A 3d rectangular box aligned with an unspecified frame F and centered at that frame's origin. More...

Public Member Functions
	Box_ ()
	Construct an uninitialized Box object; the dimensions will be garbage. More...

	Box_ (const Vec3P &halfLengths)
	Construct a Box with the given nonnegative half-dimensions. More...

Box_ &	setHalfLengths (const Vec3P &halfLengths)
	Change the half-dimensions of this box. More...

Box_ &	addToHalfLengths (const Vec3P &incr)
	Change the half-dimensions of this box by adding the given vector. More...

const Vec3P &	getHalfLengths () const
	Return the half-lengths of this box as a Vec3 from the center to the first quadrant vertex. More...

RealP	getOrderedHalfLength (int i) const
	Get lengths in order shortest to longest; 0 is shortest, 2 is longest. More...

CoordinateAxis	getOrderedAxis (int i) const
	Get axes in order shortest to longest; 0 is shortest, 2 is longest. More...

RealP	findVolume () const
	Calculate the volume of this box. More...

RealP	findArea () const
	Calculate the surface area of this box, ignoring degeneracy (meaning that all pairs of sides are counted even if coincident). More...

bool	containsPoint (const Vec3P &pt) const
	Given a point measured and expressed in the box frame, determine whether it is inside the box (we count touching the surface as inside). More...

Vec3P	findClosestPointOfSolidBox (const Vec3P &pt, bool &ptWasInside) const
	Given a point location in the box frame, return the closest point of the solid box, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method. More...

Vec3P	findClosestPointOnSurface (const Vec3P &pt, bool &ptWasInside) const
	Given a point location in the box frame, return the closest point on the box surface, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method. More...

RealP	findDistanceSqrToPoint (const Vec3P &pt) const
	Return the square of the distance from this box to a given point whose location is measured from and expressed in the box frame (at the box center). More...

Vec3P	findSupportPoint (const Vec3 &d) const
	Find a supporting point on the surface of the box in the given direction, which must be expressed in the box frame. More...

RealP	findDistanceSqrToSphere (const Geo::Sphere_< P > &sphere) const
	Return the square of the distance from this box to a given sphere whose center location is measured from and expressed in the box frame (at the box center). More...

RealP	findDistanceSqrToAlignedBox (const Geo::AlignedBox_< P > &aab) const
	Return the square of the distance from this box to an axis-aligned box whose center location is measured from and expressed in this box frame (at the box center). More...

bool	intersectsSphere (const Geo::Sphere_< P > &sphere) const
	Given a sphere with center measured and expressed in the box frame, return true if the box and sphere intersect. More...

bool	intersectsAlignedBox (const Geo::AlignedBox_< P > &aab) const
	Given an aligned box with center measured and expressed in the from of this box, return true if the two boxes intersect. More...

bool	intersectsOrientedBox (const Geo::OrientedBox_< P > &ob) const
	Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes intersect. More...

bool	mayIntersectOrientedBox (const Geo::OrientedBox_< P > &ob) const
	Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes may be intersecting. More...

Box mesh methods
Methods to use if you want to think of the box as a convex mesh.
Vec3P	getVertexPos (int vx) const
	Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More...

int	findSupportVertex (const Vec3P &d) const
	Find the vertex (0-7) that is furthest in the direction d, which is given in the box frame. More...

UnitVec3P	getVertexNormal (int vx) const
	Vertex normals point diagonally outwards from the box corners. More...

Vec3P	getEdgeCenter (int ex) const
	Return the center point of the specified edge, in the box frame. More...

UnitVec3P	getEdgeNormal (int ex) const
	Edge normals point diagonally outwards from the edge. More...

CoordinateDirection	getEdgeCoordinateDirection (int ex) const
	Return the direction of an edge, going from its first vertex to its second vertex, as a CoordinateDirection. More...

UnitVec3P	getEdgeDirection (int ex) const
	Return a unit vector aligned with the selected edge, pointing in the direction from the first vertex towards the second vertex, in the box frame. More...

CoordinateDirection	getFaceCoordinateDirection (int fx) const
	Return the outward normal for the given face as a CoordinateDirection. More...

Vec3P	getFaceCenter (int fx) const
	Return the center point position for the given face. More...

