Functions
template<class T >
static T	asin (T sine)
	Safe call to the std::asin function. More...

template<class T >
static T	asin_degree (T sine)
	Safe call to the std::asin function. More...

template<class T >
T	acos (T cosine)
	Safe call to the std::acos function. More...

template<class T >
T	acos_degree (T cosine)
	Safe call to the std::acos function. More...

template<typename GeometryTraits >
static bool	sphere_clip_vector (const typename GeometryTraits::Point &center, double r, const typename GeometryTraits::Point &p, typename GeometryTraits::Vector &v, const GeometryTraits &gt)
	Compute the intersection of a sphere (center + radius) with a ray/line (starting point + direction vector). Sphere equation is given by (x-Cx)^2+(y-Cy)^2+(z-Cz)^2=r^2 Line equation is given by (x, y, z) = p + txV. More...

template<typename GeometryTraits >
static bool	is_in_tetrahedron (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const typename GeometryTraits::Point &Pos, const GeometryTraits &gt)
	Predicate fonction to know whether the Pos position is inside the abcd tetrahedron. More...

template<typename GeometryTraits >
static GeometryTraits::Scalar	trilinear_interpolation (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const typename GeometryTraits::Point &Pos, typename GeometryTraits::Scalar vala, typename GeometryTraits::Scalar valb, typename GeometryTraits::Scalar valc, typename GeometryTraits::Scalar vald, const GeometryTraits &gt)
	Trilinear interpolation of values at tetrahedron points. More...

template<typename GeometryTraits >
static std::vector< typename GeometryTraits::Scalar >	trilinear_interpolation (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const typename GeometryTraits::Point &Pos, const std::vector< typename GeometryTraits::Scalar > &vala, const std::vector< typename GeometryTraits::Scalar > &valb, const std::vector< typename GeometryTraits::Scalar > &valc, const std::vector< typename GeometryTraits::Scalar > &vald, const GeometryTraits &gt)
	Trilinear interpolation of values at tetrahedron points. More...

template<typename GeometryTraits >
static bool	is_over_segment (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &Pos, typename GeometryTraits::Vector &diff, const GeometryTraits &gt)
	Predicate fonction to know whether the Pos position is over the ab segment. More...

template<typename GeometryTraits >
static bool	is_in_triangle (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &Pos, const GeometryTraits &gt)
	Predicate fonction to know whether the projection of point Pos on the triangle plane is in the triangle (abc). More...

template<typename GeometryTraits >
static GeometryTraits::Scalar	bilinear_interpolation (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &Pos, typename GeometryTraits::Scalar vala, typename GeometryTraits::Scalar valb, typename GeometryTraits::Scalar valc, const GeometryTraits &gt)
	Bilinear interpolation of values at triangle points. More...

template<typename GeometryTraits >
static std::vector< typename GeometryTraits::Scalar >	bilinear_interpolation (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &Pos, const std::vector< typename GeometryTraits::Scalar > &vala, const std::vector< typename GeometryTraits::Scalar > &valb, const std::vector< typename GeometryTraits::Scalar > &valc, const GeometryTraits &gt)
	Bilinear interpolation of values at triangle points. More...

template<typename GeometryTraits >
GeometryTraits::Point	quad_barycenter (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const GeometryTraits &gt)
	Compute the barycenter/mean position of a quad (given by 4 points). More...

template<typename GeometryTraits >
double	quad_perimeter (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const GeometryTraits &gt)
	Compute the perimeter of a quad (given by 4 points). More...

template<typename GeometryTraits >
double	quad_area (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const typename GeometryTraits::Point &d, const GeometryTraits &gt)
	Compute the area of a quad (given by 4 points). More...

template<typename GeometryTraits >
GeometryTraits::Scalar	triangle_rad_angle (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const GeometryTraits &gt)
	Compute the angle of a triangle (given by 3 points). More...

template<typename GeometryTraits >
GeometryTraits::Point	triangle_barycenter (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const GeometryTraits &)
	Compute the barycenter/mean position of a triangle (given by 3 points). More...

template<typename GeometryTraits >
double	triangle_perimeter (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const GeometryTraits &gt)
	Compute the perimeter of a triangle (given by 3 points). More...

template<typename GeometryTraits >
GeometryTraits::Vector	triangle_normal_unnormalized (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const GeometryTraits &gt)
	Compute the unnormalized normal of a triangle (given by 3 points). More...

template<typename GeometryTraits >
double	triangle_area (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const GeometryTraits &gt)
	Compute the area of a triangle (given by 3 points). More...

template<typename FaceGraph , typename GeometryTraits = FEVV::Geometry_traits< FaceGraph >>
double	triangle_shape_potential (const typename GeometryTraits::Point &a, const typename GeometryTraits::Point &b, const typename GeometryTraits::Point &c, const double prohib_energy, const GeometryTraits &gt)
	Compute the shape potential of a triangle (given by 3 points). Triangle "equilateralness" measure. More...

