This module contains all the mathematical functions and utilities used in the library. More...

Classes
class	vcl::Distribution< Scalar >
	The Distribution class allows to collect a set of values and then compute some statistics like average, variance, standardDeviation, and percentiles. More...

class	vcl::Histogram< ScalarType >
	The Histogram class allows to collect a set of values and then compute some statistics like average, variance, standardDeviation, and percentiles. More...

Functions
template<typename Scalar >
bool	vcl::isDegenerate (Scalar number)
	Checks if a floating point number is degenerate.

template<typename Scalar >
bool	vcl::epsilonEquals (Scalar n1, Scalar n2, Scalar epsilon=std::numeric_limits< Scalar >::epsilon())
	Checks if two floating point numbers are equal within an epsilon value.

template<typename Scalar >
Scalar	vcl::toRad (const Scalar &deg)
	Converts an angle in degrees to radians.

template<typename Scalar >
Scalar	vcl::toDeg (const Scalar &rad)
	Converts an angle in radians to degrees.

double	vcl::lnOfFactorial (int n)
	Computes and caches the result of the natural logarithm of n!

template<Point3Concept PointType>
std::vector< PointType >	vcl::sphericalFibonacciPointSet (uint n)
	Returns a vector of `n` points distributed in a unit sphere.

template<typename T >
constexpr auto	vcl::min (const T &p1, const T &p2)
	Returns the minimum between the two parameters.

template<typename Head , typename... Tail> requires (sizeof...(tail) > 0)
constexpr auto	vcl::min (const Head &head0, const Head &head1, const Tail &... tail)
	Returns the minimum between several parameters.

template<typename T >
constexpr auto	vcl::max (const T &p1, const T &p2)
	Returns the maximum between the two parameters.

template<typename Head , typename... Tail> requires (sizeof...(tail) > 0)
constexpr auto	vcl::max (const Head &head0, const Head &head1, const Tail &... tail)
	Returns the maximum between several parameters.

template<PointConcept PointType>
constexpr auto	vcl::min (const PointType &p1, const PointType &p2)
	Returns the minimum between two points.

template<PointConcept PointType>
constexpr auto	vcl::max (const PointType &p1, const PointType &p2)
	Returns the maximum between two points.

int	vcl::poissonRatioOfUniformsInteger (double L, std::mt19937 &gen)
	This subfunction generates a integer with the poisson distribution using the ratio-of-uniforms rejection method (PRUAt). This approach is STABLE even for large L (e.g. it does not suffer from the overflow limit of the classical Knuth implementation) Execution time does not depend on L, except that it matters whether is within the range where ln(n!) is tabulated.

int	vcl::poissonRandomNumber (double lambda, std::mt19937 &gen)
	algorithm poisson random number (Knuth): init: Let L ← e^−λ, k ← 0 and p ← 1. do: k ← k + 1. Generate uniform random number u in [0,1] and let p ← p × u. while p > L. return k − 1.

template<Point3Concept PointType>
PointType	vcl::randomTriangleBarycentricCoordinate (std::mt19937 &gen)
	Generate the barycentric coords of a random point over a triangle, with a uniform distribution over the triangle. It uses the parallelogram folding trick.

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >
void	vcl::setTransformMatrixRotation (MatrixType &matrix, PointType axis, const ScalarType &angleRad)
	Given an 3D axis and an angle expressed in radiants, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >
void	vcl::setTransformMatrixRotationDeg (MatrixType &matrix, PointType axis, const ScalarType &angleDeg)
	Given an 3D axis and an angle expressed in degrees, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

template<MatrixConcept MatrixType, Point3Concept PointType>
void	vcl::setTransformMatrixRotation (MatrixType &matrix, const PointType &fromVector, const PointType &toVector)
	Given two 3D vectors, fills the given matrix with a transform matrix that represents the rotation matrix from the first vector to the second vector.

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >
MatrixType	vcl::rotationMatrix (const PointType &axis, const ScalarType &angleRad)
	Given an 3D axis and an angle expressed in radiants, returns a transform matrix that represents the rotation matrix of the given axis/angle.

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >
MatrixType	vcl::rotationMatrixDeg (const PointType &axis, const ScalarType &angleDeg)
	Given an 3D axis and an angle expressed in degrees, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

template<MatrixConcept MatrixType, Point3Concept PointType>
MatrixType	vcl::rotationMatrix (const PointType &fromVector, const PointType &toVector)
	Given two 3D vectors, returns a transform matrix that represents the rotation matrix from the first vector to the second vector.

Detailed Description

This module contains all the mathematical functions and utilities used in the library.

This module depends on the Concepts module.

You can access all the concepts of VCLib by including #include <vclib/math.h>

Function Documentation

◆ epsilonEquals()

template<typename Scalar >

bool vcl::epsilonEquals	(	Scalar	n1,
		Scalar	n2,
		Scalar	epsilon = `std::numeric_limits<Scalar>::epsilon()`
	)

Checks if two floating point numbers are equal within an epsilon value.

This function returns true if the absolute difference between the two numbers is less than or equal to the epsilon value.