UnitVec3P	getFaceNormal (int fx) const
	Return the outward normal for the given face as a unit vector in the box frame. More...

void	getFaceVertices (int fx, int v[4]) const
	A face has four vertices ordered counterclockwise about the face normal. More...

void	getVertexFaces (int vx, int f[3], int w[3]) const
	Each vertex has three incident faces. More...

void	getEdgeVertices (int ex, int v[2]) const
	An edge connects two vertices. More...

void	getVertexEdges (int vx, int e[3], int w[3]) const
	Each vertex has three incident edges. More...

void	getFaceEdges (int fx, int e[4]) const
	A face has four edges, ordered by the vertex ordering: v0-v1, v1-v2, v2-v3, v3-v1. More...

void	getEdgeFaces (int ex, int f[2], int w[2]) const
	An edge is between two faces. More...

static int	getNumVertices ()
	Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More...

static int	getNumEdges ()
	Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More...

static int	getNumFaces ()
	Use bits in the vertex number to pick the signs, with 0=negative, 1=positive: More...

Detailed Description

template<class P>
class SimTK::Geo::Box_

A 3d rectangular box aligned with an unspecified frame F and centered at that frame's origin.

The box has a local frame B, centered at the box center and oriented along the box edges, and B==F. We keep track of the relative edge lengths to facilitate short-to-long processing.

Constructor & Destructor Documentation

◆ Box_() [1/2]

template<class P >

SimTK::Geo::Box_::Box_ ( )

inline

Construct an uninitialized Box object; the dimensions will be garbage.

◆ Box_() [2/2]

template<class P >

SimTK::Geo::Box_::Box_ ( const Vec3P & halfLengths )

inline

Construct a Box with the given nonnegative half-dimensions.

Cost is 4 flops to sort the edges.

Member Function Documentation

◆ setHalfLengths()

template<class P >

Box_& SimTK::Geo::Box_::setHalfLengths ( const Vec3P & halfLengths )

inline

Change the half-dimensions of this box.

Dimensions must be nonnegative. Cost is 4 flops to sort the edges.

◆ addToHalfLengths()

template<class P >

Box_& SimTK::Geo::Box_::addToHalfLengths ( const Vec3P & incr )

inline

Change the half-dimensions of this box by adding the given vector.

The result must be nonnegative. Cost is 7 flops, including resorting the edges.

◆ getHalfLengths()

template<class P >

const Vec3P& SimTK::Geo::Box_::getHalfLengths ( ) const

inline

Return the half-lengths of this box as a Vec3 from the center to the first quadrant vertex.

◆ getOrderedHalfLength()

template<class P >

RealP SimTK::Geo::Box_::getOrderedHalfLength ( int i ) const

inline

Get lengths in order shortest to longest; 0 is shortest, 2 is longest.

◆ getOrderedAxis()

template<class P >

CoordinateAxis SimTK::Geo::Box_::getOrderedAxis ( int i ) const

inline

Get axes in order shortest to longest; 0 is shortest, 2 is longest.

◆ findVolume()

template<class P >

RealP SimTK::Geo::Box_::findVolume ( ) const

inline

Calculate the volume of this box.

Cost is 4 flops.

◆ findArea()

template<class P >

RealP SimTK::Geo::Box_::findArea ( ) const

inline

Calculate the surface area of this box, ignoring degeneracy (meaning that all pairs of sides are counted even if coincident).

Cost is 6 flops.

◆ containsPoint()

template<class P >

bool SimTK::Geo::Box_::containsPoint ( const Vec3P & pt ) const

inline

Given a point measured and expressed in the box frame, determine whether it is inside the box (we count touching the surface as inside).

The point must be measured from the box center. Cost is about 5 flops.

◆ findClosestPointOfSolidBox()

template<class P >

Vec3P SimTK::Geo::Box_< P >::findClosestPointOfSolidBox	(	const Vec3P &	pt,
		bool &	ptWasInside
	)		const

inline

Given a point location in the box frame, return the closest point of the solid box, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method.

Here we define the closest point to an inside point to be the point itself. Cost is about 9 flops.

◆ findClosestPointOnSurface()

template<class P >

Vec3P SimTK::Geo::Box_< P >::findClosestPointOnSurface	(	const Vec3P &	pt,
		bool &	ptWasInside
	)		const

inline

Given a point location in the box frame, return the closest point on the box surface, and a flag saying whether the given point was inside the box, using the same definition of "inside" as the containsPoint() method.

Cost is about 9 flops for outside points, 18 for inside points.

◆ findDistanceSqrToPoint()

template<class P >

RealP SimTK::Geo::Box_::findDistanceSqrToPoint ( const Vec3P & pt ) const

inline

Return the square of the distance from this box to a given point whose location is measured from and expressed in the box frame (at the box center).

If the point is on or inside the box the returned distance is zero. Cost is about 14 flops.

◆ findSupportPoint()

template<class P >

Vec3P SimTK::Geo::Box_::findSupportPoint ( const Vec3 & d ) const

inline

Find a supporting point on the surface of the box in the given direction, which must be expressed in the box frame.

