#include <Hexahedron.h>

Static Public Attributes
static constexpr sofa::Size	NumberOfNodes = 8

static constexpr ElementType	Element_type = ElementType::HEXAHEDRON

static constexpr std::array< std::pair< sofa::Size, sofa::Size >, 4 >	xEdges
	Defines the edges of a hexahedron along the X-axis. More...

static constexpr std::array< std::pair< sofa::Size, sofa::Size >, 4 >	yEdges
	Defines the edges of a hexahedron along the Y-axis. More...

static constexpr std::array< std::pair< sofa::Size, sofa::Size >, 4 >	zEdges
	Defines the edges of a hexahedron along the Z-axis. More...

Public Member Functions
	Hexahedron ()=delete

Static Public Member Functions
template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>
static constexpr auto	center (const Node &n0, const Node &n1, const Node &n2, const Node &n3, const Node &n4, const Node &n5, const Node &n6, const Node &n7)
	Compute the center of a hexahedron. More...

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>
static constexpr auto	barycentricCoefficients (const Node &n0, const Node &n1, const Node &n2, const Node &n3, const Node &n4, const Node &n5, const Node &n6, const Node &n7, const Node &pos)
	Compute the barycentric coefficients of a node in a hexahedron. More...

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>
static constexpr auto	squaredDistanceTo (const Node &n0, const Node &n1, const Node &n2, const Node &n3, const Node &n4, const Node &n5, const Node &n6, const Node &n7, const Node &pos)
	Compute the squared distance between a node and the center of a hexahedron. More...

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>
static constexpr auto	getPositionFromBarycentricCoefficients (const Node &n0, const Node &n1, const Node &n2, const Node &n3, const Node &n4, const Node &n5, const Node &n6, const Node &n7, const sofa::type::fixed_array< SReal, 3 > &baryC)
	Compute a position from a given set of barycentric coefficients and the associated hexahedron. More...

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>
static constexpr auto	volume (const Node &n0, const Node &n1, const Node &n2, const Node &n3, const Node &n4, const Node &n5, const Node &n6, const Node &n7)
	Compute the volume of a hexahedron. More...

Attribute details

◆ Element_type

constexpr ElementType sofa::geometry::Hexahedron::Element_type = ElementType::HEXAHEDRON

staticconstexpr

◆ NumberOfNodes

constexpr sofa::Size sofa::geometry::Hexahedron::NumberOfNodes = 8

staticconstexpr

◆ xEdges

constexpr std::array<std::pair<sofa::Size, sofa::Size>, 4> sofa::geometry::Hexahedron::xEdges

staticconstexpr

Initial value:

{

{{0, 1}, {4, 5}, {3, 2}, {7, 6}}}

Defines the edges of a hexahedron along the X-axis.

This variable represents the edges of a hexahedron that are parallel to the X-axis according to the conventional node numbering. It consists of an array of 4 pairs, each pair containing the indices of the two nodes that form an edge along the X-axis.

◆ yEdges

constexpr std::array<std::pair<sofa::Size, sofa::Size>, 4> sofa::geometry::Hexahedron::yEdges

staticconstexpr

Initial value:

{

{{4, 7}, {5, 6}, {1, 2}, {0, 3}}}

Defines the edges of a hexahedron along the Y-axis.

This variable represents the edges of a hexahedron that are parallel to the Y-axis according to the conventional node numbering. It consists of an array of 4 pairs, each pair containing the indices of the two nodes that form an edge along the Y-axis.

◆ zEdges

constexpr std::array<std::pair<sofa::Size, sofa::Size>, 4> sofa::geometry::Hexahedron::zEdges

staticconstexpr

Initial value:

{

{{4, 0}, {5, 1}, {6, 2}, {7, 3}}}

Defines the edges of a hexahedron along the Z-axis.

This variable represents the edges of a hexahedron that are parallel to the Z-axis according to the conventional node numbering. It consists of an array of 4 pairs, each pair containing the indices of the two nodes that form an edge along the Z-axis.

