Represents an octahedral geometric shape defined by six points. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/Octahedron.hpp>

Public Types
using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

Public Member Functions
AXOM_HOST_DEVICE	Octahedron ()
	Default Octahedron constructor. Creates a degenerate octahedron. More...

AXOM_HOST_DEVICE	Octahedron (const PointType &p, const PointType &q, const PointType &r, const PointType &s, const PointType &t, const PointType &u)
	Creates an octahedron from the 6 points p,q,r,s,t,u. More...

AXOM_HOST_DEVICE	Octahedron (const PointType *pts)
	Octahedron constructor from an array of Points. More...

AXOM_HOST_DEVICE	Octahedron (const axom::ArrayView< PointType > pts)
	Octahedron constructor from an Array of Points. More...

AXOM_HOST_DEVICE	Octahedron (std::initializer_list< PointType > pts)
	Octahedron constructor from an initializer list of Points. More...

AXOM_HOST_DEVICE PointType &	operator[] (int idx)
	Index operator to get the i^th vertex. More...

AXOM_HOST_DEVICE const PointType &	operator[] (int idx) const
	Index operator to get the i^th vertex. More...

AXOM_HOST_DEVICE bool	equals (const Octahedron &other, double eps=1.e-24) const
	Test if this Octahedron is equal to another, within a tolerance. More...

std::ostream &	print (std::ostream &os) const
	Simple formatted print of an octahedron instance. More...

Static Public Attributes
static constexpr int	NUM_VERTS = 6

Detailed Description

template<typename T, int NDIMS = 3>
class axom::primal::Octahedron< T, NDIMS >

Represents an octahedral geometric shape defined by six points.

Template Parameters

T	the coordinate type, e.g., double, float, etc.
NDIMS	the number of spatial dimensions

There are six vertices in the octahedron, labelled P through U as the constructor's arguments. They are accessible using the square-brackets operator, with P being index 0, Q index 1, through U as index 5.

Imagine a regular octahedron with two parallel triangles, top and bottom— the end-caps, as it were. If you look "down", normal to the end-cap triangles, you will see that the vertices of the top triangle protrude beyond the edges of the bottom triangle (and vice versa). Here's a diagram showing just the end-cap triangles, omitting the other edges for clarity.

*
*         P
*         /\
*    Q -------- U
*      \      /
*      /\    /\
*    R --\  /-- T
*         \/
*         S
*
*

Now imagine looking from the side, edge-on to the end-caps. If you unroll the "side-wall" triangles, you get a triangle strip. Here's another diagram showing just the triangle strip, with the same points labeled. Points P and Q are repeated so we can show all eight faces.

*
*        Q --- S --- U --- Q
*       / \   / \   / \   /
*      /   \ /   \ /   \ /
*     P --- R --- T --- P
*
*

Member Typedef Documentation

◆ PointType

template<typename T , int NDIMS = 3>

using axom::primal::Octahedron< T, NDIMS >::PointType = Point<T, NDIMS>

◆ VectorType

template<typename T , int NDIMS = 3>

using axom::primal::Octahedron< T, NDIMS >::VectorType = Vector<T, NDIMS>

Constructor & Destructor Documentation

◆ Octahedron() [1/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Octahedron< T, NDIMS >::Octahedron ( )

inline

Default Octahedron constructor. Creates a degenerate octahedron.

◆ Octahedron() [2/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Octahedron< T, NDIMS >::Octahedron	(	const PointType &	p,
		const PointType &	q,
		const PointType &	r,
		const PointType &	s,
		const PointType &	t,
		const PointType &	u
	)

inline

Creates an octahedron from the 6 points p,q,r,s,t,u.

Parameters

[in]	Point	corresponding to vertex p of the octahedron.
[in]	Point	corresponding to vertex q of the octahedron.
[in]	Point	corresponding to vertex r of the octahedron.
[in]	Point	corresponding to vertex s of the octahedron.
[in]	Point	corresponding to vertex t of the octahedron.
[in]	Point	corresponding to vertex u of the octahedron.

p is opposite s, q is opposite t, r is opposite u.

◆ Octahedron() [3/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Octahedron< T, NDIMS >::Octahedron ( const PointType * pts )

inlineexplicit

Octahedron constructor from an array of Points.

Parameters

[in] pts An array containing at least 6 Points.

Note: It is the responsiblity of the caller to pass an array with at least 6 Points

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS.

◆ Octahedron() [4/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Octahedron< T, NDIMS >::Octahedron ( const axom::ArrayView< PointType > pts )

inlineexplicit

Octahedron constructor from an Array of Points.

Parameters

[in] pts An ArrayView containing at 6 Points.

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS, axom::ArrayView< T, DIM, SPACE >::size(), and SLIC_ASSERT.

◆ Octahedron() [5/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Octahedron< T, NDIMS >::Octahedron ( std::initializer_list< PointType > pts )

inlineexplicit

Octahedron constructor from an initializer list of Points.

Parameters

[in] pts an initializer list containing 6 Points

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS, and SLIC_ASSERT.

Member Function Documentation

◆ operator[]() [1/2]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE PointType& axom::primal::Octahedron< T, NDIMS >::operator[] ( int idx )

inline

Index operator to get the i^th vertex.

Parameters

idx	The index of the desired vertex

Precondition: idx is 0, 1, 2, 3, 4, or 5

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS, and SLIC_ASSERT.

◆ operator[]() [2/2]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE const PointType& axom::primal::Octahedron< T, NDIMS >::operator[] ( int idx ) const

inline

Index operator to get the i^th vertex.

Parameters

idx	The index of the desired vertex

Precondition: idx is 0, 1, 2, 3, 4, or 5

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS, and SLIC_ASSERT.

◆ equals()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE bool axom::primal::Octahedron< T, NDIMS >::equals	(	const Octahedron< T, NDIMS > &	other,
		double	eps = `1.e-24`
	)		const

inline

Test if this Octahedron is equal to another, within a tolerance.

Note: This function can be an expensive operation

References axom::primal::Octahedron< T, NDIMS >::NUM_VERTS, and axom::primal::squared_distance().

◆ print()

template<typename T , int NDIMS = 3>

std::ostream& axom::primal::Octahedron< T, NDIMS >::print ( std::ostream & os ) const

inline

Simple formatted print of an octahedron instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

Member Data Documentation

◆ NUM_VERTS

template<typename T , int NDIMS = 3>

constexpr int axom::primal::Octahedron< T, NDIMS >::NUM_VERTS = 6

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/Octahedron.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

template<typename T, int NDIMS = 3> class axom::primal::Octahedron< T, NDIMS >

Member Typedef Documentation

◆ PointType

◆ VectorType

Constructor & Destructor Documentation

◆ Octahedron() [1/5]

◆ Octahedron() [2/5]

◆ Octahedron() [3/5]

◆ Octahedron() [4/5]

◆ Octahedron() [5/5]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ equals()

◆ print()

Member Data Documentation

◆ NUM_VERTS

template<typename T, int NDIMS = 3>
class axom::primal::Octahedron< T, NDIMS >