Classes
struct	ProjectionInput
	Stores the findProjection() input. More...

struct	ProjectionResult
	Stores the findProjection() result. More...

Functions
template<typename T >
T	angle (const T vA0, const T vA1, const T vB0, const T vB1)

template<typename T >
T	angle2D (const T vA0, const T vA1, const T vB0, const T vB1)

template<typename T >
double	angle2DUndirected (const T vA, const T vB, const T *vC)

template<typename T >
bool	areVectorsColinear (const T vA0, const T vA1, const T vB0, const T vB1, std::array< T, 3 > coefficients=nullptr, const T tolerance=NULL)

template<typename T >
bool	isTriangleColinear2D (const T pptA, const T pptB, const T *pptC, const T tolerance)

template<typename T >
int	computeBarycentricCoordinates (const T p0, const T p1, const T *p, std::array< T, 2 > &baryCentrics, const int &dimension=3)

template<typename T >
int	computeBarycentricCoordinates (const T p0, const T p1, const T p2, const T p, std::array< T, 3 > &baryCentrics)

template<typename T >
bool	computeSegmentIntersection (const T &xA, const T &yA, const T &xB, const T &yB, const T &xC, const T &yC, const T &xD, const T &yD, T &x, T &y)

template<typename T >
int	computeTriangleAngles (const T p0, const T p1, const T *p2, std::array< T, 3 > &angles)

template<typename T >
int	computeTriangleAngleFromSides (const T s0, const T s1, const T s2, T &angle)

template<typename T >
int	computeTriangleArea (const T p0, const T p1, const T *p2, T &area)

template<typename T >
int	computeTriangleAreaFromSides (const T s0, const T s1, const T s2, T &area)

template<typename T >
int	crossProduct (const T vA0, const T vA1, const T vB0, const T vB1, std::array< T, 3 > &crossProduct)

template<typename T >
int	crossProduct (const T vA, const T vB, T *crossProduct)

template<typename T >
T	distance (const T p0, const T p1, const int &dimension=3)

template<typename T >
T	distance (const std::vector< T > &p0, const std::vector< T > &p1)

template<typename T >
T	distance2D (const T p0, const T p1)

template<typename T >
T	distanceFlatten (const std::vector< std::vector< T > > &p0, const std::vector< std::vector< T > > &p1)

template<typename T >
T	dotProduct (const T vA0, const T vA1, const T vB0, const T vB1)

template<typename T >
T	dotProduct (const T vA, const T vB, const int &dimension=3)

template<typename T >
T	dotProduct (const std::vector< T > &vA, const std::vector< T > &vB)

template<typename T >
T	dotProductFlatten (const std::vector< std::vector< T > > &vA, const std::vector< std::vector< T > > &vB)

template<typename T , typename Container , size_t dim>
int	getBoundingBox (const Container &points, std::array< std::pair< T, T >, dim > &bBox)

template<typename T >
bool	isPointInTriangle (const T p0, const T p1, const T p2, const T p)

template<typename T >
bool	isPointOnSegment (const T &x, const T &y, const T &xA, const T &yA, const T &xB, const T &yB)

template<typename T >
bool	isPointOnSegment (const T p, const T pA, const T *pB, const int &dimension=3)

template<typename T >
bool	isTriangleColinear (const T p0, const T p1, const T p2, const T tolerance=nullptr)

template<typename T >
T	magnitude (const T *v, const int &dimension=3)

template<typename T >
T	magnitude (const std::vector< T > &v)

template<typename T >
T	magnitudeFlatten (const std::vector< std::vector< T > > &v)

template<typename T >
T	magnitude (const T o, const T d)

template<typename T >
T	powInt (const T val, const int n)

template<typename T = double>
T	powIntTen (const int n)
	Compute the nth power of ten.

template<typename T1 , typename T2 >
T1	pow (const T1 val, const T2 n)

template<typename T >
void	projectOnTrianglePlane (const T p, const T a, const T normTri, T out)
	Compute euclidean projection in a triangle plane.

template<typename T >
void	projectOnEdge (const T p, const T a, const T b, T out)
	Compute euclidean projection on a 3D segment.

template<typename T >
void	computeTriangleNormal (const T a, const T b, const T c, T out)
	Compute normal vector to triangle.

template<typename T , typename triangulationType >
SimplexId	getNearestSurfaceVertex (const T *pa, std::vector< T > &dists, const triangulationType &triangulation)
	Find nearest vertex on the surface.

