Classes
class	coal::AABB
	A class describing the AABB collision structure, which is a box in 3D space determined by two diagonal points. More...

class	coal::KDOP< N >
	KDOP class describes the KDOP collision structures. K is set as the template parameter, which should be 16, 18, or 24 The KDOP structure is defined by some pairs of parallel planes defined by some axes. For K = 16, the planes are 6 AABB planes and 10 diagonal planes that cut off some space of the edges: (-1,0,0) and (1,0,0) -> indices 0 and 8 (0,-1,0) and (0,1,0) -> indices 1 and 9 (0,0,-1) and (0,0,1) -> indices 2 and 10 (-1,-1,0) and (1,1,0) -> indices 3 and 11 (-1,0,-1) and (1,0,1) -> indices 4 and 12 (0,-1,-1) and (0,1,1) -> indices 5 and 13 (-1,1,0) and (1,-1,0) -> indices 6 and 14 (-1,0,1) and (1,0,-1) -> indices 7 and 15 For K = 18, the planes are 6 AABB planes and 12 diagonal planes that cut off some space of the edges: (-1,0,0) and (1,0,0) -> indices 0 and 9 (0,-1,0) and (0,1,0) -> indices 1 and 10 (0,0,-1) and (0,0,1) -> indices 2 and 11 (-1,-1,0) and (1,1,0) -> indices 3 and 12 (-1,0,-1) and (1,0,1) -> indices 4 and 13 (0,-1,-1) and (0,1,1) -> indices 5 and 14 (-1,1,0) and (1,-1,0) -> indices 6 and 15 (-1,0,1) and (1,0,-1) -> indices 7 and 16 (0,-1,1) and (0,1,-1) -> indices 8 and 17 For K = 18, the planes are 6 AABB planes and 18 diagonal planes that cut off some space of the edges: (-1,0,0) and (1,0,0) -> indices 0 and 12 (0,-1,0) and (0,1,0) -> indices 1 and 13 (0,0,-1) and (0,0,1) -> indices 2 and 14 (-1,-1,0) and (1,1,0) -> indices 3 and 15 (-1,0,-1) and (1,0,1) -> indices 4 and 16 (0,-1,-1) and (0,1,1) -> indices 5 and 17 (-1,1,0) and (1,-1,0) -> indices 6 and 18 (-1,0,1) and (1,0,-1) -> indices 7 and 19 (0,-1,1) and (0,1,-1) -> indices 8 and 20 (-1, -1, 1) and (1, 1, -1) --> indices 9 and 21 (-1, 1, -1) and (1, -1, 1) --> indices 10 and 22 (1, -1, -1) and (-1, 1, 1) --> indices 11 and 23. More...

class	coal::kIOS
	A class describing the kIOS collision structure, which is a set of spheres. More...

struct	coal::OBB
	Oriented bounding box class. More...

struct	coal::OBBRSS
	Class merging the OBB and RSS, can handle collision and distance simultaneously. More...

struct	coal::RSS
	A class for rectangle sphere-swept bounding volume. More...

Functions
	coal::AABB::AABB ()
	Creating an AABB with zero size (low bound +inf, upper bound -inf) More...

	coal::AABB::AABB (const Vec3s &v)
	Creating an AABB at position v with zero size. More...

	coal::AABB::AABB (const Vec3s &a, const Vec3s &b)
	Creating an AABB with two endpoints a and b. More...

	coal::AABB::AABB (const AABB &core, const Vec3s &delta)
	Creating an AABB centered as core and is of half-dimension delta. More...

	coal::AABB::AABB (const Vec3s &a, const Vec3s &b, const Vec3s &c)
	Creating an AABB contains three points. More...

	coal::AABB::AABB (const AABB &other)=default

AABB &	coal::AABB::operator= (const AABB &other)=default

AABB &	coal::AABB::update (const Vec3s &a, const Vec3s &b)

bool	coal::AABB::operator== (const AABB &other) const
	Comparison operator. More...

bool	coal::AABB::operator!= (const AABB &other) const

bool	coal::AABB::contain (const AABB &other) const
	Check whether the AABB contains another AABB. More...

bool	coal::AABB::overlap (const AABB &other, AABB &overlap_part) const
	Check whether two AABB are overlap and return the overlap part. More...

bool	coal::AABB::axisOverlap (const AABB &other, int axis_id) const
	Check whether two AABB are overlapped along specific axis. More...

AABB &	coal::AABB::expand (const Vec3s &delta)
	expand the half size of the AABB by delta, and keep the center unchanged. More...

AABB &	coal::AABB::expand (const CoalScalar delta)
	expand the half size of the AABB by a scalar delta, and keep the center unchanged. More...

AABB &	coal::AABB::expand (const AABB &core, CoalScalar ratio)
	expand the aabb by increase the thickness of the plate by a ratio More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const AABB &b1, const AABB &b2)
	Check collision between two aabbs, b1 is in configuration (R0, T0) and b2 is in identity. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const AABB &b1, const AABB &b2, const CollisionRequest &request, CoalScalar &sqrDistLowerBound)
	Check collision between two aabbs, b1 is in configuration (R0, T0) and b2 is in identity. More...

EIGEN_MAKE_ALIGNED_OPERATOR_NEW	coal::KDOP< N >::KDOP ()
	Creating kDOP containing nothing. More...

	coal::KDOP< N >::KDOP (const Vec3s &v)
	Creating kDOP containing only one point. More...

	coal::KDOP< N >::KDOP (const Vec3s &a, const Vec3s &b)
	Creating kDOP containing two points. More...

bool	coal::KDOP< N >::operator== (const KDOP &other) const
	Equality operator. More...

bool	coal::KDOP< N >::operator!= (const KDOP &other) const
	Difference operator. More...

bool	coal::KDOP< N >::overlap (const KDOP< N > &other) const
	Check whether two KDOPs overlap. More...

bool	coal::KDOP< N >::overlap (const KDOP< N > &other, const CollisionRequest &request, CoalScalar &sqrDistLowerBound) const
	Check whether two KDOPs overlap. More...