The direction vector does not have to be a unit vector. The returned point will always be one of the eight vertices; we treat zeroes here as positive. Consequently if the input vector is exactly zero, the vertex in the positive orthant is returned as it would be if the input direction were (1,1,1). Cost is about 5 flops.

◆ findDistanceSqrToSphere()

template<class P >

RealP SimTK::Geo::Box_::findDistanceSqrToSphere ( const Geo::Sphere_ & sphere ) const

inline

Return the square of the distance from this box to a given sphere whose center location is measured from and expressed in the box frame (at the box center).

If the sphere intersects the box the returned distance is zero. Cost is about 17 flops.

◆ findDistanceSqrToAlignedBox()

template<class P >

RealP SimTK::Geo::Box_::findDistanceSqrToAlignedBox ( const Geo::AlignedBox_ & aab ) const

inline

Return the square of the distance from this box to an axis-aligned box whose center location is measured from and expressed in this box frame (at the box center).

If the boxes intersect the returned distance is zero. Cost is about 17 flops.

◆ intersectsSphere()

template<class P >

bool SimTK::Geo::Box_::intersectsSphere ( const Geo::Sphere_ & sphere ) const

inline

Given a sphere with center measured and expressed in the box frame, return true if the box and sphere intersect.

We are treating both objects as solids, so we'll say yes even if one object completely contains the other. We also return true if they are just touching. Cost is about 8 flops.

◆ intersectsAlignedBox()

template<class P >

bool SimTK::Geo::Box_::intersectsAlignedBox ( const Geo::AlignedBox_ & aab ) const

inline

Given an aligned box with center measured and expressed in the from of this box, return true if the two boxes intersect.

We are treating both objects as solids, so we'll say yes even if one box completely contains the other. We also return true if they are just touching. Cost is about 8 flops.

◆ intersectsOrientedBox()

template<class P >

bool SimTK::Geo::Box_::intersectsOrientedBox ( const Geo::OrientedBox_ & ob ) const

Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes intersect.

We are treating both objects as solids, so we'll say yes even if one box completely contains the other. We also return true if they are just touching. This is an exact but fairly expensive test if the boxes are separated; if you don't mind some false positives, use mayIntersectOrientedBox() instead. Cost is about 200 flops worst case (when boxes are intersecting) although it can return false in as few as 16 flops.

◆ mayIntersectOrientedBox()

template<class P >

bool SimTK::Geo::Box_::mayIntersectOrientedBox ( const Geo::OrientedBox_ & ob ) const

Given an oriented box whose pose is measured and expressed in the frame of this box, return true if the two boxes may be intersecting.

Only relatively cheap operations are performed at the expense of returning false positives sometimes (allegedly less than 10% of the time). If you need an exact determination, use intersectsOrientedBox(). Cost is about 75 flops worst case (when boxes appear to be intersecting) but can return false in as few as 16 flops.

◆ getNumVertices()

template<class P >

static int SimTK::Geo::Box_::getNumVertices ( )

inlinestatic

Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:

    000  -hx -hy -hz
    001  -hx -hy  hz
    ...
    111   hx  hy  hz

◆ getNumEdges()

template<class P >

static int SimTK::Geo::Box_::getNumEdges ( )

inlinestatic

Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:

    000  -hx -hy -hz
    001  -hx -hy  hz
    ...
    111   hx  hy  hz

◆ getNumFaces()

template<class P >

static int SimTK::Geo::Box_::getNumFaces ( )

inlinestatic

Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:

    000  -hx -hy -hz
    001  -hx -hy  hz
    ...
    111   hx  hy  hz

◆ getVertexPos()

template<class P >

Vec3P SimTK::Geo::Box_::getVertexPos ( int vx ) const

inline

Use bits in the vertex number to pick the signs, with 0=negative, 1=positive:

    000  -hx -hy -hz
    001  -hx -hy  hz
    ...
    111   hx  hy  hz

◆ findSupportVertex()

template<class P >

int SimTK::Geo::Box_::findSupportVertex ( const Vec3P & d ) const

inline

Find the vertex (0-7) that is furthest in the direction d, which is given in the box frame.

Zero coordinates in d are treated as though positive.

◆ getVertexNormal()

template<class P >

UnitVec3P SimTK::Geo::Box_::getVertexNormal ( int vx ) const

inline

Vertex normals point diagonally outwards from the box corners.

These are unit vectors with each coordinate +/- 1/sqrt(3).

◆ getEdgeCenter()

template<class P >

Vec3P SimTK::Geo::Box_::getEdgeCenter ( int ex ) const

inline

Return the center point of the specified edge, in the box frame.

◆ getEdgeNormal()

template<class P >

UnitVec3P SimTK::Geo::Box_::getEdgeNormal ( int ex ) const

inline

Edge normals point diagonally outwards from the edge.