template<typename T >
int	subtractVectors (const T a, const T b, T *out, const int &dimension=3)

template<typename T >
int	subtractVectors (const std::vector< T > &a, const std::vector< T > &b, std::vector< T > &out)

template<typename T >
int	addVectors (const T a, const T b, T *out, const int &dimension=3)

template<typename T >
int	addVectors (const std::vector< T > &a, const std::vector< T > &b, std::vector< T > &out)

template<typename T >
int	multiAddVectors (const std::vector< std::vector< T > > &a, const std::vector< std::vector< T > > &b, std::vector< std::vector< T > > &out)

template<typename T >
int	multiAddVectorsFlatten (const std::vector< std::vector< std::vector< T > > > &a, const std::vector< std::vector< std::vector< T > > > &b, std::vector< std::vector< T > > &out)

template<typename T >
int	scaleVector (const T a, const T factor, T out, const int &dimension=3)

template<typename T >
int	scaleVector (const std::vector< T > &a, const T factor, std::vector< T > &out)

template<typename T >
int	vectorProjection (const T a, const T b, T *out, const int &dimension=3)

template<typename T >
int	vectorProjection (const std::vector< T > &a, const std::vector< T > &b, std::vector< T > &out)

template<typename T >
void	addVectorsProjection (const std::vector< T > &a, const std::vector< T > &b, std::vector< T > &a_out, std::vector< T > &b_out)

template<typename T >
void	gramSchmidt (const std::vector< std::vector< T > > &a, std::vector< std::vector< T > > &out)

template<typename T >
bool	isVectorUniform (const std::vector< T > &a)

template<typename T >
bool	isVectorNull (const std::vector< T > &a)

template<typename T >
bool	isVectorNullFlatten (const std::vector< std::vector< T > > &a)

template<typename T >
int	flattenMultiDimensionalVector (const std::vector< std::vector< T > > &a, std::vector< T > &out)

template<typename T >
int	multiFlattenMultiDimensionalVector (const std::vector< std::vector< std::vector< T > > > &a, std::vector< std::vector< T > > &out)

template<typename T >
int	unflattenMultiDimensionalVector (const std::vector< T > &a, std::vector< std::vector< T > > &out, const int &no_columns=2)

template<typename T >
void	matrixMultiplication (const std::vector< std::vector< T > > &a, const std::vector< std::vector< T > > &b, std::vector< std::vector< T > > &out)

template<typename T >
void	subtractMatrices (const std::vector< std::vector< T > > &a, const std::vector< std::vector< T > > &b, std::vector< std::vector< T > > &out)

template<typename T >
void	addMatrices (const std::vector< std::vector< T > > &a, const std::vector< std::vector< T > > &b, std::vector< std::vector< T > > &out)

template<typename T >
void	scaleMatrix (const std::vector< std::vector< T > > &a, const T factor, std::vector< std::vector< T > > &out)

template<typename T >
void	transposeMatrix (const std::vector< std::vector< T > > &a, std::vector< std::vector< T > > &out)

template<typename triangulationType >
std::array< float, 3 >	computeSurfaceNormalAtPoint (const SimplexId a, const triangulationType &triangulation)
	Compute (mean) surface normal at given surface vertex.

template<typename triangulationType0 , typename triangulationType1 >
ProjectionResult	findProjection (const ProjectionInput &pi, VisitedMask &trianglesTested, std::vector< float > &dists, std::stack< SimplexId > &trianglesToTest, const bool reverseProjection, const triangulationType0 &triangulationToSmooth, const triangulationType1 &triangulation)

Function Documentation

◆ addMatrices()

template<typename T >

void ttk::Geometry::addMatrices	(	const std::vector< std::vector< T > > &	a,
		const std::vector< std::vector< T > > &	b,
		std::vector< std::vector< T > > &	out
	)

Computes the element wise addition of two matrices

Parameters

a	the first matrix
b	the second matrix
out	the resulting matrix

Definition at line 798 of file Geometry.cpp.

◆ addVectors() [1/2]

template<typename T >

int ttk::Geometry::addVectors	(	const std::vector< T > &	a,
		const std::vector< T > &	b,
		std::vector< T > &	out
	)

Computes the addition of two vectors.

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the addition between the two vectors

Returns: Returns 0 for success, negative otherwise.

Definition at line 617 of file Geometry.cpp.

◆ addVectors() [2/2]

template<typename T >

int ttk::Geometry::addVectors	(	const T *	a,
		const T *	b,
		T *	out,
		const int &	dimension = `3`
	)

Computes the addition of two vectors.

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the addition between the two vectors
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns 0 for success, negative otherwise.

Definition at line 610 of file Geometry.cpp.

◆ addVectorsProjection()

template<typename T >

void ttk::Geometry::addVectorsProjection	(	const std::vector< T > &	a,
		const std::vector< T > &	b,
		std::vector< T > &	a_out,
		std::vector< T > &	b_out
	)

Adds two vectors and project them into it

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
a_out	the projection of `a`
b_out	the projection of `b`

Definition at line 690 of file Geometry.cpp.

