Axis Aligned Bounding Box. More...

#include <aabbox3f.hpp>

Collaboration diagram for jau::math::geom::AABBox3f:

Public Types
typedef jau::function< jau::math::Vec3f(const jau::math::Vec3f &)>	transform_vec3f_func
	General purpose Vec3f transform function.

Public Member Functions
	AABBox3f () noexcept
	Create an Axis Aligned bounding box (aabbox3f) where the low and and high MAX float Values.

constexpr	AABBox3f (AABBox3f &&o) noexcept=default

constexpr	AABBox3f (const AABBox3f &o) noexcept=default

	AABBox3f (const Point3f &bl_, const Point3f &tr_) noexcept
	Create an aabbox3f with given bl (low) and tr (high)

float	area2D () const noexcept
	Returns the assumed 2D area, i.e.

const Point3f &	center () const noexcept
	Returns computed center of this aabbox3f of low() and high().

bool	contains (const AABBox3f &o) const noexcept
	Returns whether this aabbox3f fully contains given aabbox3f.

bool	contains (const float x, const float y) const noexcept
	Check if the 2D point is bounded/contained by this aabbox3f.

bool	contains (const float x, const float y, const float z) const noexcept
	Check if the 3D point is bounded/contained by this aabbox3f.

bool	contains (const Point2f &p) const noexcept
	Check if the 2D point is bounded/contained by this aabbox3f.

bool	contains (const Point3f &p) const noexcept
	Check if the 3D point is bounded/contained by this aabbox3f.

float	depth () const noexcept

bool	getRayIntersection (Vec3f &result, const Ray3f &ray, const float epsilon, const bool assumeIntersection) const noexcept
	Return intersection of a `Ray` with this bounding box, or false if none exist.

bool	hasZeroArea2D () const noexcept
	Return true if `get2DArea()` is `FloatUtil#isZero(float)`, considering epsilon.

bool	hasZeroVolume () const noexcept
	Return true if `getVolume()` is `FloatUtil#isZero(float)`, considering epsilon.

float	height () const noexcept

const Point3f &	high () const noexcept
	Returns the maximum right-top-near (xyz) coordinate.

bool	intersects (const AABBox3f &o) const noexcept
	Returns whether this aabbox3f intersects (partially contains) given aabbox3f.

bool	intersects2DRegion (const float x, const float y, const float w, const float h) const noexcept
	Check if there is a common region between this AABBox and the passed 2D region irrespective of z range.

bool	intersectsRay (const Ray3f &r) const noexcept
	Check if `Ray` intersects this bounding box.

bool	intersectsRay0 (const Ray3f ray) const noexcept
	Check if `Ray` intersects this bounding box.

bool	intersectsRay1 (const Ray3f &r) const noexcept
	Check if `Ray` intersects this bounding box.

const Point3f &	low () const noexcept
	Returns the minimum left-bottom-far (xyz) coordinate.

AABBox3f &	mapToWindow (AABBox3f &result, const Mat4f &mat4PMv, const Recti &viewport, bool useCenterZ) const noexcept
	Assume this bounding box as being in object space and compute the window bounding box.

AABBox3f &	operator= (AABBox3f &&) noexcept=default

AABBox3f &	operator= (const AABBox3f &) noexcept=default

AABBox3f &	reset () noexcept
	Reset this box to the inverse low/high, allowing the next `resize(float, float, float)` command to hit.

AABBox3f &	resize (const AABBox3f &newBox, transform_vec3f_func &transform) noexcept
	Resize the aabbox3f to encapsulate another AABox, which will be transformed on the fly first.

AABBox3f &	resize (const AABBox3f &o) noexcept
	Resize the aabbox3f to encapsulate another AABox.

AABBox3f &	resize (const float x, const float y, const float z) noexcept
	Resize the aabbox3f to encapsulate the passed xyz-coordinates.

AABBox3f &	resize (const float xyz[]) noexcept
	Resize the aabbox3f to encapsulate the passed xyz-coordinates.

