your momma's axis aligned bounding box. More...

#include <aabb_3d.h>

Inheritance diagram for lass::prim::Aabb3D< T, MinMaxPolicy >:

[legend]

Public Member Functions
	Aabb3D ()
	Construct an empty bounding box.

	Aabb3D (const TPoint &min, const TPoint &max)
	Construct bounding box, spanned by min and max.

	Aabb3D (const TPoint &point)
	Construct bounding box around a single point (min == max)

template<class MMP2>
	Aabb3D (const Aabb3D< T, MMP2 > &other)
	copy constructor.

const TPoint &	min () const
	return corner with smallest component values

const TPoint &	max () const
	Return corner with largest component values.

void	setMin (const TPoint &min)
	set corner with smallest component values

void	setMax (const TPoint &max)
	set corner with larges component values

template<class MMP2>
TSelf &	operator= (const Aabb3D< T, MMP2 > &other)
	assign one bounding box to another.

TSelf &	operator+= (const TPoint &point)
	Expand bounding box so it contains point.

template<class MMP2>
TSelf &	operator+= (const Aabb3D< T, MMP2 > &other)
	Expand boundix box so it contains the other bounding box.

void	grow (TParam iDistance)
	Expand bounding box by distance iDistance.

void	grow (TVector iDistance)
	Expand bounding box by axis-dependent distance.

void	scale (TParam iScale)
	Scale bounding box by scale iScale.

const TPointH	center () const
	Return the center point of the bounding box.

const TVector	size () const
	Return size of bounding box per axis, max - min.

const TValue	area () const
	Returns surface area of bounding box.

const TValue	volume () const
	Returns volume of bounding box.

Side	classify (const TPoint &point) const
	Classify if a point is in or outside the bounding box, or on its surface.

bool	contains (const TPoint &point) const
	Returns true if point is inside bounding box or on its surface.

template<class MMP2>
bool	contains (const Aabb3D< T, MMP2 > &other) const
	Returns true if the AABB other is inside (or on its surface) this AABB.

template<class MMP2>
bool	intersects (const Aabb3D< T, MMP2 > &other) const
	Check if two axis-aligned bounding boxes do intersect.

template<class MMP2>
bool	collides (const Aabb3D< T, MMP2 > &other) const
	Check if two axis-aligned bounding boxes do dollide.

template<class RandomGenerator>
const TPoint	random (RandomGenerator &random) const
	Return a random point so that bounding box contains it.

void	clear ()
	set AABB to an empty box

bool	isEmpty () const
	Return true if bounding box contains no points.

bool	isValid () const
	internal check to see if AABB is valid.

template<typename MMP2>
void	swap (Aabb3D< T, MMP2 > &other)
	swap two bounding boxes.

Related Symbols
(Note that these are not member symbols.)
template<typename T, class MMPa, class MMPb>
const Aabb3D< T, MMPa >	operator+ (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
	join two AABBs

template<typename T, class MMP>
const Aabb3D< T, MMP >	operator+ (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
	add a point to an AABB

template<typename T, class MMP>
const Aabb3D< T, MMP >	operator+ (const Point3D< T > &a, const Aabb3D< T, MMP > &b)
	add a point to an AABB

template<typename T, class MMP>
T	distance (const Aabb3D< T, MMP > &a, const Point3D< T > &b)
	distance between AABB and point

template<typename T, class MMPa, class MMPb>
T	distance (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b)
	distance between two AABBs

template<typename T, class MMPa, class MMPb, class MMPr>
Result	intersect (const Aabb3D< T, MMPa > &a, const Aabb3D< T, MMPb > &b, Aabb3D< T, MMPr > &result)
	Calculate the intersection of two axis aligned bounding boxes.

template<typename T>
Aabb3D< T >	aabb (const Parallelogram3D< T > &parallelogram)
	determine axis aligned bounding box of a 3D parallelogram

template<typename T, class EP, class NP>
Aabb3D< T >	aabb (const SimplePolygon3D< T, EP, NP > &polygon)
	determine axis aligned bounding box of a 3D simple polygon

template<typename T, class EP, class NP, class MMP>
SimplePolygon3D< T, EP, NP >	clip (const Aabb3D< T, MMP > &box, const Plane3D< T, EP, NP > &plane)
	Clip a plane to an AABB and get a polygon.