◆ angle()

template<typename T >

T ttk::Geometry::angle	(	const T *	vA0,
		const T *	vA1,
		const T *	vB0,
		const T *	vB1
	)

Compute the angle between two std::vectors

Parameters

vA0	xyz coordinates of vA's origin
vA1	xyz coordinates of vA's destination
vB0	xyz coordinates of vB's origin
vB1	xyz coordinates of vB's destination

Definition at line 13 of file Geometry.cpp.

◆ angle2D()

template<typename T >

T ttk::Geometry::angle2D	(	const T *	vA0,
		const T *	vA1,
		const T *	vB0,
		const T *	vB1
	)

Definition at line 20 of file Geometry.cpp.

◆ angle2DUndirected()

template<typename T >

double ttk::Geometry::angle2DUndirected	(	const T *	vA,
		const T *	vB,
		const T *	vC
	)

inline

Definition at line 33 of file Geometry.h.

◆ areVectorsColinear()

template<typename T >

bool ttk::Geometry::areVectorsColinear	(	const T *	vA0,
		const T *	vA1,
		const T *	vB0,
		const T *	vB1,
		std::array< T, 3 > *	coefficients = `nullptr`,
		const T *	tolerance = `NULL`
	)

Check if two 3D std::vectors vA and vB are colinear.

Parameters

vA0	xyz coordinates of vA's origin
vA1	xyz coordinates of vA's destination
vB0	xyz coordinates of vB's origin
vB1	xyz coordinates of vB's destination
coefficients	Optional output std::array of colinearity coefficients.
tolerance	Optional tolerance value (default: PREC_FLT)

Returns: Returns true if the std::vectors are colinear, false otherwise.

Definition at line 27 of file Geometry.cpp.

◆ computeBarycentricCoordinates() [1/2]

template<typename T >

int ttk::Geometry::computeBarycentricCoordinates	(	const T *	p0,
		const T *	p1,
		const T *	p,
		std::array< T, 2 > &	baryCentrics,
		const int &	dimension = `3`
	)

Compute the barycentric coordinates of point p with regard to the edge defined by the 3D points p0 and p1.

Parameters

p0	xyz coordinates of the first vertex of the edge
p1	xyz coordinates of the second vertex of the edge
p	xyz coordinates of the queried point
baryCentrics	Output barycentric coordinates (all in [0, 1] if `p` belongs to the edge).
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 142 of file Geometry.cpp.

◆ computeBarycentricCoordinates() [2/2]

template<typename T >

int ttk::Geometry::computeBarycentricCoordinates	(	const T *	p0,
		const T *	p1,
		const T *	p2,
		const T *	p,
		std::array< T, 3 > &	baryCentrics
	)

Compute the barycentric coordinates of point p with regard to the triangle defined by the 3D points p0, p1, and p2.

Parameters

p0	xyz coordinates of the first vertex of the triangle
p1	xyz coordinates of the second vertex of the triangle
p2	xyz coordinates of the third vertex of the triangle
p	xyz coordinates of the queried point
baryCentrics	Output barycentric coordinates (all in [0, 1] if `p` belongs to the triangle).

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 190 of file Geometry.cpp.

◆ computeSegmentIntersection()

template<typename T >

bool ttk::Geometry::computeSegmentIntersection	(	const T &	xA,
		const T &	yA,
		const T &	xB,
		const T &	yB,
		const T &	xC,
		const T &	yC,
		const T &	xD,
		const T &	yD,
		T &	x,
		T &	y
	)

Compute the intersection between two 2D segments AB and CD.

Parameters

xA	x coordinate of the first vertex of the first segment (AB)
yA	y coordinate of the first vertex of the first segment (AB)
xB	x coordinate of the second vertex of the first segment (AB)
yB	y coordinate of the second vertex of the first segment (AB)
xC	x coordinate of the first vertex of the second segment (CD)
yC	y coordinate of the first vertex of the second segment (CD)
xD	x coordinate of the second vertex of the second segment (CD)
yD	y coordinate of the second vertex of the second segment (CD)
x	x coordinate of the output intersection (if any).
y	y coordinate of the output intersection (if any).

Returns: Returns true if the segments intersect (false otherwise).

Definition at line 248 of file Geometry.cpp.

◆ computeSurfaceNormalAtPoint()

template<typename triangulationType >

std::array< float, 3 > ttk::Geometry::computeSurfaceNormalAtPoint	(	const SimplexId	a,
		const triangulationType &	triangulation
	)

Compute (mean) surface normal at given surface vertex.

Parameters

[in]	a	Surface vertex id
[in]	triangulation	Mesh

Returns: Mean of surface normals in star of a

Definition at line 754 of file Geometry.h.