AABBox3f &	resize (const Point3f &p) noexcept
	Resize the aabbox3f to encapsulate the passed xyz-coordinates.

AABBox3f &	resizeHeight (const float deltaBottom, const float deltaTop) noexcept
	Resize height of this aabbox3f with explicit bottom- and top delta values.

AABBox3f &	resizeWidth (const float deltaLeft, const float deltaRight) noexcept
	Resize width of this aabbox3f with explicit left- and right delta values.

AABBox3f &	setSize (const float low[], const float high[]) noexcept
	Set size of the aabbox3f specifying the coordinates of the low and high.

AABBox3f &	setSize (const float lx, const float ly, const float lz, const float hx, const float hy, const float hz) noexcept
	Set size of the aabbox3f specifying the coordinates of the low and high.

AABBox3f &	setSize (const Vec3f &low, const Vec3f &high) noexcept
	Set size of the aabbox3f specifying the coordinates of the low and high.

float	size () const noexcept
	Get the size of this aabbox3f where the size is represented by the length of the vector between low and high.

std::string	toString () const noexcept

AABBox3f &	transform (const Mat4f &mat, AABBox3f &out) const noexcept
	Transform this box using the given Mat4f into `out @endiliteral.`

float	volume () const noexcept
	Returns the volume, i.e.

float	width () const noexcept

Detailed Description

Axis Aligned Bounding Box.

Defined by two 3D coordinates (low and high) The low being the the lower left corner of the box, and the high being the upper right corner of the box.

A few references for collision detection, intersections:

Brian Smits: Efficiency Issues for Ray Tracing. Journal of Graphics Tools (1998).
Amy Williams. et al.: An Efficient and Robust Ray-Box Intersection Algorithm. Journal of Graphics Tools (2005).
Tavian Barnes: Fast, Branchless Ray/Bounding Box Intersections
http://www.codercorner.com/RayAABB.cpp (Updated October 2001)
http://www.realtimerendering.com/intersections.html
http://tog.acm.org/resources/GraphicsGems/gems/RayBox.c
http://www.siggraph.org/education/materials/HyperGraph/raytrace/rtinter0.htm
http://realtimecollisiondetection.net/files/levine_swept_sat.txt

Definition at line 43 of file aabbox3f.hpp.

Member Typedef Documentation

◆ transform_vec3f_func

typedef jau::function<jau::math::Vec3f(const jau::math::Vec3f&)> jau::math::geom::AABBox3f::transform_vec3f_func

General purpose Vec3f transform function.

Definition at line 257 of file aabbox3f.hpp.

Constructor & Destructor Documentation

◆ AABBox3f() [1/4]

jau::math::geom::AABBox3f::AABBox3f ( )

inlinenoexcept

Create an Axis Aligned bounding box (aabbox3f) where the low and and high MAX float Values.

Definition at line 57 of file aabbox3f.hpp.

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◆ AABBox3f() [2/4]

jau::math::geom::AABBox3f::AABBox3f	(	const Point3f &	bl_,
		const Point3f &	tr_ )

inlinenoexcept

Create an aabbox3f with given bl (low) and tr (high)

Definition at line 64 of file aabbox3f.hpp.

◆ AABBox3f() [3/4]

jau::math::geom::AABBox3f::AABBox3f ( const AABBox3f & o )

constexprdefaultnoexcept

◆ AABBox3f() [4/4]

jau::math::geom::AABBox3f::AABBox3f ( AABBox3f && o )

constexprdefaultnoexcept

Member Function Documentation

◆ operator=() [1/2]

AABBox3f & jau::math::geom::AABBox3f::operator= ( const AABBox3f & )

defaultnoexcept

◆ operator=() [2/2]

AABBox3f & jau::math::geom::AABBox3f::operator= ( AABBox3f && )

defaultnoexcept

◆ reset()

AABBox3f & jau::math::geom::AABBox3f::reset ( )

inlinenoexcept

Reset this box to the inverse low/high, allowing the next resize(float, float, float) command to hit.