template<typename T, class EP, class NP, class MMP>
SimplePolygon3D< T, EP, NP >	clip (const Aabb3D< T, MMP > &box, const SimplePolygon3D< T, EP, NP > &polygon)
	Clip a polygon to an AABB .

template<typename T, typename MMP>
Sphere3D< T >	boundingSphere (const Aabb3D< T, MMP > &box)

template<typename T, typename MMP>
bool	intersects (const Aabb3D< T, MMP > &aabb, const Sphere3D< T > &sphere)

template<typename T, typename MMP>
bool	collides (const Aabb3D< T, MMP > &aabb, const Sphere3D< T > &sphere)

template<typename T>
Aabb3D< T >	aabb (const Triangle3D< T > &triangle)
	determine axis aligned bounding box of a 3D triangle

Detailed Description

template<typename T, class MinMaxPolicy = StrictMinMax>
class lass::prim::Aabb3D< T, MinMaxPolicy >

your momma's axis aligned bounding box.

Author: Bram de Greve [BdG]

Date: 2003

An AABB (Axis Aligned Bounding Box) is a rectangular box of a given dimension (in this case a 3D box), that is often used as a simple bounding volume of another primitive or data structure.

"A form of a bounding box where the box is aligned to the axis therefore only two points in space are needed to define it. AABB's are much faster to use, and take up less memory, but are very limited in the sense that they can only be aligned to the axis.", http://www.gamedev.net/dict/term.asp?TermID=525

The way an AABB handles its minima and maxima can be set by the MinMaxPolicy. On policy StrictPolicy will enforce you to use correct minima and maxima, and on any suspicious behaviour, it will throw an exception. The other policy AutoPolicy will try to correct misbehaviour without your notice. For more information on these policies, I refer to the documentation compagning these policies.

Definition at line 88 of file aabb_3d.h.

Member Function Documentation

◆ grow() [1/2]

template<typename T, class MMP>

void lass::prim::Aabb3D< T, MMP >::grow ( TParam iDistance )

Expand bounding box by distance iDistance.

Negative values causing reversal of the bounding box will cause the box to shrink to the empty box.

Definition at line 215 of file aabb_3d.inl.

References grow().

Referenced by grow().

◆ grow() [2/2]

template<typename T, class MMP>

void lass::prim::Aabb3D< T, MMP >::grow ( TVector iDistance )

Expand bounding box by axis-dependent distance.

Negative values causing reversal of the bounding box will cause the box to shrink to the empty box.

Definition at line 225 of file aabb_3d.inl.

References clear(), and isValid().

◆ scale()

template<typename T, class MMP>

void lass::prim::Aabb3D< T, MMP >::scale ( TParam iScale )

Scale bounding box by scale iScale.

Fractions will shrink the bounding box. The origin of scaling is the center of the bounding box. Negative values of the scale have same effect as positive ones.

Definition at line 242 of file aabb_3d.inl.

References lass::num::abs(), isValid(), and size().

◆ center()

template<typename T, class MMP>

const Aabb3D< T, MMP >::TPointH lass::prim::Aabb3D< T, MMP >::center ( ) const

Return the center point of the bounding box.

We return a homogeneous point to avoid the division by two (that might not be supported by some types like integers)

Definition at line 258 of file aabb_3d.inl.

References isValid().

Referenced by boundingSphere().

◆ area()

template<typename T, class MMP>

const Aabb3D< T, MMP >::TValue lass::prim::Aabb3D< T, MMP >::area ( ) const

Returns surface area of bounding box.

the surface of a bounding box consists of three pair of rectangles

Definition at line 286 of file aabb_3d.inl.

References isEmpty(), and size().

◆ classify()

template<typename T, class MMP>

Side lass::prim::Aabb3D< T, MMP >::classify ( const TPoint & point ) const

Classify if a point is in or outside the bounding box, or on its surface.

Returns: sInside, sSurface, sOutside

Definition at line 317 of file aabb_3d.inl.

References isValid(), lass::prim::sInside, lass::prim::sOutside, and lass::prim::sSurface.

◆ contains() [1/2]

template<typename T, class MMP>

bool lass::prim::Aabb3D< T, MMP >::contains ( const TPoint & point ) const

Returns true if point is inside bounding box or on its surface.

Is equivalent to this->classify(point) != sOutside, but might be faster.

Definition at line 344 of file aabb_3d.inl.

References isValid().

Referenced by random().