◆ computeTriangleAngleFromSides()

template<typename T >

int ttk::Geometry::computeTriangleAngleFromSides	(	const T	s0,
		const T	s1,
		const T	s2,
		T &	angle
	)

Parameters

s0	length of the first side of the triangle
s1	length of the second side of the triangle
s2	length of the third side of the triangle
angle	Angle opposite to edge s2

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 321 of file Geometry.cpp.

◆ computeTriangleAngles()

template<typename T >

int ttk::Geometry::computeTriangleAngles	(	const T *	p0,
		const T *	p1,
		const T *	p2,
		std::array< T, 3 > &	angles
	)

Compute the angles of a triangle

Parameters

p0	xyz coordinates of the first vertex of the triangle
p1	xyz coordinates of the second vertex of the triangle
p2	xyz coordinates of the third vertex of the triangle
angles	Angles (p0p1, p1p2) (p1p2, p2p0) (p2p0, p0p1)

Definition at line 308 of file Geometry.cpp.

◆ computeTriangleArea()

template<typename T >

int ttk::Geometry::computeTriangleArea	(	const T *	p0,
		const T *	p1,
		const T *	p2,
		T &	area
	)

Compute the area of a 3D triangle.

Parameters

p0	xyz coordinates of the first vertex of the triangle
p1	xyz coordinates of the second vertex of the triangle
p2	xyz coordinates of the third vertex of the triangle
area	Output area.

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 281 of file Geometry.cpp.

◆ computeTriangleAreaFromSides()

template<typename T >

int ttk::Geometry::computeTriangleAreaFromSides	(	const T	s0,
		const T	s1,
		const T	s2,
		T &	area
	)

Compute the area of a triangle given length of its sides

Parameters

s0	length of the first side of the triangle
s1	length of the second side of the triangle
s2	length of the third side of the triangle
area	Output area.

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 296 of file Geometry.cpp.

◆ computeTriangleNormal()

template<typename T >

void ttk::Geometry::computeTriangleNormal	(	const T *	a,
		const T *	b,
		const T *	c,
		T *	out
	)

Compute normal vector to triangle.

Parameters

[in]	a	First triangle vertex coordinates
[in]	b	Second triangle vertex coordinates
[in]	c	Third triangle vertex coordinates
[out]	out	Result

Returns: Triangle unitary normal

Definition at line 564 of file Geometry.cpp.

◆ crossProduct() [1/2]

template<typename T >

int ttk::Geometry::crossProduct	(	const T *	vA,
		const T *	vB,
		T *	crossProduct
	)

Compute the cross product of two 3D std::vectors

Parameters

vA	xyz coordinates of vA std::vector
vB	xyz coordinates of vB std::vector
crossProduct	Output cross product.

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 354 of file Geometry.cpp.

◆ crossProduct() [2/2]

template<typename T >

int ttk::Geometry::crossProduct	(	const T *	vA0,
		const T *	vA1,
		const T *	vB0,
		const T *	vB1,
		std::array< T, 3 > &	crossProduct
	)

Compute the cross product of two 3D std::vectors

Parameters

vA0	xyz coordinates of vA's origin
vA1	xyz coordinates of vA's destination
vB0	xyz coordinates of vB's origin
vB1	xyz coordinates of vB's destination
crossProduct	Output cross product.

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 332 of file Geometry.cpp.

◆ distance() [1/2]

template<typename T >

T ttk::Geometry::distance	(	const std::vector< T > &	p0,
		const std::vector< T > &	p1
	)

Compute the Euclidean distance between two points

Parameters

p0	xyz coordinates of the first input point.
p1	xyz coordinates of the second input point.

Definition at line 374 of file Geometry.cpp.

◆ distance() [2/2]

template<typename T >

T ttk::Geometry::distance	(	const T *	p0,
		const T *	p1,
		const int &	dimension = `3`
	)

Compute the Euclidean distance between two points

Parameters

p0	xyz coordinates of the first input point.
p1	xyz coordinates of the second input point.
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Definition at line 362 of file Geometry.cpp.

◆ distance2D()

template<typename T >

T ttk::Geometry::distance2D	(	const T *	p0,
		const T *	p1
	)

inline

Definition at line 200 of file Geometry.h.

◆ distanceFlatten()

template<typename T >

T ttk::Geometry::distanceFlatten	(	const std::vector< std::vector< T > > &	p0,
		const std::vector< std::vector< T > > &	p1
	)

Compute the Euclidean distance between two vectors by first flattening them

Parameters

p0	xyz coordinates of the first input point.
p1	xyz coordinates of the second input point.

Definition at line 379 of file Geometry.cpp.

◆ dotProduct() [1/3]

template<typename T >

T ttk::Geometry::dotProduct	(	const std::vector< T > &	vA,
		const std::vector< T > &	vB
	)

Compute the dot product of two std::vectors

Parameters

vA	coordinates of vA std::vector
vB	coordinates of vB std::vector

Returns: Returns Output dot product

Definition at line 407 of file Geometry.cpp.