CoalScalar	coal::KDOP< N >::distance (const KDOP< N > &other, Vec3s P=NULL, Vec3s Q=NULL) const
	The distance between two KDOP<N>. Not implemented. More...

KDOP< N > &	coal::KDOP< N >::operator+= (const Vec3s &p)
	Merge the point and the KDOP. More...

KDOP< N > &	coal::KDOP< N >::operator+= (const KDOP< N > &other)
	Merge two KDOPs. More...

KDOP< N >	coal::KDOP< N >::operator+ (const KDOP< N > &other) const
	Create a KDOP by mergin two KDOPs. More...

CoalScalar	coal::KDOP< N >::size () const
	Size of the kDOP (used in BV_Splitter to order two kDOPs) More...

Vec3s	coal::KDOP< N >::center () const
	The (AABB) center. More...

CoalScalar	coal::KDOP< N >::width () const
	The (AABB) width. More...

CoalScalar	coal::KDOP< N >::height () const
	The (AABB) height. More...

CoalScalar	coal::KDOP< N >::depth () const
	The (AABB) depth. More...

CoalScalar	coal::KDOP< N >::volume () const
	The (AABB) volume. More...

CoalScalar	coal::KDOP< N >::dist (short i) const

CoalScalar &	coal::KDOP< N >::dist (short i)

bool	coal::KDOP< N >::inside (const Vec3s &p) const

template<short N>
bool	coal::overlap (const Matrix3s &, const Vec3s &, const KDOP< N > &, const KDOP< N > &)

template<short N>
bool	coal::overlap (const Matrix3s &, const Vec3s &, const KDOP< N > &, const KDOP< N > &, const CollisionRequest &, CoalScalar &)

template<short N>
KDOP< N >	coal::translate (const KDOP< N > &bv, const Vec3s &t)
	translate the KDOP BV More...

bool	coal::kIOS::kIOS_Sphere::operator== (const kIOS_Sphere &other) const

bool	coal::kIOS::kIOS_Sphere::operator!= (const kIOS_Sphere &other) const

EIGEN_MAKE_ALIGNED_OPERATOR_NEW bool	coal::kIOS::operator== (const kIOS &other) const
	Equality operator. More...

bool	coal::kIOS::operator!= (const kIOS &other) const
	Difference operator. More...

bool	coal::kIOS::contain (const Vec3s &p) const
	Check whether the kIOS contains a point. More...

bool	coal::kIOS::overlap (const kIOS &other) const
	Check collision between two kIOS. More...

bool	coal::kIOS::overlap (const kIOS &other, const CollisionRequest &, CoalScalar &sqrDistLowerBound) const
	Check collision between two kIOS. More...

CoalScalar	coal::kIOS::distance (const kIOS &other, Vec3s P=NULL, Vec3s Q=NULL) const
	The distance between two kIOS. More...

kIOS &	coal::kIOS::operator+= (const Vec3s &p)
	A simple way to merge the kIOS and a point. More...

kIOS &	coal::kIOS::operator+= (const kIOS &other)
	Merge the kIOS and another kIOS. More...

kIOS	coal::kIOS::operator+ (const kIOS &other) const
	Return the merged kIOS of current kIOS and the other one. More...

CoalScalar	coal::kIOS::size () const
	size of the kIOS (used in BV_Splitter to order two kIOSs) More...

const Vec3s &	coal::kIOS::center () const
	Center of the kIOS. More...

CoalScalar	coal::kIOS::width () const
	Width of the kIOS. More...

CoalScalar	coal::kIOS::height () const
	Height of the kIOS. More...

CoalScalar	coal::kIOS::depth () const
	Depth of the kIOS. More...

CoalScalar	coal::kIOS::volume () const
	Volume of the kIOS. More...

kIOS	coal::translate (const kIOS &bv, const Vec3s &t)
	Translate the kIOS BV. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const kIOS &b1, const kIOS &b2)
	Check collision between two kIOSs, b1 is in configuration (R0, T0) and b2 is in identity. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const kIOS &b1, const kIOS &b2, const CollisionRequest &request, CoalScalar &sqrDistLowerBound)
	Check collision between two kIOSs, b1 is in configuration (R0, T0) and b2 is in identity. More...

CoalScalar	coal::distance (const Matrix3s &R0, const Vec3s &T0, const kIOS &b1, const kIOS &b2, Vec3s P=NULL, Vec3s Q=NULL)
	Approximate distance between two kIOS bounding volumes. More...

	coal::OBB::OBB ()

bool	coal::OBB::operator== (const OBB &other) const
	Equality operator. More...

bool	coal::OBB::operator!= (const OBB &other) const
	Difference operator. More...

bool	coal::OBB::contain (const Vec3s &p) const
	Check whether the OBB contains a point. More...

bool	coal::OBB::overlap (const OBB &other) const

bool	coal::OBB::overlap (const OBB &other, const CollisionRequest &request, CoalScalar &sqrDistLowerBound) const

CoalScalar	coal::OBB::distance (const OBB &other, Vec3s P=NULL, Vec3s Q=NULL) const
	Distance between two OBBs, not implemented. More...

OBB &	coal::OBB::operator+= (const Vec3s &p)
	A simple way to merge the OBB and a point (the result is not compact). More...

OBB &	coal::OBB::operator+= (const OBB &other)
	Merge the OBB and another OBB (the result is not compact). More...

OBB	coal::OBB::operator+ (const OBB &other) const
	Return the merged OBB of current OBB and the other one (the result is not compact). More...

CoalScalar	coal::OBB::size () const
	Size of the OBB (used in BV_Splitter to order two OBBs) More...

const Vec3s &	coal::OBB::center () const
	Center of the OBB. More...

CoalScalar	coal::OBB::width () const
	Width of the OBB. More...