◆ contains() [2/2]

template<typename T, class MMP>

template<class MMP2>

bool lass::prim::Aabb3D< T, MMP >::contains ( const Aabb3D< T, MMP2 > & other ) const

Returns true if the AABB other is inside (or on its surface) this AABB.

Is equivalent to this->contains(other.min()) && this->contains(other.max()).
if other is an empty AABB, it will always return true (an empty set is always a part of any other set).

Definition at line 361 of file aabb_3d.inl.

References Aabb3D(), isValid(), max(), and min().

◆ intersects()

template<typename T, class MMP>

template<class MMP2>

bool lass::prim::Aabb3D< T, MMP >::intersects ( const Aabb3D< T, MMP2 > & other ) const

Check if two axis-aligned bounding boxes do intersect.

Returns

false intersection of the AABBs is empty.
true intersection of the AABBs is not empty.

FAQ: What's the difference between this->intersects(other) and this->collides(other) ?: When two AABB are touching each other (surface to surface), the intersection isn't empty. i.e. the intersection is the line of points that belong to both the surfaces of the AABBs. In that case, the intersection is a degenerated AABB though, one with volume()==0. In collision detection however, you don't want this degenerated case of intersection to be considered as a collision. Two bodies may touch, but the must not have an overlap thas has a non-zero volume. That's why we have two methods: intersects returns true on touching AABBs, collides will return false. Of course, in the non-degenerate cases, they behave the same.

Use the seperating axis test to test if two AABB's do intersect: GOMEZ M. (1999), Simple Intersection Tests For Games, Gamasutra, http://www.gamasutra.com, http://www.gamasutra.com/features/19991018/Gomez_3.htm

Definition at line 392 of file aabb_3d.inl.

References Aabb3D(), isValid(), max(), and min().

Referenced by intersect().

◆ collides()

template<typename T, class MMP>

template<class MMP2>

bool lass::prim::Aabb3D< T, MMP >::collides ( const Aabb3D< T, MMP2 > & other ) const

Check if two axis-aligned bounding boxes do dollide.

Returns

true the AABBs do collide.
false they don't.

FAQ: What's the difference between this->intersects(other) and this->collides(other) ?: When two AABB are touching each other (surface to surface), the intersection isn't empty. i.e. the intersection is the line of points that belong to both the surfaces of the AABBs. In that case, the intersection is a degenerated AABB though, one with volume()==0. In collision detection however, you don't want this degenerated case of intersection to be considered as a collision. Two bodies may touch, but the must not have an overlap thas has a non-zero volume. That's why we have two methods: intersects returns true on touching AABBs, collides will return false. Of course, in the non-degenerate cases, they behave the same.

Use the seperating axis test to test if two AABB's do intersect: GOMEZ M. (1999), Simple Intersection Tests For Games, Gamasutra, http://www.gamasutra.com, http://www.gamasutra.com/features/19991018/Gomez_3.htm

Definition at line 424 of file aabb_3d.inl.

References Aabb3D(), isValid(), max(), and min().

◆ isEmpty()

template<typename T, class MMP>

bool lass::prim::Aabb3D< T, MMP >::isEmpty ( ) const

Return true if bounding box contains no points.

i.e. this->contains(Point3<T>(x, y, z)) will return false for all possible values of x, y and z.

Definition at line 472 of file aabb_3d.inl.

References isValid().

Referenced by Aabb3D(), area(), clear(), distance(), distance(), setMax(), size(), lass::prim::Transformation3D< U >::transform(), and volume().

◆ isValid()

template<typename T, class MMP>

bool lass::prim::Aabb3D< T, MMP >::isValid ( ) const

internal check to see if AABB is valid.

There are two valid states for the AABB:

max_.x < min_.x which means the box is empty
max_.x >= min_.x && max_.y >= min_.y && max_.z >= min_.z which means the box is not empty. That gives us an invalid state as well:
max_.x >= min_.x && (max_.y < min_.y || max_.z < min_.z). This state would cause isEmpty() to yield false, while there's still nothing in it (there's no single point for which contains(p) would return true.

When the regular minmax policies are used (StrictMinMax and AutoMinMax), there's no way any AABB would become invalid, and this test counts as an invariant to the box. However, when using the UncheckedMinMax policy, you're on your own.

Definition at line 495 of file aabb_3d.inl.

Referenced by Aabb3D(), Aabb3D(), center(), classify(), clear(), collides(), contains(), contains(), grow(), intersect(), intersects(), isEmpty(), operator+=(), operator+=(), random(), and scale().