Returns: this aabbox3f for chaining

Definition at line 91 of file aabbox3f.hpp.

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◆ high()

const Point3f & jau::math::geom::AABBox3f::high ( ) const

inlinenoexcept

Returns the maximum right-top-near (xyz) coordinate.

Definition at line 99 of file aabbox3f.hpp.

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◆ low()

const Point3f & jau::math::geom::AABBox3f::low ( ) const

inlinenoexcept

Returns the minimum left-bottom-far (xyz) coordinate.

Definition at line 102 of file aabbox3f.hpp.

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◆ center()

const Point3f & jau::math::geom::AABBox3f::center ( ) const

inlinenoexcept

Returns computed center of this aabbox3f of low() and high().

Definition at line 105 of file aabbox3f.hpp.

◆ size()

float jau::math::geom::AABBox3f::size ( ) const

inlinenoexcept

Get the size of this aabbox3f where the size is represented by the length of the vector between low and high.

Returns: a float representing the size of the aabbox3f

Definition at line 112 of file aabbox3f.hpp.

◆ width()

float jau::math::geom::AABBox3f::width ( ) const

inlinenoexcept

Definition at line 114 of file aabbox3f.hpp.

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◆ height()

float jau::math::geom::AABBox3f::height ( ) const

inlinenoexcept

Definition at line 116 of file aabbox3f.hpp.

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◆ depth()

float jau::math::geom::AABBox3f::depth ( ) const

inlinenoexcept

Definition at line 118 of file aabbox3f.hpp.

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◆ volume()

float jau::math::geom::AABBox3f::volume ( ) const

inlinenoexcept

Returns the volume, i.e.

width * height * depth

Definition at line 121 of file aabbox3f.hpp.

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◆ hasZeroVolume()

bool jau::math::geom::AABBox3f::hasZeroVolume ( ) const

inlinenoexcept

Return true if getVolume() is FloatUtil#isZero(float), considering epsilon.

Definition at line 124 of file aabbox3f.hpp.

◆ area2D()

float jau::math::geom::AABBox3f::area2D ( ) const

inlinenoexcept

Returns the assumed 2D area, i.e.

width * height while assuming low and high lies on same plane.

Definition at line 127 of file aabbox3f.hpp.

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◆ hasZeroArea2D()

bool jau::math::geom::AABBox3f::hasZeroArea2D ( ) const

inlinenoexcept

Return true if get2DArea() is FloatUtil#isZero(float), considering epsilon.

Definition at line 130 of file aabbox3f.hpp.

◆ setSize() [1/3]

AABBox3f & jau::math::geom::AABBox3f::setSize	(	const float	low[],
		const float	high[] )

inlinenoexcept

Set size of the aabbox3f specifying the coordinates of the low and high.

Parameters

low	min xyz-coordinates
high	max xyz-coordinates

Returns: this aabbox3f for chaining

Definition at line 140 of file aabbox3f.hpp.

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◆ setSize() [2/3]

AABBox3f & jau::math::geom::AABBox3f::setSize	(	const float	lx,
		const float	ly,
		const float	lz,
		const float	hx,
		const float	hy,
		const float	hz )

inlinenoexcept

Set size of the aabbox3f specifying the coordinates of the low and high.

Parameters

lx	min x-coordinate
ly	min y-coordnate
lz	min z-coordinate
hx	max x-coordinate
hy	max y-coordinate
hz	max z-coordinate

Returns: this aabbox3f for chaining

Definition at line 156 of file aabbox3f.hpp.

◆ setSize() [3/3]

AABBox3f & jau::math::geom::AABBox3f::setSize	(	const Vec3f &	low,
		const Vec3f &	high )

inlinenoexcept

Set size of the aabbox3f specifying the coordinates of the low and high.

Parameters

low	min xyz-coordinates
high	max xyz-coordinates

Returns: this aabbox3f for chaining

Definition at line 172 of file aabbox3f.hpp.

