sofa::geometry::Triangle Struct Reference

#include <Triangle.h>

Static Public Attributes
static constexpr sofa::Size	NumberOfNodes = 3
static constexpr ElementType	Element_type = ElementType::TRIANGLE

Public Member Functions
	Triangle ()=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	area (const Node &n0, const Node &n1, const Node &n2)
	Compute the area of a triangle. 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	getBarycentricCoordinates (const Node &p0, const Node &n0, const Node &n1, const Node &n2)
	Compute the barycentric coordinates of the input point in the Triangle. It can be interpreted as masses placed at the vertices of Triangle (n0, n1, n2), such that the point is the center of mass of these masses. 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	normal (const Node &n0, const Node &n1, const Node &n2)
	Compute the normal of a triangle. 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 bool	isPointInTriangle (const Node &p0, const Node &n0, const Node &n1, const Node &n2, sofa::type::Vec< 3, T > &baryCoefs)
	Test if input point is inside Triangle (n0, n1, n2) using Triangle. More...
template<typename TReal >
static constexpr bool	rayIntersection (const sofa::type::Vec< 3, TReal > &n0, const sofa::type::Vec< 3, TReal > &n1, const sofa::type::Vec< 3, TReal > &n2, const sofa::type::Vec< 3, TReal > &origin, const sofa::type::Vec< 3, TReal > &direction, TReal &t, TReal &u, TReal &v)
	Test if a ray intersects a triangle, and gives barycentric coordinates of the intersection if applicable. More...
template<typename TReal >
static constexpr bool	rayIntersection (const sofa::type::Vec< 3, TReal > &n0, const sofa::type::Vec< 3, TReal > &n1, const sofa::type::Vec< 3, TReal > &n2, const sofa::type::Vec< 3, TReal > &origin, const sofa::type::Vec< 3, TReal > &direction)
	Test if a ray intersects a triangle. More...

Attribute details

Element_type

constexpr ElementType sofa::geometry::Triangle::Element_type = ElementType::TRIANGLE

staticconstexpr

NumberOfNodes

constexpr sofa::Size sofa::geometry::Triangle::NumberOfNodes = 3

staticconstexpr

Constructor details

Triangle()

sofa::geometry::Triangle::Triangle ( )

delete

Function details

area()

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::Triangle::area ( const Node &  n0, const Node &  n1, const Node &  n2  )

inlinestaticconstexpr

Compute the area of a triangle.

Remarks

Depending of the type of Node, it will either use a optimized version or a generic one

Optimizations are enabled for sofa::type::Vec and the dimension (2D or 3D)

Template Parameters

Node	iterable container (or sofa::type::Vec with cross() and norm())
T	scalar

Parameters

n0,n1,n2

nodes of the triangle

Returns

Area of the triangle (a T scalar)

getBarycentricCoordinates()

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::Triangle::getBarycentricCoordinates ( const Node &  p0, const Node &  n0, const Node &  n1, const Node &  n2  )

inlinestaticconstexpr

Compute the barycentric coordinates of the input point in the Triangle. It can be interpreted as masses placed at the vertices of Triangle (n0, n1, n2), such that the point is the center of mass of these masses.

Template Parameters

Node	iterable container
T	scalar

Parameters

p0	position of the input point to compute the coefficients
n0,n1,n2	nodes of the triangle

Returns

sofa::type::Vec<3, T> barycentric coefficients of each vertex of the Triangle. These masses can be zero or negative; they are all positive if and only if the point is inside the Triangle.

isPointInTriangle()

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 bool sofa::geometry::Triangle::isPointInTriangle ( const Node &  p0, const Node &  n0, const Node &  n1, const Node &  n2, sofa::type::Vec< 3, T > &  baryCoefs  )

inlinestaticconstexpr

Test if input point is inside Triangle (n0, n1, n2) using Triangle.

See also

getBarycentricCoordinates . The point is inside the Triangle if and only if Those coordinates are all positive.

Template Parameters

Node	iterable container
T	scalar

Parameters

p0	position of the point to test
n0,n1,n2	nodes of the triangle
output	parameter: sofa::type::Vec<3, T> barycentric coordinates of the input point in Triangle

Returns

bool result if point is inside Triangle.

normal()

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::Triangle::normal ( const Node &  n0, const Node &  n1, const Node &  n2  )

inlinestaticconstexpr

Compute the normal of a triangle.

Remarks

triangle normal computation is only possible in 3D

normal returned is not normalized

Template Parameters

Node	iterable container (or sofa::type::Vec with cross() and norm())
T	scalar

Parameters

n0,n1,n2

nodes of the triangle

Returns

Vec3 normal of this triangle

rayIntersection() [1/2]

template<typename TReal >

static constexpr bool sofa::geometry::Triangle::rayIntersection ( const sofa::type::Vec< 3, TReal > &  n0, const sofa::type::Vec< 3, TReal > &  n1, const sofa::type::Vec< 3, TReal > &  n2, const sofa::type::Vec< 3, TReal > &  origin, const sofa::type::Vec< 3, TReal > &  direction  )

inlinestaticconstexpr

Test if a ray intersects a triangle.

Remarks

Implementation for 3D only

Template Parameters

Node	iterable container (or sofa::type::Vec with cross() and norm())
T	scalar

Parameters

n0,n1,n2

nodes of the triangle

Returns

either if the given ray intersects the given triangle or not

rayIntersection() [2/2]

template<typename TReal >

static constexpr bool sofa::geometry::Triangle::rayIntersection ( const sofa::type::Vec< 3, TReal > &  n0, const sofa::type::Vec< 3, TReal > &  n1, const sofa::type::Vec< 3, TReal > &  n2, const sofa::type::Vec< 3, TReal > &  origin, const sofa::type::Vec< 3, TReal > &  direction, TReal &  t, TReal &  u, TReal &  v  )

inlinestaticconstexpr

Test if a ray intersects a triangle, and gives barycentric coordinates of the intersection if applicable.

Remarks

Implementation for 3D only

Template Parameters

Node	iterable container (or sofa::type::Vec with cross() and norm())
T	scalar

Parameters

n0,n1,n2	nodes of the triangle
t,u,v	barycentric coefficients of the potential intersection in the triangle

Returns

either if the given ray intersects the given triangle or not