Friends And Related Symbol Documentation

◆ distance() [1/2]

template<typename T, class MMP>

T distance	(	const Aabb3D< T, MMP > &	a,
		const Point3D< T > &	b )

distance between AABB and point

Parameters

a	AABB
b	point

Returns: absolute distance between point and AABB. If point is inside AABB, distance is 0.

Precondition: a should not be empty. Undefined behaviour if it is empty.

Definition at line 573 of file aabb_3d.inl.

◆ distance() [2/2]

template<typename T, class MMPa, class MMPb>

T distance	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b )

distance between two AABBs

Parameters

a	AABB
b	AABB

Returns: absolute distance. If one AABB is completely inside the other, distance is 0.

Precondition: a and b should not be empty. Undefined behaviour if they are.

Definition at line 590 of file aabb_3d.inl.

◆ intersect()

template<typename T, class MMPa, class MMPb, class MMPr>

Result intersect	(	const Aabb3D< T, MMPa > &	a,
		const Aabb3D< T, MMPb > &	b,
		Aabb3D< T, MMPr > &	result )

Calculate the intersection of two axis aligned bounding boxes.

Parameters

a	the first AABB :)
b	the second AABB
result	the intersection of a and b. In contrary to other intersection functions, this output argument will always be assigned, even if there's no result. By no result we mean: the intersection is empty. For most other intersection functions, we can't assign a meaning full value if there's no intersection, so we don't. However, in this case we can assign an empty AABB. And that's exactly what we do. So, the output argument is always valid, even if the return value suggests otherwise (in fact, you don't have to bother the return value this time)

Returns

rNone intersection of the AABBs is empty. result is an empty AABB.
rOne intersection of the AABBs is not empty. result contains intersection.

Definition at line 617 of file aabb_3d.inl.

◆ clip() [1/2]

template<typename T, class EP, class NP, class MMP>

SimplePolygon3D< T, EP, NP > clip	(	const Aabb3D< T, MMP > &	box,
		const Plane3D< T, EP, NP > &	plane )

Clip a plane to an AABB and get a polygon.

See also: lass::prim::Plane3D; lass::prim::SimplePolygon3D

Parameters

box	[in] the Aabb to clip to
plane	[in] the plane to be clipped

Returns: the clipped polygon.

Definition at line 80 of file aabb_3d_simple_polygon_3d.h.

◆ clip() [2/2]

template<typename T, class EP, class NP, class MMP>

SimplePolygon3D< T, EP, NP > clip	(	const Aabb3D< T, MMP > &	box,
		const SimplePolygon3D< T, EP, NP > &	polygon )

Clip a polygon to an AABB .

See also: lass::prim::SimplePolygon3D

Parameters

box	[in] the Aabb to clip to
polygon	[in] the polygon to be clipped

Returns: the clipped polygon.

Definition at line 174 of file aabb_3d_simple_polygon_3d.h.

◆ boundingSphere()

template<typename T, typename MMP>

Sphere3D< T > boundingSphere ( const Aabb3D< T, MMP > & box )

See also: lass::prim::Sphere3D

Definition at line 73 of file aabb_3d_sphere_3d.h.

◆ intersects()

template<typename T, typename MMP>

bool intersects	(	const Aabb3D< T, MMP > &	aabb,
		const Sphere3D< T > &	sphere )

See also: lass::prim::Sphere3D

Definition at line 86 of file aabb_3d_sphere_3d.h.

◆ collides()

template<typename T, typename MMP>

bool collides	(	const Aabb3D< T, MMP > &	aabb,
		const Sphere3D< T > &	sphere )

See also: lass::prim::Sphere3D

Definition at line 110 of file aabb_3d_sphere_3d.h.

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

Public Member Functions

Related Symbols

Detailed Description

Member Function Documentation

◆ grow() [1/2]

◆ grow() [2/2]

◆ scale()

◆ center()

◆ area()

◆ classify()

◆ contains() [1/2]

◆ contains() [2/2]

◆ intersects()

◆ collides()

◆ isEmpty()

◆ isValid()

Friends And Related Symbol Documentation

◆ distance() [1/2]

◆ distance() [2/2]

◆ intersect()

◆ clip() [1/2]

◆ clip() [2/2]

◆ boundingSphere()

◆ intersects()

◆ collides()