◆ resizeWidth()

AABBox3f & jau::math::geom::AABBox3f::resizeWidth	(	const float	deltaLeft,
		const float	deltaRight )

inlinenoexcept

Resize width of this aabbox3f with explicit left- and right delta values.

Parameters

deltaLeft	positive value will expand width, otherwise shrink width
deltaRight	positive value will expand width, otherwise shrink width

Returns: this aabbox3f for chaining

Definition at line 185 of file aabbox3f.hpp.

◆ resizeHeight()

AABBox3f & jau::math::geom::AABBox3f::resizeHeight	(	const float	deltaBottom,
		const float	deltaTop )

inlinenoexcept

Resize height of this aabbox3f with explicit bottom- and top delta values.

Parameters

deltaBottom	positive value will expand height, otherwise shrink height
deltaTop	positive value will expand height, otherwise shrink height

Returns: this aabbox3f for chaining

Definition at line 207 of file aabbox3f.hpp.

◆ resize() [1/5]

AABBox3f & jau::math::geom::AABBox3f::resize ( const AABBox3f & o )

inlinenoexcept

Resize the aabbox3f to encapsulate another AABox.

Parameters

newBox aabbox3f to be encapsulated in

Returns: this aabbox3f for chaining

Definition at line 228 of file aabbox3f.hpp.

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◆ resize() [2/5]

AABBox3f & jau::math::geom::AABBox3f::resize	(	const AABBox3f &	newBox,
		transform_vec3f_func &	transform )

inlinenoexcept

Resize the aabbox3f to encapsulate another AABox, which will be transformed on the fly first.

Parameters

newBox	aabbox3f to be encapsulated in
transform	the transform function, applied on newBox on the fly
tmpV3	temporary storage

Returns: this aabbox3f for chaining

Definition at line 266 of file aabbox3f.hpp.

◆ resize() [3/5]

AABBox3f & jau::math::geom::AABBox3f::resize	(	const float	x,
		const float	y,
		const float	z )

inlinenoexcept

Resize the aabbox3f to encapsulate the passed xyz-coordinates.

Parameters

x	x-axis coordinate value
y	y-axis coordinate value
z	z-axis coordinate value

Returns: this aabbox3f for chaining

Definition at line 306 of file aabbox3f.hpp.

◆ resize() [4/5]

AABBox3f & jau::math::geom::AABBox3f::resize ( const float xyz[] )

inlinenoexcept

Resize the aabbox3f to encapsulate the passed xyz-coordinates.

Parameters

xyz	xyz-axis coordinate values

Returns: this aabbox3f for chaining

Definition at line 338 of file aabbox3f.hpp.

◆ resize() [5/5]

AABBox3f & jau::math::geom::AABBox3f::resize ( const Point3f & p )

inlinenoexcept

Resize the aabbox3f to encapsulate the passed xyz-coordinates.

Parameters

xyz	xyz-axis coordinate values

Returns: this aabbox3f for chaining

Definition at line 348 of file aabbox3f.hpp.

◆ contains() [1/5]

bool jau::math::geom::AABBox3f::contains	(	const float	x,
		const float	y ) const

inlinenoexcept

Check if the 2D point is bounded/contained by this aabbox3f.

Returns: true if {x, y} belongs to {low, high}

Definition at line 356 of file aabbox3f.hpp.

◆ contains() [2/5]

bool jau::math::geom::AABBox3f::contains ( const Point2f & p ) const

inlinenoexcept

Check if the 2D point is bounded/contained by this aabbox3f.

Returns: true if p belongs to {low, high}

Definition at line 365 of file aabbox3f.hpp.

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◆ contains() [3/5]

bool jau::math::geom::AABBox3f::contains	(	const float	x,
		const float	y,
		const float	z ) const

inlinenoexcept

Check if the 3D point is bounded/contained by this aabbox3f.

Returns: true if {x, y, z} belongs to {low, high}

Definition at line 371 of file aabbox3f.hpp.

◆ contains() [4/5]

bool jau::math::geom::AABBox3f::contains ( const Point3f & p ) const

inlinenoexcept

Check if the 3D point is bounded/contained by this aabbox3f.