◆ dotProduct() [2/3]

template<typename T >

T ttk::Geometry::dotProduct	(	const T *	vA,
		const T *	vB,
		const int &	dimension = `3`
	)

Compute the dot product of two std::vectors

Parameters

vA	coordinates of vA std::vector
vB	coordinates of vB std::vector
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns Output dot product

Definition at line 399 of file Geometry.cpp.

◆ dotProduct() [3/3]

template<typename T >

T ttk::Geometry::dotProduct	(	const T *	vA0,
		const T *	vA1,
		const T *	vB0,
		const T *	vB1
	)

Compute the dot product of two 3D std::vectors

Parameters

vA0	xyz coordinates of vA's origin
vA1	xyz coordinates of vA's destination
vB0	xyz coordinates of vB's origin
vB1	xyz coordinates of vB's destination

Returns: Returns Output dot product

Definition at line 388 of file Geometry.cpp.

◆ dotProductFlatten()

template<typename T >

T ttk::Geometry::dotProductFlatten	(	const std::vector< std::vector< T > > &	vA,
		const std::vector< std::vector< T > > &	vB
	)

Compute the dot product of two multi dimensional std::vectors by first flattening them

Parameters

vA	coordinates of vA std::vector
vB	coordinates of vB std::vector

Returns: Returns Output dot product

Definition at line 412 of file Geometry.cpp.

◆ findProjection()

template<typename triangulationType0 , typename triangulationType1 >

ProjectionResult ttk::Geometry::findProjection	(	const ProjectionInput &	pi,
		VisitedMask &	trianglesTested,
		std::vector< float > &	dists,
		std::stack< SimplexId > &	trianglesToTest,
		const bool	reverseProjection,
		const triangulationType0 &	triangulationToSmooth,
		const triangulationType1 &	triangulation
	)

Definition at line 891 of file Geometry.h.

◆ flattenMultiDimensionalVector()

template<typename T >

int ttk::Geometry::flattenMultiDimensionalVector	(	const std::vector< std::vector< T > > &	a,
		std::vector< T > &	out
	)

Flatten a multi dimensional vector (representing a rectangular/square matrix)

Parameters

a	multi dimensional vector
out	flattened vector

Returns: Returns 0 for success, negative otherwise

Definition at line 742 of file Geometry.cpp.

◆ getBoundingBox()

template<typename T , typename Container , size_t dim>

int ttk::Geometry::getBoundingBox	(	const Container &	points,
		std::array< std::pair< T, T >, dim > &	bBox
	)

Compute the bounding box of a point set.

Parameters

points	Vector of points. Each entry is a std::array<float, dim> whose size is equal to the dimension of the space embedding the points.
bBox	Output bounding box. The number of entries in this std::array is equal to the dimension of the space embedding the points.

Returns: Returns 0 upon success, negative values otherwise.

Definition at line 273 of file Geometry.h.

◆ getNearestSurfaceVertex()

template<typename T , typename triangulationType >

SimplexId ttk::Geometry::getNearestSurfaceVertex	(	const T *	pa,
		std::vector< T > &	dists,
		const triangulationType &	triangulation
	)

Find nearest vertex on the surface.

Parameters

[in]	pa	Input point
[in]	dists	Pre-allocated distances vector
[in]	triangulation	Surface triangulation

Returns: Nearest vertex id on the surface

Definition at line 517 of file Geometry.h.

◆ gramSchmidt()

template<typename T >

void ttk::Geometry::gramSchmidt	(	const std::vector< std::vector< T > > &	a,
		std::vector< std::vector< T > > &	out
	)

Computes the Gram-Schmidt orthogonalization process. That is, given a set of vectors, it returns a set (of same size) of orthogonal vectors spanning the same subspace.

Parameters

a	the set of vectors to orthogonalize
out	the orthogonalized vectors

Definition at line 701 of file Geometry.cpp.

◆ isPointInTriangle()

template<typename T >

bool ttk::Geometry::isPointInTriangle	(	const T *	p0,
		const T *	p1,
		const T *	p2,
		const T *	p
	)

Check if the point p is inside the triangle (p0, p1, p2).

Parameters

p0	xyz coordinates of the first vertex of the triangle
p1	xyz coordinates of the second vertex of the triangle
p2	xyz coordinates of the third vertex of the triangle
p	xyz coordinates of the queried point

Returns: Returns true if p is in the triangle, false otherwise.

Definition at line 421 of file Geometry.cpp.

◆ isPointOnSegment() [1/2]

template<typename T >

bool ttk::Geometry::isPointOnSegment	(	const T &	x,
		const T &	y,
		const T &	xA,
		const T &	yA,
		const T &	xB,
		const T &	yB
	)

Check if a 2D point xy lies on a 2D segment AB.