Function Documentation

◆ acos()

template<class T >

T FEVV::Operators::Geometry::acos ( T cosine )

inline

Safe call to the std::acos function.

Parameters

[in] cosine The cosine value.

Returns: The arccos (in rad) of cosine value, cosine value being truncated to [-1,1] range to avoid input domain error.

Definition at line 64 of file AngleOperations.hpp.

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◆ acos_degree()

template<class T >

T FEVV::Operators::Geometry::acos_degree ( T cosine )

inline

Safe call to the std::acos function.

Parameters

[in] cosine The cosine value.

Returns: The arccos (in degree) of cosine value, cosine value being truncated to [-1,1] range to avoid input domain error.

Definition at line 83 of file AngleOperations.hpp.

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◆ asin()

template<class T >

static T FEVV::Operators::Geometry::asin ( T sine )

static

Safe call to the std::asin function.

Parameters

[in] sine The sinus value.

Returns: The arcsin (in rad) of sine value, sine value being truncated to [-1,1] range to avoid input domain error.

Definition at line 31 of file AngleOperations.hpp.

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◆ asin_degree()

template<class T >

static T FEVV::Operators::Geometry::asin_degree ( T sine )

static

Safe call to the std::asin function.

Parameters

[in] sine The sinus value.

Returns: The arcsin (in degree) of sine value, sine value being truncated to [-1,1] range to avoid input domain error.

Definition at line 50 of file AngleOperations.hpp.

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◆ bilinear_interpolation() [1/2]

template<typename GeometryTraits >

static std::vector< typename GeometryTraits::Scalar > FEVV::Operators::Geometry::bilinear_interpolation	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	Pos,
		const std::vector< typename GeometryTraits::Scalar > &	vala,
		const std::vector< typename GeometryTraits::Scalar > &	valb,
		const std::vector< typename GeometryTraits::Scalar > &	valc,
		const GeometryTraits &	gt
	)

inlinestatic

Bilinear interpolation of values at triangle points.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	Pos	The point for which the bilinear interpolations of values are computed.
[in]	vala	The vector of values at the first point.
[in]	valb	The vector of values at the second point.
[in]	valc	The vector of values at the third point.
[in]	gt	The geometry trait object.

Returns: The vector of the bilinear interpolation of values at a, b, c positions for Pos position.

Precondition: Pos must be inside the triangle (abc), else the bilinear interpolation coefficients are truncated to [0,1].

Definition at line 413 of file Interpolation.hpp.

◆ bilinear_interpolation() [2/2]

template<typename GeometryTraits >

static GeometryTraits::Scalar FEVV::Operators::Geometry::bilinear_interpolation	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	Pos,
		typename GeometryTraits::Scalar	vala,
		typename GeometryTraits::Scalar	valb,
		typename GeometryTraits::Scalar	valc,
		const GeometryTraits &	gt
	)

inlinestatic

Bilinear interpolation of values at triangle points.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	Pos	The point for which the bilinear interpolation of values is computed.
[in]	vala	The value of the first point.
[in]	valb	The value of the second point.
[in]	valc	The value of the third point.
[in]	gt	The geometry trait object.

Returns: The bilinear interpolation of values vala, valb, valc, and vald, at Pos position.

Precondition: Pos must be inside the triangle (abc), else the bilinear interpolation coefficients are truncated to [0,1].

Definition at line 352 of file Interpolation.hpp.

◆ is_in_tetrahedron()

template<typename GeometryTraits >

static bool FEVV::Operators::Geometry::is_in_tetrahedron	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const typename GeometryTraits::Point &	Pos,
		const GeometryTraits &	gt
	)

inlinestatic

Predicate fonction to know whether the Pos position is inside the abcd tetrahedron.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
[in]	Pos	The point that is either inside or outside the tetrahedron (abcd).
[in]	gt	The geometry trait object.

Returns: True if Pos is inside the tetrahedron (abcd), else false.

Definition at line 36 of file Interpolation.hpp.

◆ is_in_triangle()

template<typename GeometryTraits >

static bool FEVV::Operators::Geometry::is_in_triangle	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	Pos,
		const GeometryTraits &	gt
	)

inlinestatic

Predicate fonction to know whether the projection of point Pos on the triangle plane is in the triangle (abc).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	Pos	The point whose projection is either inside or outside the triangle (abc).
[in]	gt	The geometry trait object.