Parameters

[in]	n1	the first number to compare
[in]	n2	the second number to compare
[in]	epsilon	the epsilon value to use for the check

Returns: true if the numbers are equal within the epsilon value, false otherwise.

◆ isDegenerate()

template<typename Scalar >

bool vcl::isDegenerate ( Scalar number )

Checks if a floating point number is degenerate.

A floating point number is degenerate if it is infinite or NaN.

Parameters

[in] number the number to check

Returns: true if the number is degenerate, false otherwise.

◆ lnOfFactorial()

double vcl::lnOfFactorial ( int n )

inline

Computes and caches the result of the natural logarithm of n!

If n > 1024, uses the Stirling approximation.

Parameters

[in] n the number for which to compute the natural logarithm of the factorial.

Returns: the natural logarithm of n!.

◆ max() [1/3]

template<typename Head , typename... Tail>
requires (sizeof...(tail) > 0)

constexpr auto vcl::max	(	const Head &	head0,
		const Head &	head1,
		const Tail &...	tail
	)

constexpr

Returns the maximum between several parameters.

Given a list of parameters, this function returns the maximum between all of them.

Example:

auto m = vcl::max(1, 2, 3, 4, 5); // m = 5

vcl::Segment

A class representing a line segment in n-dimensional space. The class is parameterized by a PointConc...

Definition segment.h:43

vcl::max

constexpr auto max(const T &p1, const T &p2)

Returns the maximum between the two parameters.

Definition min_max.h:83

Parameters

[in]	head0	The first parameter.
[in]	head1	The second parameter.
[in]	tail	The rest of the parameters.

Returns: The maximum between the parameters.

◆ max() [2/3]

template<PointConcept PointType>

constexpr auto vcl::max	(	const PointType &	p1,
		const PointType &	p2
	)

constexpr

Returns the maximum between two points.

This function returns a point that contains the maximum value between each component of the two input points.

Parameters

[in]	p1	The first point.
[in]	p2	The second point.

Returns: The point containing the maximum value between the two input points.

◆ max() [3/3]

template<typename T >

constexpr auto vcl::max	(	const T &	p1,
		const T &	p2
	)

constexpr

Returns the maximum between the two parameters.

Parameters

[in]	p1	The first parameter.
[in]	p2	The second parameter.

Returns: The maximum between the two parameters.

◆ min() [1/3]

template<typename Head , typename... Tail>
requires (sizeof...(tail) > 0)

constexpr auto vcl::min	(	const Head &	head0,
		const Head &	head1,
		const Tail &...	tail
	)

constexpr

Returns the minimum between several parameters.

Given a list of parameters, this function returns the minimum between all of them.

Example:

auto m = vcl::min(1, 2, 3, 4, 5); // m = 1

vcl::min

constexpr auto min(const T &p1, const T &p2)

Returns the minimum between the two parameters.

Definition min_max.h:42

Parameters

[in]	head0	The first parameter.
[in]	head1	The second parameter.
[in]	tail	The rest of the parameters.

Returns: The minimum between the parameters.

◆ min() [2/3]

template<PointConcept PointType>

constexpr auto vcl::min	(	const PointType &	p1,
		const PointType &	p2
	)

constexpr

Returns the minimum between two points.

This function returns a point that contains the minimum value between each component of the two input points.

Parameters

[in]	p1	The first point.
[in]	p2	The second point.

Returns: The point containing the minimum value between the two input points.

◆ min() [3/3]

template<typename T >

constexpr auto vcl::min	(	const T &	p1,
		const T &	p2
	)

constexpr

Returns the minimum between the two parameters.

Parameters

[in]	p1	The first parameter.
[in]	p2	The second parameter.

Returns: The minimum between the two parameters.

◆ poissonRandomNumber()

int vcl::poissonRandomNumber	(	double	lambda,
		std::mt19937 &	gen
	)

inline

algorithm poisson random number (Knuth): init: Let L ← e^−λ, k ← 0 and p ← 1. do: k ← k + 1. Generate uniform random number u in [0,1] and let p ← p × u. while p > L. return k − 1.

Parameters

lambda
gen

Returns

◆ poissonRatioOfUniformsInteger()

int vcl::poissonRatioOfUniformsInteger	(	double	L,
		std::mt19937 &	gen
	)

inline

This subfunction generates a integer with the poisson distribution using the ratio-of-uniforms rejection method (PRUAt). This approach is STABLE even for large L (e.g. it does not suffer from the overflow limit of the classical Knuth implementation) Execution time does not depend on L, except that it matters whether is within the range where ln(n!) is tabulated.

Reference:

E. Stadlober "The ratio of uniforms approach for generating discrete random variates". Journal of Computational and Applied Mathematics, vol. 31, no. 1, 1990, pp. 181-189.

Partially adapted/inspired from some subfunctions of the Agner Fog stocc library ( www.agner.org/random ) Same licensing scheme.