CoalScalar	coal::OBB::height () const
	Height of the OBB. More...

CoalScalar	coal::OBB::depth () const
	Depth of the OBB. More...

CoalScalar	coal::OBB::volume () const
	Volume of the OBB. More...

OBB	coal::translate (const OBB &bv, const Vec3s &t)
	Translate the OBB bv. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const OBB &b1, const OBB &b2)
	Check collision between two obbs, b1 is in configuration (R0, T0) and b2 is in identity. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const OBB &b1, const OBB &b2, const CollisionRequest &request, CoalScalar &sqrDistLowerBound)
	Check collision between two obbs, b1 is in configuration (R0, T0) and b2 is in identity. More...

bool	coal::obbDisjoint (const Matrix3s &B, const Vec3s &T, const Vec3s &a, const Vec3s &b)

bool	coal::OBBRSS::operator== (const OBBRSS &other) const
	Equality operator. More...

bool	coal::OBBRSS::operator!= (const OBBRSS &other) const
	Difference operator. More...

bool	coal::OBBRSS::contain (const Vec3s &p) const
	Check whether the OBBRSS contains a point. More...

bool	coal::OBBRSS::overlap (const OBBRSS &other) const
	Check collision between two OBBRSS. More...

bool	coal::OBBRSS::overlap (const OBBRSS &other, const CollisionRequest &request, CoalScalar &sqrDistLowerBound) const

CoalScalar	coal::OBBRSS::distance (const OBBRSS &other, Vec3s P=NULL, Vec3s Q=NULL) const
	Distance between two OBBRSS; P and Q , is not NULL, returns the nearest points. More...

OBBRSS &	coal::OBBRSS::operator+= (const Vec3s &p)
	Merge the OBBRSS and a point. More...

OBBRSS &	coal::OBBRSS::operator+= (const OBBRSS &other)
	Merge two OBBRSS. More...

OBBRSS	coal::OBBRSS::operator+ (const OBBRSS &other) const
	Merge two OBBRSS. More...

CoalScalar	coal::OBBRSS::size () const
	Size of the OBBRSS (used in BV_Splitter to order two OBBRSS) More...

const Vec3s &	coal::OBBRSS::center () const
	Center of the OBBRSS. More...

CoalScalar	coal::OBBRSS::width () const
	Width of the OBRSS. More...

CoalScalar	coal::OBBRSS::height () const
	Height of the OBBRSS. More...

CoalScalar	coal::OBBRSS::depth () const
	Depth of the OBBRSS. More...

CoalScalar	coal::OBBRSS::volume () const
	Volume of the OBBRSS. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const OBBRSS &b1, const OBBRSS &b2)
	Check collision between two OBBRSS, b1 is in configuration (R0, T0) and b2 is in indentity. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const OBBRSS &b1, const OBBRSS &b2, const CollisionRequest &request, CoalScalar &sqrDistLowerBound)

CoalScalar	coal::distance (const Matrix3s &R0, const Vec3s &T0, const OBBRSS &b1, const OBBRSS &b2, Vec3s P=NULL, Vec3s Q=NULL)
	Computate distance between two OBBRSS, b1 is in configuation (R0, T0) and b2 is in indentity; P and Q, is not NULL, returns the nearest points. More...

	coal::RSS::RSS ()
	More...

bool	coal::RSS::operator== (const RSS &other) const
	Equality operator. More...

bool	coal::RSS::operator!= (const RSS &other) const
	Difference operator. More...

bool	coal::RSS::contain (const Vec3s &p) const
	Check whether the RSS contains a point. More...

bool	coal::RSS::overlap (const RSS &other) const
	Check collision between two RSS. More...

bool	coal::RSS::overlap (const RSS &other, const CollisionRequest &, CoalScalar &sqrDistLowerBound) const
	Not implemented. More...

CoalScalar	coal::RSS::distance (const RSS &other, Vec3s P=NULL, Vec3s Q=NULL) const
	the distance between two RSS; P and Q, if not NULL, return the nearest points More...

RSS &	coal::RSS::operator+= (const Vec3s &p)
	A simple way to merge the RSS and a point, not compact. More...

RSS &	coal::RSS::operator+= (const RSS &other)
	Merge the RSS and another RSS. More...

RSS	coal::RSS::operator+ (const RSS &other) const
	Return the merged RSS of current RSS and the other one. More...

CoalScalar	coal::RSS::size () const
	Size of the RSS (used in BV_Splitter to order two RSSs) More...

const Vec3s &	coal::RSS::center () const
	The RSS center. More...

CoalScalar	coal::RSS::width () const
	Width of the RSS. More...

CoalScalar	coal::RSS::height () const
	Height of the RSS. More...

CoalScalar	coal::RSS::depth () const
	Depth of the RSS. More...

CoalScalar	coal::RSS::volume () const
	Volume of the RSS. More...

bool	coal::RSS::overlap (const RSS &other, RSS &) const
	Check collision between two RSS and return the overlap part. For RSS, we return nothing, as the overlap part of two RSSs usually is not a RSS. More...

CoalScalar	coal::distance (const Matrix3s &R0, const Vec3s &T0, const RSS &b1, const RSS &b2, Vec3s P=NULL, Vec3s Q=NULL)
	distance between two RSS bounding volumes P and Q (optional return values) are the closest points in the rectangles, not the RSS. But the direction P - Q is the correct direction for cloest points Notice that P and Q are both in the local frame of the first RSS (not global frame and not even the local frame of object 1) More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const RSS &b1, const RSS &b2)
	Check collision between two RSSs, b1 is in configuration (R0, T0) and b2 is in identity. More...

bool	coal::overlap (const Matrix3s &R0, const Vec3s &T0, const RSS &b1, const RSS &b2, const CollisionRequest &request, CoalScalar &sqrDistLowerBound)
	Check collision between two RSSs, b1 is in configuration (R0, T0) and b2 is in identity. More...

Variables
Vec3s	coal::AABB::min_
	The min point in the AABB. More...