Returns: true if p belongs to (low.x, high.x) and y belong to (low.y, high.y)

Definition at line 381 of file aabbox3f.hpp.

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◆ intersects()

bool jau::math::geom::AABBox3f::intersects ( const AABBox3f & o ) const

inlinenoexcept

Returns whether this aabbox3f intersects (partially contains) given aabbox3f.

Definition at line 384 of file aabbox3f.hpp.

◆ contains() [5/5]

bool jau::math::geom::AABBox3f::contains ( const AABBox3f & o ) const

inlinenoexcept

Returns whether this aabbox3f fully contains given aabbox3f.

Definition at line 402 of file aabbox3f.hpp.

◆ intersects2DRegion()

bool jau::math::geom::AABBox3f::intersects2DRegion	(	const float	x,
		const float	y,
		const float	w,
		const float	h ) const

inlinenoexcept

Check if there is a common region between this AABBox and the passed 2D region irrespective of z range.

Parameters

x	lower left x-coord
y	lower left y-coord
w	width
h	hight

Returns: true if this AABBox might have a common region with this 2D region

Definition at line 420 of file aabbox3f.hpp.

◆ intersectsRay0()

bool jau::math::geom::AABBox3f::intersectsRay0 ( const Ray3f ray ) const

inlinenoexcept

Check if Ray intersects this bounding box.

Versions uses the SAT[1], testing 6 axes with branching.

Original code for OBBs from MAGIC. Rewritten for AABBs and reorganized for early exits[2].

[1] SAT = Separating Axis Theorem
[2] http://www.codercorner.com/RayAABB.cpp

Parameters

ray

Returns: true if ray intersects with this box, otherwise false

Definition at line 451 of file aabbox3f.hpp.

◆ intersectsRay1()

bool jau::math::geom::AABBox3f::intersectsRay1 ( const Ray3f & r ) const

inlinenoexcept

Check if Ray intersects this bounding box.

Fast, Branchless Ray/Bounding Box Intersections[3]

This variant of intersectsRay() is a bit slower but handles NaNs more consistently.

The idea to eliminate branches by relying on IEEE 754 floating point properties goes back to Brian Smits[1], and the implementation was fleshed out by Amy Williams. et al.[2].

[1] Brian Smits: Efficiency Issues for Ray Tracing. Journal of Graphics Tools (1998).
[2] Amy Williams. et al.: An Efficient and Robust Ray-Box Intersection Algorithm. Journal of Graphics Tools (2005).
[3] Tavian Barnes: Fast, Branchless Ray/Bounding Box Intersections
[4] SAT = Separating Axis Theorem
[5] http://www.codercorner.com/RayAABB.cpp

Parameters

ray

Returns: true if ray intersects with this box, otherwise false

Definition at line 492 of file aabbox3f.hpp.

◆ intersectsRay()

bool jau::math::geom::AABBox3f::intersectsRay ( const Ray3f & r ) const

inlinenoexcept

Check if Ray intersects this bounding box.

Fast, Branchless Ray/Bounding Box Intersections[3]

This variant of intersectsRay0() is a faster and doesn't handles NaNs perfectly. However, it may only cause false positives, which will be checked later.

The idea to eliminate branches by relying on IEEE 754 floating point properties goes back to Brian Smits[1], and the implementation was fleshed out by Amy Williams. et al.[2].

[1] Brian Smits: Efficiency Issues for Ray Tracing. Journal of Graphics Tools (1998).
[2] Amy Williams. et al.: An Efficient and Robust Ray-Box Intersection Algorithm. Journal of Graphics Tools (2005).
[3] Tavian Barnes: Fast, Branchless Ray/Bounding Box Intersections
[4] SAT = Separating Axis Theorem
[5] http://www.codercorner.com/RayAABB.cpp

Parameters

ray

Returns: true if ray intersects with this box, otherwise false

Definition at line 533 of file aabbox3f.hpp.