Parameters

x	x coordinate of the input point.
y	y coordinate of the input point.
xA	x coordinate of the first vertex of the segment [AB]
yA	y coordinate of the first vertex of the segment [AB]
xB	x coordinate of the second vertex of the segment [AB]
yB	y coordinate of the second vertex of the segment [AB]

Returns: Returns true if the point lies on the segment, false otherwise.

Definition at line 443 of file Geometry.cpp.

◆ isPointOnSegment() [2/2]

template<typename T >

bool ttk::Geometry::isPointOnSegment	(	const T *	p,
		const T *	pA,
		const T *	pB,
		const int &	dimension = `3`
	)

Check if a point p lies on a segment AB.

Parameters

p	xyz coordinates of the input point.
pA	xyz coordinates of the first vertex of the segment [AB]
pB	xyz coordinate of the second vertex of the segment [AB]
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns true if the point lies on the segment, false otherwise.

Definition at line 451 of file Geometry.cpp.

◆ isTriangleColinear()

template<typename T >

bool ttk::Geometry::isTriangleColinear	(	const T *	p0,
		const T *	p1,
		const T *	p2,
		const T *	tolerance = `nullptr`
	)

Check if all the edges of a triangle are colinear.

Parameters

p0	xyz coordinates of the first vertex of the triangle.
p1	xyz coordinates of the second vertex of the triangle.
p2	xyz coordinates of the third vertex of the triangle.
tolerance	Optional tolerance value (default: PREC_FLT)

Returns: Returns true if all the edges are colinear (false otherwise).

Definition at line 466 of file Geometry.cpp.

◆ isTriangleColinear2D()

template<typename T >

bool ttk::Geometry::isTriangleColinear2D	(	const T *	pptA,
		const T *	pptB,
		const T *	pptC,
		const T	tolerance
	)

Definition at line 130 of file Geometry.cpp.

◆ isVectorNull()

template<typename T >

bool ttk::Geometry::isVectorNull ( const std::vector< T > & a )

Test if the vector is null (have all values almost equal to 0)

Parameters

a	coordinates of the vector.

Returns: Returns true if the vector is null, false otherwise

Definition at line 727 of file Geometry.cpp.

◆ isVectorNullFlatten()

template<typename T >

bool ttk::Geometry::isVectorNullFlatten ( const std::vector< std::vector< T > > & a )

Test if the vector is null (have all values almost equal to 0) after flattening it

Parameters

a	coordinates of the vector.

Returns: Returns true if the vector is null, false otherwise

Definition at line 735 of file Geometry.cpp.

◆ isVectorUniform()

template<typename T >

bool ttk::Geometry::isVectorUniform ( const std::vector< T > & a )

Test if the vector have uniform values

Parameters

a	coordinates of the vector.

Returns: Returns true if the vector have uniform values, false otherwise

Definition at line 719 of file Geometry.cpp.

◆ magnitude() [1/3]

template<typename T >

T ttk::Geometry::magnitude ( const std::vector< T > & v )

Compute the magnitude of a std::vector v.

Parameters

v	coordinates of the input std::vector.

Returns: Returns the magnitude upon success, negative values otherwise.

Definition at line 514 of file Geometry.cpp.

◆ magnitude() [2/3]

template<typename T >

T ttk::Geometry::magnitude	(	const T *	o,
		const T *	d
	)

Compute the magnitude of a 3D std::vector.

Parameters

o	xyz coordinates of the std::vector's origin
d	xyz coordinates of the std::vector's destination

Definition at line 526 of file Geometry.cpp.

◆ magnitude() [3/3]

template<typename T >

T ttk::Geometry::magnitude	(	const T *	v,
		const int &	dimension = `3`
	)

Compute the magnitude of a std::vector v.

Parameters

v	coordinates of the input std::vector.
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns the magnitude upon success, negative values otherwise.

Definition at line 509 of file Geometry.cpp.

◆ magnitudeFlatten()

template<typename T >

T ttk::Geometry::magnitudeFlatten ( const std::vector< std::vector< T > > & v )

Compute the magnitude of a multi dimensional std::vector v by first flattening it

Parameters

v	coordinates of the input std::vector.

Returns: Returns the magnitude upon success, negative values otherwise.

Definition at line 519 of file Geometry.cpp.

◆ matrixMultiplication()

template<typename T >

void ttk::Geometry::matrixMultiplication	(	const std::vector< std::vector< T > > &	a,
		const std::vector< std::vector< T > > &	b,
		std::vector< std::vector< T > > &	out
	)

Computes the matrix multiplication between two matrixes

Parameters

a	the first matrix
b	the second matrix
out	the resulting matrix

Definition at line 777 of file Geometry.cpp.