Vec3s	coal::AABB::max_
	The max point in the AABB. More...

Eigen::Array< CoalScalar, N, 1 >	coal::KDOP< N >::dist_
	Origin's distances to N KDOP planes. More...

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Vec3s	coal::kIOS::kIOS_Sphere::o

CoalScalar	coal::kIOS::kIOS_Sphere::r

static constexpr size_t	coal::kIOS::max_num_spheres = 5

kIOS_Sphere	coal::kIOS::spheres [max_num_spheres]
	The (at most) five spheres for intersection. More...

unsigned int	coal::kIOS::num_spheres
	The number of spheres, no larger than 5. More...

OBB	coal::kIOS::obb
	@ OBB related with kIOS More...

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Matrix3s	coal::OBB::axes
	Orientation of OBB. axis[i] is the ith column of the orientation matrix for the box; it is also the i-th principle direction of the box. We assume that axis[0] corresponds to the axis with the longest box edge, axis[1] corresponds to the shorter one and axis[2] corresponds to the shortest one. More...

Vec3s	coal::OBB::To
	Center of OBB. More...

Vec3s	coal::OBB::extent
	Half dimensions of OBB. More...

EIGEN_MAKE_ALIGNED_OPERATOR_NEW OBB	coal::OBBRSS::obb
	OBB member, for rotation. More...

RSS	coal::OBBRSS::rss
	RSS member, for distance. More...

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Matrix3s	coal::RSS::axes
	Orientation of RSS. axis[i] is the ith column of the orientation matrix for the RSS; it is also the i-th principle direction of the RSS. We assume that axis[0] corresponds to the axis with the longest length, axis[1] corresponds to the shorter one and axis[2] corresponds to the shortest one. More...

Vec3s	coal::RSS::Tr
	Origin of the rectangle in RSS. More...

CoalScalar	coal::RSS::length [2]
	Side lengths of rectangle. More...

CoalScalar	coal::RSS::radius
	Radius of sphere summed with rectangle to form RSS. More...

Bounding volume API
Common API to BVs.
bool	coal::AABB::contain (const Vec3s &p) const
	Check whether the AABB contains a point. More...

bool	coal::AABB::overlap (const AABB &other) const
	Check whether two AABB are overlap. More...

bool	coal::AABB::overlap (const Plane &p) const
	Check whether AABB overlaps a plane. More...

bool	coal::AABB::overlap (const Halfspace &hs) const
	Check whether AABB overlaps a halfspace. More...

bool	coal::AABB::overlap (const AABB &other, const CollisionRequest &request, CoalScalar &sqrDistLowerBound) const
	Check whether two AABB are overlap. More...

CoalScalar	coal::AABB::distance (const AABB &other) const
	Distance between two AABBs. More...

CoalScalar	coal::AABB::distance (const AABB &other, Vec3s P, Vec3s Q) const
	Distance between two AABBs; P and Q, should not be NULL, return the nearest points. More...

AABB &	coal::AABB::operator+= (const Vec3s &p)
	Merge the AABB and a point. More...

AABB &	coal::AABB::operator+= (const AABB &other)
	Merge the AABB and another AABB. More...

AABB	coal::AABB::operator+ (const AABB &other) const
	Return the merged AABB of current AABB and the other one. More...

CoalScalar	coal::AABB::size () const
	Size of the AABB (used in BV_Splitter to order two AABBs) More...

Vec3s	coal::AABB::center () const
	Center of the AABB. More...

CoalScalar	coal::AABB::width () const
	Width of the AABB. More...

CoalScalar	coal::AABB::height () const
	Height of the AABB. More...

CoalScalar	coal::AABB::depth () const
	Depth of the AABB. More...

CoalScalar	coal::AABB::volume () const
	Volume of the AABB. More...

Detailed Description

Classes of different types of bounding volume.

Function Documentation

◆ AABB() [1/6]

coal::AABB::AABB ( )

Creating an AABB with zero size (low bound +inf, upper bound -inf)

◆ AABB() [2/6]

coal::AABB::AABB	(	const AABB &	core,
		const Vec3s &	delta
	)

inline

Creating an AABB centered as core and is of half-dimension delta.

◆ AABB() [3/6]

coal::AABB::AABB ( const AABB & other )

default

◆ AABB() [4/6]

coal::AABB::AABB	(	const Vec3s &	a,
		const Vec3s &	b
	)

inline

Creating an AABB with two endpoints a and b.

◆ AABB() [5/6]

coal::AABB::AABB	(	const Vec3s &	a,
		const Vec3s &	b,
		const Vec3s &	c
	)

inline

Creating an AABB contains three points.

◆ AABB() [6/6]

coal::AABB::AABB ( const Vec3s & v )

inline

Creating an AABB at position v with zero size.

◆ axisOverlap()

bool coal::AABB::axisOverlap	(	const AABB &	other,
		int	axis_id
	)		const

inline

Check whether two AABB are overlapped along specific axis.

◆ center() [1/6]

Vec3s coal::AABB::center ( ) const

inline

Center of the AABB.

◆ center() [2/6]

template<short N>

Vec3s coal::KDOP< N >::center ( ) const

inline

The (AABB) center.

◆ center() [3/6]

const Vec3s& coal::kIOS::center ( ) const

inline

Center of the kIOS.

◆ center() [4/6]

const Vec3s& coal::OBB::center ( ) const

inline

Center of the OBB.

◆ center() [5/6]

const Vec3s& coal::OBBRSS::center ( ) const

inline

Center of the OBBRSS.

◆ center() [6/6]

const Vec3s& coal::RSS::center ( ) const

inline

The RSS center.

◆ contain() [1/6]

bool coal::AABB::contain ( const AABB & other ) const

inline

Check whether the AABB contains another AABB.

◆ contain() [2/6]

bool coal::AABB::contain ( const Vec3s & p ) const

inline

Check whether the AABB contains a point.