◆ getRayIntersection()

bool jau::math::geom::AABBox3f::getRayIntersection	(	Vec3f &	result,
		const Ray3f &	ray,
		const float	epsilon,
		const bool	assumeIntersection ) const

inlinenoexcept

Return intersection of a Ray with this bounding box, or false if none exist.

>Original code by Andrew Woo, from "Graphics Gems", Academic Press, 1990 [2]
Optimized code by Pierre Terdiman, 2000 (~20-30% faster on my Celeron 500)
Epsilon value added by Klaus Hartmann.

Method is based on the requirements:

the integer representation of 0.0f is 0x00000000
the sign bit of the float is the most significant one

Report bugs: p.ter.nosp@m.dima.nosp@m.n@cod.nosp@m.erco.nosp@m.rner..nosp@m.com (original author)

[1] http://www.codercorner.com/RayAABB.cpp (Updated October 2001)
[2] http://tog.acm.org/resources/GraphicsGems/gems/RayBox.c

Parameters

result	vec3
ray
epsilon
assumeIntersection	if true, method assumes an intersection, i.e. by pre-checking via `intersectsRay(Ray)`. In this case method will not validate a possible non-intersection and just computes coordinates.

Returns: true with having intersection coordinates stored in result, or false if none exists

Definition at line 578 of file aabbox3f.hpp.

◆ transform()

AABBox3f & jau::math::geom::AABBox3f::transform	(	const Mat4f &	mat,
		AABBox3f &	out ) const

inlinenoexcept

Transform this box using the given Mat4f into out @endiliteral.

Parameters

mat	transformation Mat4f
out	the resulting AABBox3f

Returns: the resulting AABBox3f for chaining

Definition at line 771 of file aabbox3f.hpp.

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◆ mapToWindow()

AABBox3f & jau::math::geom::AABBox3f::mapToWindow	(	AABBox3f &	result,
		const Mat4f &	mat4PMv,
		const Recti &	viewport,
		bool	useCenterZ ) const

inlinenoexcept

Assume this bounding box as being in object space and compute the window bounding box.

If useCenterZ is true, only 4 mapObjToWinCoords operations are made on points [1..4] using getCenter()'s z-value. Otherwise 8 mapObjToWinCoords operation on all 8 points are performed.

 .z() ------ [4]
  |          |
  |          |
 .y() ------ [3]

Parameters

mat4PMv	[projection] x [modelview] matrix, i.e. P x Mv
viewport	viewport rectangle
useCenterZ
vec3Tmp0	3 component vector for temp storage
vec4Tmp1	4 component vector for temp storage
vec4Tmp2	4 component vector for temp storage

Returns

Definition at line 803 of file aabbox3f.hpp.

◆ toString()

std::string jau::math::geom::AABBox3f::toString ( ) const

inlinenoexcept

Definition at line 840 of file aabbox3f.hpp.

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

include/jau/math/geom/aabbox3f.hpp

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ transform_vec3f_func

Constructor & Destructor Documentation

◆ AABBox3f() [1/4]

◆ AABBox3f() [2/4]

◆ AABBox3f() [3/4]

◆ AABBox3f() [4/4]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ reset()

◆ high()

◆ low()

◆ center()

◆ size()

◆ width()

◆ height()

◆ depth()

◆ volume()

◆ hasZeroVolume()

◆ area2D()

◆ hasZeroArea2D()

◆ setSize() [1/3]

◆ setSize() [2/3]

◆ setSize() [3/3]

◆ resizeWidth()

◆ resizeHeight()

◆ resize() [1/5]

◆ resize() [2/5]

◆ resize() [3/5]

◆ resize() [4/5]

◆ resize() [5/5]

◆ contains() [1/5]

◆ contains() [2/5]

◆ contains() [3/5]

◆ contains() [4/5]

◆ intersects()

◆ contains() [5/5]

◆ intersects2DRegion()

◆ intersectsRay0()

◆ intersectsRay1()

◆ intersectsRay()

◆ getRayIntersection()

◆ transform()

◆ mapToWindow()

◆ toString()