These are unit vectors with one coordinate zero and the others +/- 1/sqrt(2).

◆ getEdgeCoordinateDirection()

template<class P >

CoordinateDirection SimTK::Geo::Box_::getEdgeCoordinateDirection ( int ex ) const

inline

Return the direction of an edge, going from its first vertex to its second vertex, as a CoordinateDirection.

◆ getEdgeDirection()

template<class P >

UnitVec3P SimTK::Geo::Box_::getEdgeDirection ( int ex ) const

inline

Return a unit vector aligned with the selected edge, pointing in the direction from the first vertex towards the second vertex, in the box frame.

For a box, all edges are aligned with the coordinate system axes so the returned vector will have only one non-zero component which will be 1 or -1.

◆ getFaceCoordinateDirection()

template<class P >

CoordinateDirection SimTK::Geo::Box_::getFaceCoordinateDirection ( int fx ) const

inline

Return the outward normal for the given face as a CoordinateDirection.

◆ getFaceCenter()

template<class P >

Vec3P SimTK::Geo::Box_::getFaceCenter ( int fx ) const

inline

Return the center point position for the given face.

This will be a vector with one non-zero component of magnitude equal to one of the box half-dimensions, with the appropriate sign.

◆ getFaceNormal()

template<class P >

UnitVec3P SimTK::Geo::Box_::getFaceNormal ( int fx ) const

inline

Return the outward normal for the given face as a unit vector in the box frame.

This will have only one non-zero component which will be 1 or -1.

◆ getFaceVertices()

template<class P >

void SimTK::Geo::Box_< P >::getFaceVertices	(	int	fx,
		int	v[4]
	)		const

inline

A face has four vertices ordered counterclockwise about the face normal.

◆ getVertexFaces()

template<class P >

void SimTK::Geo::Box_< P >::getVertexFaces	(	int	vx,
		int	f[3],
		int	w[3]
	)		const

inline

Each vertex has three incident faces.

Return the face numbers (0-5) and which of the four face vertices is this one (0-3).

◆ getEdgeVertices()

template<class P >

void SimTK::Geo::Box_< P >::getEdgeVertices	(	int	ex,
		int	v[2]
	)		const

inline

An edge connects two vertices.

◆ getVertexEdges()

template<class P >

void SimTK::Geo::Box_< P >::getVertexEdges	(	int	vx,
		int	e[3],
		int	w[3]
	)		const

inline

Each vertex has three incident edges.

Return the edge numbers (0-11) and which of the two edge vertices is this one (0-1).

◆ getFaceEdges()

template<class P >

void SimTK::Geo::Box_< P >::getFaceEdges	(	int	fx,
		int	e[4]
	)		const

inline

A face has four edges, ordered by the vertex ordering: v0-v1, v1-v2, v2-v3, v3-v1.

◆ getEdgeFaces()

template<class P >

void SimTK::Geo::Box_< P >::getEdgeFaces	(	int	ex,
		int	f[2],
		int	w[2]
	)		const

inline

An edge is between two faces.

Return the face numbers (0-5) and which one of the four edges on each face is this edge (0-3).

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

Public Member Functions

Box mesh methods

Detailed Description

template<class P> class SimTK::Geo::Box_< P >

Constructor & Destructor Documentation

◆ Box_() [1/2]

◆ Box_() [2/2]

Member Function Documentation

◆ setHalfLengths()

◆ addToHalfLengths()

◆ getHalfLengths()

◆ getOrderedHalfLength()

◆ getOrderedAxis()

◆ findVolume()

◆ findArea()

◆ containsPoint()

◆ findClosestPointOfSolidBox()

◆ findClosestPointOnSurface()

◆ findDistanceSqrToPoint()

◆ findSupportPoint()

◆ findDistanceSqrToSphere()

◆ findDistanceSqrToAlignedBox()

◆ intersectsSphere()

◆ intersectsAlignedBox()

◆ intersectsOrientedBox()

◆ mayIntersectOrientedBox()

◆ getNumVertices()

◆ getNumEdges()

◆ getNumFaces()

◆ getVertexPos()

◆ findSupportVertex()

◆ getVertexNormal()

◆ getEdgeCenter()

◆ getEdgeNormal()

◆ getEdgeCoordinateDirection()

◆ getEdgeDirection()

◆ getFaceCoordinateDirection()

◆ getFaceCenter()

◆ getFaceNormal()

◆ getFaceVertices()

◆ getVertexFaces()

◆ getEdgeVertices()

◆ getVertexEdges()

◆ getFaceEdges()

◆ getEdgeFaces()

template<class P>
class SimTK::Geo::Box_< P >