◆ contain() [3/6]

bool coal::kIOS::contain ( const Vec3s & p ) const

Check whether the kIOS contains a point.

◆ contain() [4/6]

bool coal::OBB::contain ( const Vec3s & p ) const

Check whether the OBB contains a point.

◆ contain() [5/6]

bool coal::OBBRSS::contain ( const Vec3s & p ) const

inline

Check whether the OBBRSS contains a point.

◆ contain() [6/6]

bool coal::RSS::contain ( const Vec3s & p ) const

Check whether the RSS contains a point.

◆ depth() [1/6]

CoalScalar coal::AABB::depth ( ) const

inline

Depth of the AABB.

◆ depth() [2/6]

template<short N>

CoalScalar coal::KDOP< N >::depth ( ) const

inline

The (AABB) depth.

◆ depth() [3/6]

CoalScalar coal::kIOS::depth ( ) const

Depth of the kIOS.

◆ depth() [4/6]

CoalScalar coal::OBB::depth ( ) const

inline

Depth of the OBB.

◆ depth() [5/6]

CoalScalar coal::OBBRSS::depth ( ) const

inline

Depth of the OBBRSS.

◆ depth() [6/6]

CoalScalar coal::RSS::depth ( ) const

inline

Depth of the RSS.

◆ dist() [1/2]

template<short N>

CoalScalar& coal::KDOP< N >::dist ( short i )

inline

◆ dist() [2/2]

template<short N>

CoalScalar coal::KDOP< N >::dist ( short i ) const

inline

◆ distance() [1/10]

CoalScalar coal::AABB::distance ( const AABB & other ) const

Distance between two AABBs.

◆ distance() [2/10]

CoalScalar coal::AABB::distance	(	const AABB &	other,
		Vec3s *	P,
		Vec3s *	Q
	)		const

Distance between two AABBs; P and Q, should not be NULL, return the nearest points.

◆ distance() [3/10]

template<short N>

CoalScalar coal::KDOP< N >::distance	(	const KDOP< N > &	other,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)		const

The distance between two KDOP<N>. Not implemented.

◆ distance() [4/10]

CoalScalar coal::kIOS::distance	(	const kIOS &	other,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)		const

The distance between two kIOS.

◆ distance() [5/10]

CoalScalar coal::distance	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const kIOS &	b1,
		const kIOS &	b2,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)

Approximate distance between two kIOS bounding volumes.

Todo:: P and Q is not returned, need implementation

◆ distance() [6/10]

CoalScalar coal::distance	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const OBBRSS &	b1,
		const OBBRSS &	b2,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)

inline

Computate distance between two OBBRSS, b1 is in configuation (R0, T0) and b2 is in indentity; P and Q, is not NULL, returns the nearest points.

◆ distance() [7/10]

CoalScalar coal::distance	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const RSS &	b1,
		const RSS &	b2,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)

distance between two RSS bounding volumes P and Q (optional return values) are the closest points in the rectangles, not the RSS. But the direction P - Q is the correct direction for cloest points Notice that P and Q are both in the local frame of the first RSS (not global frame and not even the local frame of object 1)

◆ distance() [8/10]

CoalScalar coal::OBB::distance	(	const OBB &	other,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)		const

Distance between two OBBs, not implemented.

◆ distance() [9/10]

CoalScalar coal::OBBRSS::distance	(	const OBBRSS &	other,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)		const

inline

Distance between two OBBRSS; P and Q , is not NULL, returns the nearest points.

◆ distance() [10/10]

CoalScalar coal::RSS::distance	(	const RSS &	other,
		Vec3s *	P = `NULL`,
		Vec3s *	Q = `NULL`
	)		const

the distance between two RSS; P and Q, if not NULL, return the nearest points

◆ expand() [1/3]

AABB& coal::AABB::expand	(	const AABB &	core,
		CoalScalar	ratio
	)

inline

expand the aabb by increase the thickness of the plate by a ratio

◆ expand() [2/3]

AABB& coal::AABB::expand ( const CoalScalar delta )

inline

expand the half size of the AABB by a scalar delta, and keep the center unchanged.

◆ expand() [3/3]

AABB& coal::AABB::expand ( const Vec3s & delta )

inline

expand the half size of the AABB by delta, and keep the center unchanged.

◆ height() [1/6]

CoalScalar coal::AABB::height ( ) const

inline

Height of the AABB.

◆ height() [2/6]

template<short N>

CoalScalar coal::KDOP< N >::height ( ) const

inline

The (AABB) height.

◆ height() [3/6]

CoalScalar coal::kIOS::height ( ) const

Height of the kIOS.

◆ height() [4/6]

CoalScalar coal::OBB::height ( ) const

inline

Height of the OBB.

◆ height() [5/6]

CoalScalar coal::OBBRSS::height ( ) const

inline

Height of the OBBRSS.

◆ height() [6/6]

CoalScalar coal::RSS::height ( ) const

inline

Height of the RSS.

◆ inside()

template<short N>

bool coal::KDOP< N >::inside ( const Vec3s & p ) const

◆ KDOP() [1/3]

template<short N>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW coal::KDOP< N >::KDOP ( )

Creating kDOP containing nothing.

◆ KDOP() [2/3]

template<short N>

coal::KDOP< N >::KDOP	(	const Vec3s &	a,
		const Vec3s &	b
	)

Creating kDOP containing two points.

◆ KDOP() [3/3]

template<short N>

coal::KDOP< N >::KDOP ( const Vec3s & v )

Creating kDOP containing only one point.

◆ OBB()

coal::OBB::OBB ( )

inline

◆ obbDisjoint()

bool coal::obbDisjoint	(	const Matrix3s &	B,
		const Vec3s &	T,
		const Vec3s &	a,
		const Vec3s &	b
	)

Check collision between two boxes

Parameters

B,T	orientation and position of first box,
a	half dimensions of first box,
b	half dimensions of second box. The second box is in identity configuration.