◆ multiAddVectors()

template<typename T >

int ttk::Geometry::multiAddVectors	(	const std::vector< std::vector< T > > &	a,
		const std::vector< std::vector< T > > &	b,
		std::vector< std::vector< T > > &	out
	)

Computes the pairwise addition of pairs of two vectors.

Parameters

a	coordinates of the first vectors
b	coordinates of the second vectors
out	the pairwise addition between the vectors

Definition at line 625 of file Geometry.cpp.

◆ multiAddVectorsFlatten()

template<typename T >

int ttk::Geometry::multiAddVectorsFlatten	(	const std::vector< std::vector< std::vector< T > > > &	a,
		const std::vector< std::vector< std::vector< T > > > &	b,
		std::vector< std::vector< T > > &	out
	)

Computes the pairwise addition of pairs of two vectors by first flattening them.

Parameters

a	coordinates of the first vectors
b	coordinates of the second vectors
out	the pairwise addition between the vectors

Definition at line 635 of file Geometry.cpp.

◆ multiFlattenMultiDimensionalVector()

template<typename T >

int ttk::Geometry::multiFlattenMultiDimensionalVector	(	const std::vector< std::vector< std::vector< T > > > &	a,
		std::vector< std::vector< T > > &	out
	)

Flatten an ensemble of multi dimensional vector (representing a rectangular/square matrix)

Parameters

a	multi dimensional vector
out	flattened vector

Definition at line 752 of file Geometry.cpp.

◆ pow()

template<typename T1 , typename T2 >

T1 ttk::Geometry::pow	(	const T1	val,
		const T2	n
	)

inline

Compute the power of an arithmetic value (redirect to std::pow with a floating-point exponent and to Geometry::powInt with an integer exponent)

Definition at line 456 of file Geometry.h.

◆ powInt()

template<typename T >

T ttk::Geometry::powInt	(	const T	val,
		const int	n
	)

inline

Compute the integer power of a floating-point value (std::pow is optimised for floating-point exponents)

Definition at line 383 of file Geometry.h.

◆ powIntTen()

template<typename T = double>

T ttk::Geometry::powIntTen ( const int n )

inline

Compute the nth power of ten.

Definition at line 405 of file Geometry.h.

◆ projectOnEdge()

template<typename T >

void ttk::Geometry::projectOnEdge	(	const T *	p,
		const T *	a,
		const T *	b,
		T *	out
	)

Compute euclidean projection on a 3D segment.

Parameters

[in]	p	Point to be projected
[in]	a	First segment vertex coordinates
[in]	b	Second segment vertex coordinates
[out]	out	Result

Returns: Projection coordinates

Definition at line 550 of file Geometry.cpp.

◆ projectOnTrianglePlane()

template<typename T >

void ttk::Geometry::projectOnTrianglePlane	(	const T *	p,
		const T *	a,
		const T *	normTri,
		T *	out
	)

Compute euclidean projection in a triangle plane.

Parameters

[in]	p	Point to be projected
[in]	a	Triangle vertex coordinates
[in]	normTri	Triangle normal vector
[out]	out	Result

Returns: Projection coordinates

Definition at line 538 of file Geometry.cpp.

◆ scaleMatrix()

template<typename T >

void ttk::Geometry::scaleMatrix	(	const std::vector< std::vector< T > > &	a,
		const T	factor,
		std::vector< std::vector< T > > &	out
	)

Scale a matrix by a scalar value

Parameters

a	the input matrix
factor	scale factor
out	the resulting matrix

Definition at line 808 of file Geometry.cpp.

◆ scaleVector() [1/2]

template<typename T >

int ttk::Geometry::scaleVector	(	const std::vector< T > &	a,
		const T	factor,
		std::vector< T > &	out
	)

Scale a vector by a scalar value.

Parameters

a	coordinates of the first vector
factor	scale factor
out	the scaled vector

Returns: Returns 0 for success, negative otherwise.

Definition at line 657 of file Geometry.cpp.

◆ scaleVector() [2/2]

template<typename T >

int ttk::Geometry::scaleVector	(	const T *	a,
		const T	factor,
		T *	out,
		const int &	dimension = `3`
	)

Scale a vector by a scalar value.

Parameters

a	coordinates of the first vector
factor	scale factor
out	the scaled vector
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns 0 for success, negative otherwise.

Definition at line 647 of file Geometry.cpp.

◆ subtractMatrices()

template<typename T >

void ttk::Geometry::subtractMatrices	(	const std::vector< std::vector< T > > &	a,
		const std::vector< std::vector< T > > &	b,
		std::vector< std::vector< T > > &	out
	)

Computes the element wise subtraction of two matrices (b subtracted by a)

Parameters

a	the first matrix
b	the second matrix
out	the resulting matrix

Definition at line 788 of file Geometry.cpp.

