const FT &qy, const FT &qz)

Function Documentation

CGAL_KERNEL_INLINE Comparison_result cmp_dist_to_pointC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 259 of file predicates/kernel_ftC3.h.

References CGAL_NTS, CGAL::compare(), and squared_distanceC3().

Referenced by cmp_dist_to_point(), has_larger_dist_to_pointC3(), and has_smaller_dist_to_pointC3().

{
  return CGAL_NTS compare(squared_distanceC3(px,py,pz,qx,qy,qz),
                          squared_distanceC3(px,py,pz,rx,ry,rz));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE Comparison_result cmp_signed_dist_to_directionC3	(	const FT &	pa,
		const FT &	pb,
		const FT &	pc,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 292 of file predicates/kernel_ftC3.h.

References CGAL_NTS, CGAL::compare(), and scaled_distance_to_directionC3().

Referenced by cmp_signed_dist_to_plane(), has_larger_signed_dist_to_directionC3(), and has_smaller_signed_dist_to_directionC3().

{
  return CGAL_NTS compare(scaled_distance_to_directionC3(pa,pb,pc,px,py,pz),
                          scaled_distance_to_directionC3(pa,pb,pc,qx,qy,qz));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE Comparison_result cmp_signed_dist_to_planeC3	(	const FT &	ppx,
		const FT &	ppy,
		const FT &	ppz,
		const FT &	pqx,
		const FT &	pqy,
		const FT &	pqz,
		const FT &	prx,
		const FT &	pry,
		const FT &	prz,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 328 of file predicates/kernel_ftC3.h.

References sign_of_determinant3x3().

Referenced by cmp_signed_dist_to_plane(), has_larger_signed_dist_to_planeC3(), and has_smaller_signed_dist_to_planeC3().

{
  return Comparison_result(sign_of_determinant3x3(
              pqx-ppx, pqy-ppy, pqz-ppz,
              prx-ppx, pry-ppy, prz-ppz,
              qx-px,   qy-py,   qz-pz));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool collinear_are_ordered_along_lineC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 149 of file predicates/kernel_ftC3.h.

Referenced by collinear_are_ordered_along_line().

{
  if (px < qx) return !(rx < qx);
  if (qx < px) return !(qx < rx);
  if (py < qy) return !(ry < qy);
  if (qy < py) return !(qy < ry);
  if (pz < qz) return !(rz < qz);
  if (qz < pz) return !(qz < rz);
  return true; // p==q
}

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool collinear_are_strictly_ordered_along_lineC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 167 of file predicates/kernel_ftC3.h.

Referenced by collinear_are_strictly_ordered_along_line().

{
  if (px < qx) return (qx < rx);
  if (qx < px) return (rx < qx);
  if (py < qy) return (qy < ry);
  if (qy < py) return (ry < qy);
  if (pz < qz) return (qz < rz);
  if (qz < pz) return (rz < qz);
  return false; // p==q
}

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool collinearC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 96 of file predicates/kernel_ftC3.h.

References sign_of_determinant2x2(), and ZERO.

Referenced by collinear().

{
  FT dpx = px-rx;
  FT dqx = qx-rx;
  FT dpy = py-ry;
  FT dqy = qy-ry;
  if (sign_of_determinant2x2(dpx, dqx, dpy, dqy) != ZERO)
      return false;
  FT dpz = pz-rz;
  FT dqz = qz-rz;
  return sign_of_determinant2x2(dpx, dqx, dpz, dqz) == ZERO
      && sign_of_determinant2x2(dpy, dqy, dpz, dqz) == ZERO;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_BEGIN_NAMESPACE CGAL_KERNEL_MEDIUM_INLINE Comparison_result compare_lexicographically_xyzC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 61 of file predicates/kernel_ftC3.h.

References CGAL_NTS, CGAL::compare(), and EQUAL.

Referenced by compare_lexicographically_xyz().