◆ operator!=() [1/7]

bool coal::AABB::operator!= ( const AABB & other ) const

inline

◆ operator!=() [2/7]

template<short N>

bool coal::KDOP< N >::operator!= ( const KDOP< N > & other ) const

inline

Difference operator.

◆ operator!=() [3/7]

bool coal::kIOS::operator!= ( const kIOS & other ) const

inline

Difference operator.

◆ operator!=() [4/7]

bool coal::kIOS::kIOS_Sphere::operator!= ( const kIOS_Sphere & other ) const

inline

◆ operator!=() [5/7]

bool coal::OBB::operator!= ( const OBB & other ) const

inline

Difference operator.

◆ operator!=() [6/7]

bool coal::OBBRSS::operator!= ( const OBBRSS & other ) const

inline

Difference operator.

◆ operator!=() [7/7]

bool coal::RSS::operator!= ( const RSS & other ) const

inline

Difference operator.

◆ operator+() [1/6]

AABB coal::AABB::operator+ ( const AABB & other ) const

inline

Return the merged AABB of current AABB and the other one.

◆ operator+() [2/6]

template<short N>

KDOP<N> coal::KDOP< N >::operator+ ( const KDOP< N > & other ) const

Create a KDOP by mergin two KDOPs.

◆ operator+() [3/6]

kIOS coal::kIOS::operator+ ( const kIOS & other ) const

Return the merged kIOS of current kIOS and the other one.

◆ operator+() [4/6]

OBB coal::OBB::operator+ ( const OBB & other ) const

Return the merged OBB of current OBB and the other one (the result is not compact).

◆ operator+() [5/6]

OBBRSS coal::OBBRSS::operator+ ( const OBBRSS & other ) const

inline

Merge two OBBRSS.

◆ operator+() [6/6]

RSS coal::RSS::operator+ ( const RSS & other ) const

Return the merged RSS of current RSS and the other one.

◆ operator+=() [1/12]

AABB& coal::AABB::operator+= ( const AABB & other )

inline

Merge the AABB and another AABB.

◆ operator+=() [2/12]

template<short N>

KDOP<N>& coal::KDOP< N >::operator+= ( const KDOP< N > & other )

Merge two KDOPs.

◆ operator+=() [3/12]

kIOS& coal::kIOS::operator+= ( const kIOS & other )

inline

Merge the kIOS and another kIOS.

◆ operator+=() [4/12]

OBB& coal::OBB::operator+= ( const OBB & other )

inline

Merge the OBB and another OBB (the result is not compact).

◆ operator+=() [5/12]

OBBRSS& coal::OBBRSS::operator+= ( const OBBRSS & other )

inline

Merge two OBBRSS.

◆ operator+=() [6/12]

RSS& coal::RSS::operator+= ( const RSS & other )

inline

Merge the RSS and another RSS.

◆ operator+=() [7/12]

AABB& coal::AABB::operator+= ( const Vec3s & p )

inline

Merge the AABB and a point.

◆ operator+=() [8/12]

template<short N>

KDOP<N>& coal::KDOP< N >::operator+= ( const Vec3s & p )

Merge the point and the KDOP.

◆ operator+=() [9/12]

kIOS& coal::kIOS::operator+= ( const Vec3s & p )

A simple way to merge the kIOS and a point.

◆ operator+=() [10/12]

OBB& coal::OBB::operator+= ( const Vec3s & p )

A simple way to merge the OBB and a point (the result is not compact).

◆ operator+=() [11/12]

OBBRSS& coal::OBBRSS::operator+= ( const Vec3s & p )

inline

Merge the OBBRSS and a point.

◆ operator+=() [12/12]

RSS& coal::RSS::operator+= ( const Vec3s & p )

A simple way to merge the RSS and a point, not compact.

Todo:: This function may have some bug.

◆ operator=()

AABB& coal::AABB::operator= ( const AABB & other )

default

◆ operator==() [1/7]

bool coal::AABB::operator== ( const AABB & other ) const

inline

Comparison operator.

◆ operator==() [2/7]

template<short N>

bool coal::KDOP< N >::operator== ( const KDOP< N > & other ) const

inline

Equality operator.

◆ operator==() [3/7]

EIGEN_MAKE_ALIGNED_OPERATOR_NEW bool coal::kIOS::operator== ( const kIOS & other ) const

inline

Equality operator.

◆ operator==() [4/7]

bool coal::kIOS::kIOS_Sphere::operator== ( const kIOS_Sphere & other ) const

inline

◆ operator==() [5/7]

bool coal::OBB::operator== ( const OBB & other ) const

inline

Equality operator.

◆ operator==() [6/7]

bool coal::OBBRSS::operator== ( const OBBRSS & other ) const

inline

Equality operator.

◆ operator==() [7/7]

bool coal::RSS::operator== ( const RSS & other ) const

inline

Equality operator.

◆ overlap() [1/28]

bool coal::AABB::overlap ( const AABB & other ) const

inline

Check whether two AABB are overlap.

◆ overlap() [2/28]

bool coal::AABB::overlap	(	const AABB &	other,
		AABB &	overlap_part
	)		const

inline

Check whether two AABB are overlap and return the overlap part.

◆ overlap() [3/28]

bool coal::AABB::overlap	(	const AABB &	other,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)		const

Check whether two AABB are overlap.

◆ overlap() [4/28]

bool coal::AABB::overlap ( const Halfspace & hs ) const

Check whether AABB overlaps a halfspace.

◆ overlap() [5/28]

template<short N>

bool coal::KDOP< N >::overlap ( const KDOP< N > & other ) const

Check whether two KDOPs overlap.

◆ overlap() [6/28]

template<short N>

bool coal::KDOP< N >::overlap	(	const KDOP< N > &	other,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)		const

Check whether two KDOPs overlap.

Returns: true if collision happens.

Return values

sqrDistLowerBound squared lower bound on distance between boxes if they do not overlap.