◆ subtractVectors() [1/2]

template<typename T >

int ttk::Geometry::subtractVectors	(	const std::vector< T > &	a,
		const std::vector< T > &	b,
		std::vector< T > &	out
	)

Computes the difference between two vectors (b subtracted by a).

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the difference between the two vectors

Returns: Returns 0 for success, negative otherwise.

Definition at line 602 of file Geometry.cpp.

◆ subtractVectors() [2/2]

template<typename T >

int ttk::Geometry::subtractVectors	(	const T *	a,
		const T *	b,
		T *	out,
		const int &	dimension = `3`
	)

Computes the difference between two vectors (b subtracted by a).

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the difference between the two vectors
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns 0 for success, negative otherwise.

Definition at line 592 of file Geometry.cpp.

◆ transposeMatrix()

template<typename T >

void ttk::Geometry::transposeMatrix	(	const std::vector< std::vector< T > > &	a,
		std::vector< std::vector< T > > &	out
	)

Transpose a matrix

Parameters

a	the input matrix
out	the resulting matrix

Definition at line 818 of file Geometry.cpp.

◆ unflattenMultiDimensionalVector()

template<typename T >

int ttk::Geometry::unflattenMultiDimensionalVector	(	const std::vector< T > &	a,
		std::vector< std::vector< T > > &	out,
		const int &	no_columns = `2`
	)

Unflatten a vector to a multi dimensional vector (representing a rectangular/square matrix)

Parameters

a	vector
out	multi dimensional vector
no_columns	number of columns of the output multi dimensional vector

Returns: Returns 0 for success, negative otherwise

Definition at line 762 of file Geometry.cpp.

◆ vectorProjection() [1/2]

template<typename T >

int ttk::Geometry::vectorProjection	(	const std::vector< T > &	a,
		const std::vector< T > &	b,
		std::vector< T > &	out
	)

Computes the projection of vector a onto the vector b

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the projected vector

Returns: Returns 0 for success, negative otherwise.

Definition at line 682 of file Geometry.cpp.

◆ vectorProjection() [2/2]

template<typename T >

int ttk::Geometry::vectorProjection	(	const T *	a,
		const T *	b,
		T *	out,
		const int &	dimension = `3`
	)

Computes the projection of vector a onto the vector b

Parameters

a	coordinates of the first vector
b	coordinates of the second vector
out	the projected vector
dimension	Optional parameter that specifies the dimension of the point set (by default 3).

Returns: Returns 0 for success, negative otherwise.

Definition at line 665 of file Geometry.cpp.

Classes

Functions

Function Documentation

◆ addMatrices()

◆ addVectors() [1/2]

◆ addVectors() [2/2]

◆ addVectorsProjection()

◆ angle()

◆ angle2D()

◆ angle2DUndirected()

◆ areVectorsColinear()

◆ computeBarycentricCoordinates() [1/2]

◆ computeBarycentricCoordinates() [2/2]

◆ computeSegmentIntersection()

◆ computeSurfaceNormalAtPoint()

◆ computeTriangleAngleFromSides()

◆ computeTriangleAngles()

◆ computeTriangleArea()

◆ computeTriangleAreaFromSides()

◆ computeTriangleNormal()

◆ crossProduct() [1/2]

◆ crossProduct() [2/2]

◆ distance() [1/2]

◆ distance() [2/2]

◆ distance2D()

◆ distanceFlatten()

◆ dotProduct() [1/3]

◆ dotProduct() [2/3]

◆ dotProduct() [3/3]

◆ dotProductFlatten()

◆ findProjection()

◆ flattenMultiDimensionalVector()

◆ getBoundingBox()

◆ getNearestSurfaceVertex()

◆ gramSchmidt()

◆ isPointInTriangle()

◆ isPointOnSegment() [1/2]

◆ isPointOnSegment() [2/2]

◆ isTriangleColinear()

◆ isTriangleColinear2D()

◆ isVectorNull()

◆ isVectorNullFlatten()

◆ isVectorUniform()

◆ magnitude() [1/3]

◆ magnitude() [2/3]

◆ magnitude() [3/3]

◆ magnitudeFlatten()

◆ matrixMultiplication()

◆ multiAddVectors()

◆ multiAddVectorsFlatten()

◆ multiFlattenMultiDimensionalVector()

◆ pow()

◆ powInt()

◆ powIntTen()

◆ projectOnEdge()

◆ projectOnTrianglePlane()

◆ scaleMatrix()

◆ scaleVector() [1/2]

◆ scaleVector() [2/2]

◆ subtractMatrices()

◆ subtractVectors() [1/2]

◆ subtractVectors() [2/2]

◆ transposeMatrix()

◆ unflattenMultiDimensionalVector()

◆ vectorProjection() [1/2]

◆ vectorProjection() [2/2]