{
  Comparison_result c = CGAL_NTS compare(px, qx);
  if (c != EQUAL) return c;
  c = CGAL_NTS compare(py, qy);
  if (c != EQUAL) return c;
  return CGAL_NTS compare(pz, qz);
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE Orientation coplanar_orientationC3	(	const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz,
		const FT &	sx,
		const FT &	sy,
		const FT &	sz,
		const FT &	px,
		const FT &	py,
		const FT &	pz
	)

Definition at line 129 of file predicates/kernel_ftC3.h.

References COLLINEAR, and orientationC2().

Referenced by coplanar_orientation().

{
  Orientation oxy_qrs = orientationC2(qx,qy,rx,ry,sx,sy);
  if (oxy_qrs != COLLINEAR)
      return Orientation( oxy_qrs * orientationC2(qx,qy,rx,ry,px,py));
  Orientation oyz_qrs = orientationC2(qy,qz,ry,rz,sy,sz);
  if (oyz_qrs != COLLINEAR)
      return Orientation( oyz_qrs * orientationC2(qy,qz,ry,rz,py,pz));
  Orientation oxz_qrs = orientationC2(qx,qz,rx,rz,sx,sz);
  assert(oxz_qrs != COLLINEAR);
  return Orientation( oxz_qrs * orientationC2(qx,qz,rx,rz,px,pz));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool dominanceC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 85 of file predicates/kernel_ftC3.h.

References CGAL_NTS, CGAL::compare(), and SMALLER.

{
  return CGAL_NTS compare(px, qx) != SMALLER && 
         CGAL_NTS compare(py, qy) != SMALLER &&
         CGAL_NTS compare(pz, qz) != SMALLER;
}

Here is the call graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool equal_directionC3	(	const FT &	dx1,
		const FT &	dy1,
		const FT &	dz1,
		const FT &	dx2,
		const FT &	dy2,
		const FT &	dz2
	)

Definition at line 184 of file predicates/kernel_ftC3.h.

References CGAL_NTS, sign(), sign_of_determinant2x2(), and ZERO.

{
  return sign_of_determinant2x2(dx1, dy1, dx2, dy2) == ZERO
      && sign_of_determinant2x2(dx1, dz1, dx2, dz2) == ZERO
      && sign_of_determinant2x2(dy1, dz1, dy2, dz2) == ZERO
      && CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
      && CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
      && CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2);
}

Here is the call graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_larger_dist_to_pointC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 271 of file predicates/kernel_ftC3.h.

References cmp_dist_to_pointC3(), and LARGER.

Referenced by has_larger_dist_to_point().

{
  return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == LARGER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_larger_signed_dist_to_directionC3	(	const FT &	pa,
		const FT &	pb,
		const FT &	pc,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 305 of file predicates/kernel_ftC3.h.

References cmp_signed_dist_to_directionC3(), and LARGER.

Referenced by has_larger_signed_dist_to_plane().

{
  return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == LARGER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_larger_signed_dist_to_planeC3	(	const FT &	ppx,
		const FT &	ppy,
		const FT &	ppz,
		const FT &	pqx,
		const FT &	pqy,
		const FT &	pqz,
		const FT &	prx,
		const FT &	pry,
		const FT &	prz,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 345 of file predicates/kernel_ftC3.h.

References cmp_signed_dist_to_planeC3(), and LARGER.

Referenced by has_larger_signed_dist_to_plane().

{
    return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
            prx, pry, prz, px, py, pz, qx, qy, qz) == LARGER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_smaller_dist_to_pointC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz
	)

Definition at line 282 of file predicates/kernel_ftC3.h.

References cmp_dist_to_pointC3(), and SMALLER.

Referenced by has_smaller_dist_to_point().

{
  return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == SMALLER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_smaller_signed_dist_to_directionC3	(	const FT &	pa,
		const FT &	pb,
		const FT &	pc,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 317 of file predicates/kernel_ftC3.h.

References cmp_signed_dist_to_directionC3(), and SMALLER.

Referenced by has_smaller_signed_dist_to_plane().

{
  return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == SMALLER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool has_smaller_signed_dist_to_planeC3	(	const FT &	ppx,
		const FT &	ppy,
		const FT &	ppz,
		const FT &	pqx,
		const FT &	pqy,
		const FT &	pqz,
		const FT &	prx,
		const FT &	pry,
		const FT &	prz,
		const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 360 of file predicates/kernel_ftC3.h.