Constructor details

◆ Hexahedron()

sofa::geometry::Hexahedron::Hexahedron ( )

delete

Function details

◆ barycentricCoefficients()

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>

static constexpr auto sofa::geometry::Hexahedron::barycentricCoefficients	(	const Node &	n0,
		const Node &	n1,
		const Node &	n2,
		const Node &	n3,
		const Node &	n4,
		const Node &	n5,
		const Node &	n6,
		const Node &	n7,
		const Node &	pos
	)

inlinestaticconstexpr

Compute the barycentric coefficients of a node in a hexahedron.

Remarks: Due to some optimizations, the order of nodes given as parameter is necessary.

Template Parameters

Node	iterable container, with operator[]
T	scalar

Parameters

n0,n1,n2,n3,n4,n5,n6,n7	nodes of the hexahedron
pos	position of the node from which the coefficients will be computed

Returns: A Vec3 container with the barycentric coefficients of the given node

◆ center()

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>

static constexpr auto sofa::geometry::Hexahedron::center	(	const Node &	n0,
		const Node &	n1,
		const Node &	n2,
		const Node &	n3,
		const Node &	n4,
		const Node &	n5,
		const Node &	n6,
		const Node &	n7
	)

inlinestaticconstexpr

Compute the center of a hexahedron.

Remarks: The order of nodes given as parameter is not necessary.

Template Parameters

Node	iterable container, with operator[]
T	scalar

Parameters

n0,n1,n2,n3,n4,n5,n6,n7 nodes of the hexahedron

Returns: Center of the hexahedron (same type as the given nodes)

◆ getPositionFromBarycentricCoefficients()

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>

static constexpr auto sofa::geometry::Hexahedron::getPositionFromBarycentricCoefficients	(	const Node &	n0,
		const Node &	n1,
		const Node &	n2,
		const Node &	n3,
		const Node &	n4,
		const Node &	n5,
		const Node &	n6,
		const Node &	n7,
		const sofa::type::fixed_array< SReal, 3 > &	baryC
	)

inlinestaticconstexpr

Compute a position from a given set of barycentric coefficients and the associated hexahedron.

Remarks: The order of nodes given as parameter is necessary.

Template Parameters

Node	iterable container, with operator* applicable with a scalar
T	scalar

Parameters

n0,n1,n2,n3,n4,n5,n6,n7	nodes of the hexahedron
baryC	barycentric coefficients

Returns: Position computed from the coefficients, as a Node type

◆ squaredDistanceTo()

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>

static constexpr auto sofa::geometry::Hexahedron::squaredDistanceTo	(	const Node &	n0,
		const Node &	n1,
		const Node &	n2,
		const Node &	n3,
		const Node &	n4,
		const Node &	n5,
		const Node &	n6,
		const Node &	n7,
		const Node &	pos
	)

inlinestaticconstexpr

Compute the squared distance between a node and the center of a hexahedron.

Remarks: Due to some optimizations, the order of nodes given as parameter is necessary.

Template Parameters

Node	iterable container, with operator[]
T	scalar

Parameters

n0,n1,n2,n3,n4,n5,n6,n7	nodes of the hexahedron
pos	position of the node from which the distance will be computed

Returns: Distance from the node and the center of the hexahedron, as a T scalar

◆ volume()

template<typename Node , typename T = std::decay_t<decltype(*std::begin(std::declval<Node>()))>, typename = std::enable_if_t<std::is_scalar_v<T>>>

static constexpr auto sofa::geometry::Hexahedron::volume	(	const Node &	n0,
		const Node &	n1,
		const Node &	n2,
		const Node &	n3,
		const Node &	n4,
		const Node &	n5,
		const Node &	n6,
		const Node &	n7
	)

inlinestaticconstexpr

Compute the volume of a hexahedron.

Remarks: non optimized version: just return the sum of the 6 inner-tetrahedra

Template Parameters

Node	iterable container
T	scalar

Parameters

n0,n1,n2,n3,n4,n5,n6,n7 nodes of the hexahedron

Returns: Volume of the hexahedron, as a T scalar

Static Public Attributes

Public Member Functions

Static Public Member Functions

Attribute details

◆ Element_type

◆ NumberOfNodes

◆ xEdges

◆ yEdges

◆ zEdges

Constructor details

◆ Hexahedron()

Function details

◆ barycentricCoefficients()

◆ center()

◆ getPositionFromBarycentricCoefficients()

◆ squaredDistanceTo()

◆ volume()