Returns: True if the projection of point Pos is inside the triangle (abc), else false.

Definition at line 303 of file Interpolation.hpp.

◆ is_over_segment()

template<typename GeometryTraits >

static bool FEVV::Operators::Geometry::is_over_segment	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	Pos,
		typename GeometryTraits::Vector &	diff,
		const GeometryTraits &	gt
	)

inlinestatic

Predicate fonction to know whether the Pos position is over the ab segment.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	Pos	The point that is either over or beside the segment (ab).
[out]	diff	The orthogonal vector to translate Pos onto the segment (ab) (or line when Pos is not over the segment).
[in]	gt	The geometry trait object.

Returns: True if Pos is over the segment (ab), else false.

Definition at line 252 of file Interpolation.hpp.

◆ quad_area()

template<typename GeometryTraits >

double FEVV::Operators::Geometry::quad_area	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const GeometryTraits &	gt
	)

inline

Compute the area of a quad (given by 4 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
	gt	The geometry trait object.

Returns: The quad area (double Scalar).

Remarks: This works for any side length.

Definition at line 90 of file quads.hpp.

◆ quad_barycenter()

template<typename GeometryTraits >

GeometryTraits::Point FEVV::Operators::Geometry::quad_barycenter	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const GeometryTraits &	gt
	)

inline

Compute the barycenter/mean position of a quad (given by 4 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
[in]	gt	The geometry trait object.

Returns: The barycenter/mean position of the 4 input points (Point).

Definition at line 38 of file quads.hpp.

◆ quad_perimeter()

template<typename GeometryTraits >

double FEVV::Operators::Geometry::quad_perimeter	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const GeometryTraits &	gt
	)

inline

Compute the perimeter of a quad (given by 4 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
[in]	gt	The geometry trait object.

Returns: The quad perimeter (double Scalar).

Definition at line 63 of file quads.hpp.

◆ sphere_clip_vector()

template<typename GeometryTraits >

static bool FEVV::Operators::Geometry::sphere_clip_vector	(	const typename GeometryTraits::Point &	center,
		double	r,
		const typename GeometryTraits::Point &	p,
		typename GeometryTraits::Vector &	v,
		const GeometryTraits &	gt
	)

static

Compute the intersection of a sphere (center + radius) with a ray/line (starting point + direction vector). Sphere equation is given by (x-Cx)^2+(y-Cy)^2+(z-Cz)^2=r^2 Line equation is given by (x, y, z) = p + txV.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	center	The sphere center.
[in]	r	The sphere radius.
[in]	p	The starting point/origin of the ray/line.
[in,out]	v	The ray/line direction to clip by the sphere when an intersection occurs in the direction of v.
[in]	gt	The geometry trait object.

Returns: True if there is an intersection between the sphere and the ray starting at p position and going along the v direction, not farther than the v' length.

Precondition: p must be inside the sphere.

Definition at line 39 of file ClippingAndIntersection.hpp.

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◆ triangle_area()

template<typename GeometryTraits >

double FEVV::Operators::Geometry::triangle_area	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const GeometryTraits &	gt
	)

inline

Compute the area of a triangle (given by 3 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
	gt	The geometry trait object.

Returns: The triangle area (double Scalar).

Definition at line 106 of file triangles.hpp.

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◆ triangle_barycenter()

template<typename GeometryTraits >

GeometryTraits::Point FEVV::Operators::Geometry::triangle_barycenter	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const GeometryTraits &
	)

inline

Compute the barycenter/mean position of a triangle (given by 3 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	gt	The geometry trait object.

Returns: The barycenter/mean position of the 3 input points (Point).

Definition at line 37 of file triangles.hpp.

◆ triangle_normal_unnormalized()

template<typename GeometryTraits >

GeometryTraits::Vector FEVV::Operators::Geometry::triangle_normal_unnormalized	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const GeometryTraits &	gt
	)

inline

Compute the unnormalized normal of a triangle (given by 3 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	gt	The geometry trait object.

Returns: The triangle unnormalized normal (Vector).

Definition at line 83 of file triangles.hpp.

◆ triangle_perimeter()

template<typename GeometryTraits >

double FEVV::Operators::Geometry::triangle_perimeter	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const GeometryTraits &	gt
	)

inline

Compute the perimeter of a triangle (given by 3 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	gt	The geometry trait object.

Returns: The triangle perimeter (double Scalar).

Definition at line 60 of file triangles.hpp.

◆ triangle_rad_angle()

template<typename GeometryTraits >

GeometryTraits::Scalar FEVV::Operators::Geometry::triangle_rad_angle	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const GeometryTraits &	gt
	)

inline

Compute the angle of a triangle (given by 3 points).