◆ overlap() [7/28]

bool coal::kIOS::overlap ( const kIOS & other ) const

Check collision between two kIOS.

◆ overlap() [8/28]

bool coal::kIOS::overlap	(	const kIOS &	other,
		const CollisionRequest &	,
		CoalScalar &	sqrDistLowerBound
	)		const

Check collision between two kIOS.

◆ overlap() [9/28]

template<short N>

bool coal::overlap	(	const Matrix3s &	,
		const Vec3s &	,
		const KDOP< N > &	,
		const KDOP< N > &
	)

◆ overlap() [10/28]

template<short N>

bool coal::overlap	(	const Matrix3s &	,
		const Vec3s &	,
		const KDOP< N > &	,
		const KDOP< N > &	,
		const CollisionRequest &	,
		CoalScalar &
	)

◆ overlap() [11/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const AABB &	b1,
		const AABB &	b2
	)

Check collision between two aabbs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [12/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const AABB &	b1,
		const AABB &	b2,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)

Check collision between two aabbs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [13/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const kIOS &	b1,
		const kIOS &	b2
	)

Check collision between two kIOSs, b1 is in configuration (R0, T0) and b2 is in identity.

Todo:: Not efficient

◆ overlap() [14/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const kIOS &	b1,
		const kIOS &	b2,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)

Check collision between two kIOSs, b1 is in configuration (R0, T0) and b2 is in identity.

Todo:: Not efficient

◆ overlap() [15/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const OBB &	b1,
		const OBB &	b2
	)

Check collision between two obbs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [16/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const OBB &	b1,
		const OBB &	b2,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)

Check collision between two obbs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [17/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const OBBRSS &	b1,
		const OBBRSS &	b2
	)

inline

Check collision between two OBBRSS, b1 is in configuration (R0, T0) and b2 is in indentity.

◆ overlap() [18/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const OBBRSS &	b1,
		const OBBRSS &	b2,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)

inline

Check collision between two OBBRSS

Parameters

R0,T0	configuration of b1
b1	first OBBRSS in configuration (R0, T0)
b2	second OBBRSS in identity position

Return values

sqrDistLowerBound squared lower bound on the distance if OBBRSS do not overlap.

◆ overlap() [19/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const RSS &	b1,
		const RSS &	b2
	)

Check collision between two RSSs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [20/28]

bool coal::overlap	(	const Matrix3s &	R0,
		const Vec3s &	T0,
		const RSS &	b1,
		const RSS &	b2,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)

Check collision between two RSSs, b1 is in configuration (R0, T0) and b2 is in identity.

◆ overlap() [21/28]

bool coal::OBB::overlap ( const OBB & other ) const

Check collision between two OBB

Returns: true if collision happens.

◆ overlap() [22/28]

bool coal::OBB::overlap	(	const OBB &	other,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)		const

Check collision between two OBB

Returns: true if collision happens.

Return values

sqrDistLowerBound squared lower bound on distance between boxes if they do not overlap.

◆ overlap() [23/28]

bool coal::OBBRSS::overlap ( const OBBRSS & other ) const

inline

Check collision between two OBBRSS.

◆ overlap() [24/28]

bool coal::OBBRSS::overlap	(	const OBBRSS &	other,
		const CollisionRequest &	request,
		CoalScalar &	sqrDistLowerBound
	)		const

inline

Check collision between two OBBRSS

Return values

sqrDistLowerBound squared lower bound on distance between objects if they do not overlap.

◆ overlap() [25/28]

bool coal::AABB::overlap ( const Plane & p ) const

Check whether AABB overlaps a plane.

◆ overlap() [26/28]

bool coal::RSS::overlap ( const RSS & other ) const

Check collision between two RSS.

◆ overlap() [27/28]

bool coal::RSS::overlap	(	const RSS &	other,
		const CollisionRequest &	,
		CoalScalar &	sqrDistLowerBound
	)		const

inline

Not implemented.

◆ overlap() [28/28]

bool coal::RSS::overlap	(	const RSS &	other,
		RSS &
	)		const

inline

Check collision between two RSS and return the overlap part. For RSS, we return nothing, as the overlap part of two RSSs usually is not a RSS.

◆ RSS()

coal::RSS::RSS ( )

inline

Default constructor with default values

◆ size() [1/6]

CoalScalar coal::AABB::size ( ) const

inline

Size of the AABB (used in BV_Splitter to order two AABBs)

◆ size() [2/6]

template<short N>

CoalScalar coal::KDOP< N >::size ( ) const

inline

Size of the kDOP (used in BV_Splitter to order two kDOPs)

◆ size() [3/6]

CoalScalar coal::kIOS::size ( ) const

size of the kIOS (used in BV_Splitter to order two kIOSs)

◆ size() [4/6]

CoalScalar coal::OBB::size ( ) const

inline

Size of the OBB (used in BV_Splitter to order two OBBs)

◆ size() [5/6]

CoalScalar coal::OBBRSS::size ( ) const

inline

Size of the OBBRSS (used in BV_Splitter to order two OBBRSS)

◆ size() [6/6]

CoalScalar coal::RSS::size ( ) const

inline

Size of the RSS (used in BV_Splitter to order two RSSs)

◆ translate() [1/3]

template<short N>

KDOP<N> coal::translate	(	const KDOP< N > &	bv,
		const Vec3s &	t
	)

translate the KDOP BV

◆ translate() [2/3]

kIOS coal::translate	(	const kIOS &	bv,
		const Vec3s &	t
	)

Translate the kIOS BV.

◆ translate() [3/3]

OBB coal::translate	(	const OBB &	bv,
		const Vec3s &	t
	)

Translate the OBB bv.

◆ update()

AABB& coal::AABB::update	(	const Vec3s &	a,
		const Vec3s &	b
	)

inline

◆ volume() [1/6]

CoalScalar coal::AABB::volume ( ) const

inline

Volume of the AABB.