Parameters

L
gen

Returns

◆ randomTriangleBarycentricCoordinate()

template<Point3Concept PointType>

PointType vcl::randomTriangleBarycentricCoordinate ( std::mt19937 & gen )

Generate the barycentric coords of a random point over a triangle, with a uniform distribution over the triangle. It uses the parallelogram folding trick.

Parameters

gen

Returns

◆ rotationMatrix() [1/2]

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >

MatrixType vcl::rotationMatrix	(	const PointType &	axis,
		const ScalarType &	angleRad
	)

Given an 3D axis and an angle expressed in radiants, returns a transform matrix that represents the rotation matrix of the given axis/angle.

The MatrixType must be at least a 3x3 matrix having the setIdentity() member function. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving the identity values in the other cells of the matrix.

Parameters

axis
angleRad

Returns

◆ rotationMatrix() [2/2]

template<MatrixConcept MatrixType, Point3Concept PointType>

MatrixType vcl::rotationMatrix	(	const PointType &	fromVector,
		const PointType &	toVector
	)

Given two 3D vectors, returns a transform matrix that represents the rotation matrix from the first vector to the second vector.

The MatrixType must be at least a 3x3 matrix having the setIdentity() member function. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving the identity values in the other cells of the matrix.

Parameters

fromVector
toVector

Returns

◆ rotationMatrixDeg()

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >

MatrixType vcl::rotationMatrixDeg	(	const PointType &	axis,
		const ScalarType &	angleDeg
	)

Given an 3D axis and an angle expressed in degrees, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

The MatrixType must be at least a 3x3 matrix having the setIdentity() member function. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving the identity values in the other cells of the matrix.

Parameters

axis
angleDeg

Returns

◆ setTransformMatrixRotation() [1/2]

template<MatrixConcept MatrixType, Point3Concept PointType>

void vcl::setTransformMatrixRotation	(	MatrixType &	matrix,
		const PointType &	fromVector,
		const PointType &	toVector
	)

Given two 3D vectors, fills the given matrix with a transform matrix that represents the rotation matrix from the first vector to the second vector.

The given matrix must be at least a 3x3 matrix. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving unchanged the other values.

Parameters

matrix
fromVector
toVector

◆ setTransformMatrixRotation() [2/2]

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >

void vcl::setTransformMatrixRotation	(	MatrixType &	matrix,
		PointType	axis,
		const ScalarType &	angleRad
	)

Given an 3D axis and an angle expressed in radiants, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

The given matrix must be at least a 3x3 matrix. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving unchanged the other values.

Parameters

matrix
axis
angleRad

◆ setTransformMatrixRotationDeg()

template<MatrixConcept MatrixType, Point3Concept PointType, typename ScalarType >

void vcl::setTransformMatrixRotationDeg	(	MatrixType &	matrix,
		PointType	axis,
		const ScalarType &	angleDeg
	)

Given an 3D axis and an angle expressed in degrees, fills the given matrix with a transform matrix that represents the rotation matrix of the given axis/angle.

The given matrix must be at least a 3x3 matrix. If the matrix is a higher than 3x3 (e.g. 4x4), only the 3x3 submatrix will be set, leaving unchanged the other values.

Parameters

matrix
axis
angleDeg

◆ sphericalFibonacciPointSet()

template<Point3Concept PointType>

std::vector< PointType > vcl::sphericalFibonacciPointSet ( uint n )

Returns a vector of n points distributed in a unit sphere.

This function returns a vector of n points that are uniformly distributed on a unit sphere, using the Spherical Fibonacci Point Sets algorithm described in the paper "Spherical Fibonacci Mapping" by Benjamin Keinert, Matthias Innmann, Michael Sanger, and Marc Stamminger (TOG 2015).

Template Parameters

PointType The type of the point to generate. This type must satisfy the Point3Concept concept.

Parameters

[in] n The number of points to generate.

Returns: A vector of n points distributed in a unit sphere.

◆ toDeg()

template<typename Scalar >

Scalar vcl::toDeg ( const Scalar & rad )

Converts an angle in radians to degrees.

Parameters

[in] rad the angle in radians

Returns: the angle in degrees.

◆ toRad()

template<typename Scalar >

Scalar vcl::toRad ( const Scalar & deg )

Converts an angle in degrees to radians.

Parameters

[in] deg the angle in degrees

Returns: the angle in radians.ù

Classes

Functions

Detailed Description

Function Documentation

◆ epsilonEquals()

◆ isDegenerate()

◆ lnOfFactorial()

◆ max() [1/3]

◆ max() [2/3]

◆ max() [3/3]

◆ min() [1/3]

◆ min() [2/3]

◆ min() [3/3]

◆ poissonRandomNumber()

◆ poissonRatioOfUniformsInteger()

◆ randomTriangleBarycentricCoordinate()

◆ rotationMatrix() [1/2]

◆ rotationMatrix() [2/2]

◆ rotationMatrixDeg()

◆ setTransformMatrixRotation() [1/2]

◆ setTransformMatrixRotation() [2/2]

◆ setTransformMatrixRotationDeg()

◆ sphericalFibonacciPointSet()

◆ toDeg()

◆ toRad()