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	gt	The geometry trait object.

Returns: The triangle angle in rad (Scalar).

Definition at line 32 of file triangle_rad_angle.hpp.

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◆ triangle_shape_potential()

template<typename FaceGraph , typename GeometryTraits = FEVV::Geometry_traits< FaceGraph >>

double FEVV::Operators::Geometry::triangle_shape_potential	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const double	prohib_energy,
		const GeometryTraits &	gt
	)

inline

Compute the shape potential of a triangle (given by 3 points). Triangle "equilateralness" measure.

Template Parameters

FaceGraph	a Mesh type that provides a Model of the FaceGraph Concept through a boost::graph_traits<> specialization.
GeometryTraits	The geometric kernel when available. This is defaulted to FEVV::Geometry_traits<FaceGraph>.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	PROHIB_ENERGY	The maximum authorized value, e.g. returns that value if smaller than the computed shape potential. This parameter is needed because when we compute the mesh quality using the sum of shape potential of each triangle, the sum may overflow.
[in]	gt	The geometry trait object.

Returns: The triangle shape potential (double Scalar).

Definition at line 138 of file triangles.hpp.

◆ trilinear_interpolation() [1/2]

template<typename GeometryTraits >

static std::vector< typename GeometryTraits::Scalar > FEVV::Operators::Geometry::trilinear_interpolation	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const typename GeometryTraits::Point &	Pos,
		const std::vector< typename GeometryTraits::Scalar > &	vala,
		const std::vector< typename GeometryTraits::Scalar > &	valb,
		const std::vector< typename GeometryTraits::Scalar > &	valc,
		const std::vector< typename GeometryTraits::Scalar > &	vald,
		const GeometryTraits &	gt
	)

inlinestatic

Trilinear interpolation of values at tetrahedron points.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
[in]	Pos	The point for which the trilinear interpolations of values are computed.
[in]	vala	The vector of values at the first point.
[in]	valb	The vector of values at the second point.
[in]	valc	The vector of values at the third point.
[in]	vald	The vector of values at the fourth point.
[in]	gt	The geometry trait object.

Returns: The vector of the trilinear interpolation of values at a, b, c, d positions for Pos position.

Precondition: Pos must be inside the tetrahedron (abcd), else the trilinear interpolation coefficients are truncated to [0,1].

Definition at line 204 of file Interpolation.hpp.

◆ trilinear_interpolation() [2/2]

template<typename GeometryTraits >

static GeometryTraits::Scalar FEVV::Operators::Geometry::trilinear_interpolation	(	const typename GeometryTraits::Point &	a,
		const typename GeometryTraits::Point &	b,
		const typename GeometryTraits::Point &	c,
		const typename GeometryTraits::Point &	d,
		const typename GeometryTraits::Point &	Pos,
		typename GeometryTraits::Scalar	vala,
		typename GeometryTraits::Scalar	valb,
		typename GeometryTraits::Scalar	valc,
		typename GeometryTraits::Scalar	vald,
		const GeometryTraits &	gt
	)

inlinestatic

Trilinear interpolation of values at tetrahedron points.

Template Parameters

GeometryTraits The geometric kernel.

Parameters

[in]	a	The first point.
[in]	b	The second point.
[in]	c	The third point.
[in]	d	The fourth point.
[in]	Pos	The point for which the trilinear interpolation of values is computed.
[in]	vala	The value of the first point.
[in]	valb	The value of the second point.
[in]	valc	The value of the third point.
[in]	vald	The value of the fourth point.
[in]	gt	The geometry trait object.

Returns: The trilinear interpolation of values vala, valb, valc, and vald, at Pos position.

Precondition: Pos must be inside the tetrahedron (abcd), else the trilinear interpolation coefficients are truncated to [0,1].

Definition at line 110 of file Interpolation.hpp.

Functions

Function Documentation

◆ acos()

◆ acos_degree()

◆ asin()

◆ asin_degree()

◆ bilinear_interpolation() [1/2]

◆ bilinear_interpolation() [2/2]

◆ is_in_tetrahedron()

◆ is_in_triangle()

◆ is_over_segment()

◆ quad_area()

◆ quad_barycenter()

◆ quad_perimeter()

◆ sphere_clip_vector()

◆ triangle_area()

◆ triangle_barycenter()

◆ triangle_normal_unnormalized()

◆ triangle_perimeter()

◆ triangle_rad_angle()

◆ triangle_shape_potential()

◆ trilinear_interpolation() [1/2]

◆ trilinear_interpolation() [2/2]