◆ volume() [2/6]

template<short N>

CoalScalar coal::KDOP< N >::volume ( ) const

inline

The (AABB) volume.

◆ volume() [3/6]

CoalScalar coal::kIOS::volume ( ) const

Volume of the kIOS.

◆ volume() [4/6]

CoalScalar coal::OBB::volume ( ) const

inline

Volume of the OBB.

◆ volume() [5/6]

CoalScalar coal::OBBRSS::volume ( ) const

inline

Volume of the OBBRSS.

◆ volume() [6/6]

CoalScalar coal::RSS::volume ( ) const

inline

Volume of the RSS.

◆ width() [1/6]

CoalScalar coal::AABB::width ( ) const

inline

Width of the AABB.

◆ width() [2/6]

template<short N>

CoalScalar coal::KDOP< N >::width ( ) const

inline

The (AABB) width.

◆ width() [3/6]

CoalScalar coal::kIOS::width ( ) const

Width of the kIOS.

◆ width() [4/6]

CoalScalar coal::OBB::width ( ) const

inline

Width of the OBB.

◆ width() [5/6]

CoalScalar coal::OBBRSS::width ( ) const

inline

Width of the OBRSS.

◆ width() [6/6]

CoalScalar coal::RSS::width ( ) const

inline

Width of the RSS.

Variable Documentation

◆ axes [1/2]

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Matrix3s coal::OBB::axes

Orientation of OBB. axis[i] is the ith column of the orientation matrix for the box; it is also the i-th principle direction of the box. We assume that axis[0] corresponds to the axis with the longest box edge, axis[1] corresponds to the shorter one and axis[2] corresponds to the shortest one.

◆ axes [2/2]

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Matrix3s coal::RSS::axes

Orientation of RSS. axis[i] is the ith column of the orientation matrix for the RSS; it is also the i-th principle direction of the RSS. We assume that axis[0] corresponds to the axis with the longest length, axis[1] corresponds to the shorter one and axis[2] corresponds to the shortest one.

◆ dist_

template<short N>

Eigen::Array<CoalScalar, N, 1> coal::KDOP< N >::dist_

protected

Origin's distances to N KDOP planes.

◆ extent

Vec3s coal::OBB::extent

Half dimensions of OBB.

◆ length

CoalScalar coal::RSS::length[2]

Side lengths of rectangle.

◆ max_

Vec3s coal::AABB::max_

The max point in the AABB.

◆ max_num_spheres

constexpr size_t coal::kIOS::max_num_spheres = 5

staticconstexpr

◆ min_

Vec3s coal::AABB::min_

The min point in the AABB.

◆ num_spheres

unsigned int coal::kIOS::num_spheres

The number of spheres, no larger than 5.

◆ o

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Vec3s coal::kIOS::kIOS_Sphere::o

◆ obb [1/2]

OBB coal::kIOS::obb

@ OBB related with kIOS

◆ obb [2/2]

EIGEN_MAKE_ALIGNED_OPERATOR_NEW OBB coal::OBBRSS::obb

OBB member, for rotation.

◆ r

CoalScalar coal::kIOS::kIOS_Sphere::r

◆ radius

CoalScalar coal::RSS::radius

Radius of sphere summed with rectangle to form RSS.

◆ rss

RSS coal::OBBRSS::rss

RSS member, for distance.

◆ spheres

kIOS_Sphere coal::kIOS::spheres[max_num_spheres]

The (at most) five spheres for intersection.

◆ To

Vec3s coal::OBB::To

Center of OBB.

◆ Tr

Vec3s coal::RSS::Tr

Origin of the rectangle in RSS.

Classes

Functions

Variables

Bounding volume API

Detailed Description

Function Documentation

◆ AABB() [1/6]

◆ AABB() [2/6]

◆ AABB() [3/6]

◆ AABB() [4/6]

◆ AABB() [5/6]

◆ AABB() [6/6]

◆ axisOverlap()

◆ center() [1/6]

◆ center() [2/6]

◆ center() [3/6]

◆ center() [4/6]

◆ center() [5/6]

◆ center() [6/6]

◆ contain() [1/6]

◆ contain() [2/6]

◆ contain() [3/6]

◆ contain() [4/6]

◆ contain() [5/6]

◆ contain() [6/6]

◆ depth() [1/6]

◆ depth() [2/6]

◆ depth() [3/6]

◆ depth() [4/6]

◆ depth() [5/6]

◆ depth() [6/6]

◆ dist() [1/2]

◆ dist() [2/2]

◆ distance() [1/10]

◆ distance() [2/10]

◆ distance() [3/10]

◆ distance() [4/10]

◆ distance() [5/10]

◆ distance() [6/10]

◆ distance() [7/10]

◆ distance() [8/10]

◆ distance() [9/10]

◆ distance() [10/10]

◆ expand() [1/3]

◆ expand() [2/3]

◆ expand() [3/3]

◆ height() [1/6]

◆ height() [2/6]

◆ height() [3/6]

◆ height() [4/6]

◆ height() [5/6]

◆ height() [6/6]

◆ inside()

◆ KDOP() [1/3]

◆ KDOP() [2/3]

◆ KDOP() [3/3]

◆ OBB()

◆ obbDisjoint()

◆ operator!=() [1/7]

◆ operator!=() [2/7]

◆ operator!=() [3/7]

◆ operator!=() [4/7]

◆ operator!=() [5/7]

◆ operator!=() [6/7]

◆ operator!=() [7/7]

◆ operator+() [1/6]

◆ operator+() [2/6]

◆ operator+() [3/6]

◆ operator+() [4/6]

◆ operator+() [5/6]

◆ operator+() [6/6]

◆ operator+=() [1/12]

◆ operator+=() [2/12]

◆ operator+=() [3/12]

◆ operator+=() [4/12]

◆ operator+=() [5/12]

◆ operator+=() [6/12]

◆ operator+=() [7/12]

◆ operator+=() [8/12]

◆ operator+=() [9/12]