halfspaceD3indexed< PT, PD, INDX > Class Template Reference

Define a 3D half space with three ordered points. More...

#include <halfspaceD3indexed.h>

Inheritance diagram for halfspaceD3indexed< PT, PD, INDX >:

Collaboration diagram for halfspaceD3indexed< PT, PD, INDX >:

List of all members.

Public Member Functions
	halfspaceD3indexed (PT const *pts, INDX i0_, INDX i1_, INDX i2_)
	Construct the plane with anticlockwise point ordering.
void	normalcalculate ()
	Calculate the normal the ordered points.
boolc	isInside (PT const &x) const
	Is the point inside the half space?
boolc	isInsideOrOnBoundary (PT const &x) const
	Is the point on or inside the half space?
PD const	distancefromhalfspace (PT const &w) const
	A measure of the distance from the plane to the point w without a square root.
Public Attributes
PT const &	p0
	Start point.
PT const &	p1
	Second point.
PT const &	p2
	End point.
PT	normal
	Normal.
INDX	i0
	Index to p0.
INDX	i1
	Index to p1.
INDX	i2
	Index to p2.

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Detailed Description

template<typename PT, typename PD, typename INDX>
class halfspaceD3indexed< PT, PD, INDX >

Define a 3D half space with three ordered points.

The inside of the half space is on the anti clockwise side of the plane with the three points.

Definition at line 19 of file halfspaceD3indexed.h.

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Constructor & Destructor Documentation

template<typename PT, typename PD, typename INDX>

halfspaceD3indexed< PT, PD, INDX >::halfspaceD3indexed	(	PT const *	pts,
		INDX	i0_,
		INDX	i1_,
		INDX	i2_
	)			[inline]

Construct the plane with anticlockwise point ordering.

The normal is outwards on the anticlockwise side of the plane.

Definition at line 43 of file halfspaceD3indexed.h.

References halfspaceD3indexed< PT, PD, INDX >::normalcalculate().

    : p0(pts[i0_]), p1(pts[i1_]), p2(pts[i2_]),
      i0(i0_), i1(i1_), i2(i2_)
    { normalcalculate(); }

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Member Function Documentation

template<typename PT, typename PD, typename INDX>

PD const halfspaceD3indexed< PT, PD, INDX >::distancefromhalfspace

(

PT const &

w

)

const [inline]

A measure of the distance from the plane to the point w without a square root.

ie N^2*d^2 where d is the vanilla distance function.

Definition at line 66 of file halfspaceD3indexed.h.

References halfspaceD3indexed< PT, PD, INDX >::normal, and halfspaceD3indexed< PT, PD, INDX >::p0.

    { 
      PT p;
      p.x=normal.x*normal.x*(p0.x-w.x);
      p.y=normal.y*normal.y*(p0.y-w.y);
      p.z=normal.z*normal.z*(p0.z-w.z);
      return p.x*p.x+p.y*p.y+p.z*p.z;
    }

template<typename PT, typename PD, typename INDX>

boolc halfspaceD3indexed< PT, PD, INDX >::isInside

(

PT const &

x

)

const [inline, virtual]

Is the point inside the half space?

Implements partitionspace< PT >.

Definition at line 57 of file halfspaceD3indexed.h.

References halfspaceD3indexed< PT, PD, INDX >::normal, and halfspaceD3indexed< PT, PD, INDX >::p0.

    { return 0 < normal.x*(x.x-p0.x)+normal.y*(x.y-p0.y)+normal.z*(x.z-p0.z); }

template<typename PT, typename PD, typename INDX>

boolc halfspaceD3indexed< PT, PD, INDX >::isInsideOrOnBoundary

(

PT const &

x

)

const [inline]

Is the point on or inside the half space?

Definition at line 60 of file halfspaceD3indexed.h.

References halfspaceD3indexed< PT, PD, INDX >::normal, and halfspaceD3indexed< PT, PD, INDX >::p0.

    { return 0 < zero<PD>::val+normal.x*(x.x-p0.x)+normal.y*(x.y-p0.y)+normal.z*(x.z-p0.z); }

template<typename PT , typename PD , typename INDX >

void halfspaceD3indexed< PT, PD, INDX >::normalcalculate

(

)

[inline]

Calculate the normal the ordered points.

Definition at line 82 of file halfspaceD3indexed.h.

References halfspaceD3indexed< PT, PD, INDX >::normal, halfspaceD3indexed< PT, PD, INDX >::p0, halfspaceD3indexed< PT, PD, INDX >::p1, and halfspaceD3indexed< PT, PD, INDX >::p2.

Referenced by halfspaceD3indexed< PT, PD, INDX >::halfspaceD3indexed().

{
  PT u(p2 - p1);
  PT v(p0 - p1);

  normal.x=u.y*v.z-v.y*u.z;
  normal.y=u.z*v.x-u.x*v.z;
  normal.z=u.x*v.y-u.y*v.x;
}

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Member Data Documentation

template<typename PT, typename PD, typename INDX>

INDX halfspaceD3indexed< PT, PD, INDX >::i0

Index to p0.

Definition at line 33 of file halfspaceD3indexed.h.

template<typename PT, typename PD, typename INDX>

INDX halfspaceD3indexed< PT, PD, INDX >::i1

Index to p1.

Definition at line 35 of file halfspaceD3indexed.h.

template<typename PT, typename PD, typename INDX>

INDX halfspaceD3indexed< PT, PD, INDX >::i2

Index to p2.

Definition at line 37 of file halfspaceD3indexed.h.

template<typename PT, typename PD, typename INDX>

PT halfspaceD3indexed< PT, PD, INDX >::normal

Normal.

Definition at line 30 of file halfspaceD3indexed.h.

Referenced by halfspaceD3indexed< PT, PD, INDX >::distancefromhalfspace(), halfspaceD3indexed< PT, PD, INDX >::isInside(), halfspaceD3indexed< PT, PD, INDX >::isInsideOrOnBoundary(), and halfspaceD3indexed< PT, PD, INDX >::normalcalculate().

template<typename PT, typename PD, typename INDX>

PT const& halfspaceD3indexed< PT, PD, INDX >::p0

Start point.

Definition at line 24 of file halfspaceD3indexed.h.

Referenced by halfspaceD3indexed< PT, PD, INDX >::distancefromhalfspace(), halfspaceD3indexed< PT, PD, INDX >::isInside(), halfspaceD3indexed< PT, PD, INDX >::isInsideOrOnBoundary(), and halfspaceD3indexed< PT, PD, INDX >::normalcalculate().

template<typename PT, typename PD, typename INDX>

PT const& halfspaceD3indexed< PT, PD, INDX >::p1

Second point.

Definition at line 26 of file halfspaceD3indexed.h.

Referenced by halfspaceD3indexed< PT, PD, INDX >::normalcalculate().

template<typename PT, typename PD, typename INDX>

PT const& halfspaceD3indexed< PT, PD, INDX >::p2

End point.

Definition at line 28 of file halfspaceD3indexed.h.

Referenced by halfspaceD3indexed< PT, PD, INDX >::normalcalculate().

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

• mathlib/halfspaceD3indexed.h