References cmp_signed_dist_to_planeC3(), and SMALLER.

Referenced by has_smaller_signed_dist_to_plane().

{
    return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
            prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE Orientation orientationC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz,
		const FT &	sx,
		const FT &	sy,
		const FT &	sz
	)

Definition at line 115 of file predicates/kernel_ftC3.h.

References sign_of_determinant3x3().

Referenced by orientation(), and side_of_bounded_sphereC3().

{
  return Orientation(sign_of_determinant3x3(qx-px,rx-px,sx-px,
                                            qy-py,ry-py,sy-py,
                                            qz-pz,rz-pz,sz-pz));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE Bounded_side side_of_bounded_sphereC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz,
		const FT &	sx,
		const FT &	sy,
		const FT &	sz,
		const FT &	tx,
		const FT &	ty,
		const FT &	tz
	)

Definition at line 238 of file predicates/kernel_ftC3.h.

References orientationC3(), s, and side_of_oriented_sphereC3().

Referenced by side_of_bounded_sphere().

{
  Oriented_side s = side_of_oriented_sphereC3(px, py, pz,
                                              qx, qy, qz,
                                              rx, ry, rz,
                                              sx, sy, sz,
                                              tx, ty, tz);
  Orientation o = orientationC3(px, py, pz,
                                qx, qy, qz,
                                rx, ry, rz,
                                sx, sy, sz);
  return Bounded_side(s * o);
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_LARGE_INLINE Oriented_side side_of_oriented_planeC3	(	const FT &	a,
		const FT &	b,
		const FT &	c,
		const FT &	d,
		const FT &	px,
		const FT &	py,
		const FT &	pz
	)

Definition at line 198 of file predicates/kernel_ftC3.h.

References CGAL_NTS, and sign().

{
  return Oriented_side(CGAL_NTS sign(a*px + b*py + c*pz +d));
}

Here is the call graph for this function:

CGAL_KERNEL_LARGE_INLINE Oriented_side side_of_oriented_sphereC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz,
		const FT &	rx,
		const FT &	ry,
		const FT &	rz,
		const FT &	sx,
		const FT &	sy,
		const FT &	sz,
		const FT &	tx,
		const FT &	ty,
		const FT &	tz
	)

Definition at line 207 of file predicates/kernel_ftC3.h.

References CGAL_NTS, sign_of_determinant4x4(), and square().

Referenced by side_of_bounded_sphereC3(), and side_of_oriented_sphere().

{
  FT ptx = px - tx;
  FT pty = py - ty;
  FT ptz = pz - tz;
  FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
  FT qtx = qx - tx;
  FT qty = qy - ty;
  FT qtz = qz - tz;
  FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
  FT rtx = rx - tx;
  FT rty = ry - ty;
  FT rtz = rz - tz;
  FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
  FT stx = sx - tx;
  FT sty = sy - ty;
  FT stz = sz - tz;
  FT st2 = CGAL_NTS square(stx) + CGAL_NTS square(sty) + CGAL_NTS square(stz);
  return Oriented_side(sign_of_determinant4x4(ptx,pty,ptz,pt2,
                                              rtx,rty,rtz,rt2,
                                              qtx,qty,qtz,qt2,
                                              stx,sty,stz,st2));
}

Here is the call graph for this function:

Here is the caller graph for this function:

CGAL_KERNEL_MEDIUM_INLINE bool strict_dominanceC3	(	const FT &	px,
		const FT &	py,
		const FT &	pz,
		const FT &	qx,
		const FT &	qy,
		const FT &	qz
	)

Definition at line 74 of file predicates/kernel_ftC3.h.

References CGAL_NTS, CGAL::compare(), and LARGER.

{
  return CGAL_NTS compare(px, qx) == LARGER &&
         CGAL_NTS compare(py, qy) == LARGER &&
         CGAL_NTS compare(pz, qz) == LARGER;
}

Here is the call graph for this function: