Core data structure and utilities. More...

Classes
class	BoundingBox
	Simple class for representing a bounding box. More...

class	InvalidInputException
	Exception indicating invalid input passed to a function. More...

class	SolverException
	Exception indicating failure so solve an equation system. More...

class	AllocationException
	Exception indicating failure to allocate a new resource. More...

class	TopologyException
	Exception indicating a topological error has occurred. More...

class	IOException
	Exception indicating an error occurred while performing IO. More...

class	Matrix< Scalar, M, N >
	Base class for MxN matrix. More...

class	MemoryUsage
	A simple class to retrieve memory usage information. More...

class	Handle
	Base class for all entity handles types. More...

class	Vertex
	this type represents a vertex (internally it is basically an index) More...

class	Halfedge
	this type represents a halfedge (internally it is basically an index) More...

class	Edge
	this type represents an edge (internally it is basically an index) More...

class	Face
	this type represents a face (internally it is basically an index) More...

class	VertexProperty< T >
	Vertex property of type T. More...

class	HalfedgeProperty< T >
	Halfedge property of type T. More...

class	EdgeProperty< T >
	Edge property of type T. More...

class	FaceProperty< T >
	Face property of type T. More...

class	ObjectProperty< T >
	Object property of type T. More...

class	SurfaceMesh
	A halfedge data structure for polygonal meshes. More...

class	Timer
	A simple timer class. More...

struct	IOFlags
	Common IO flags for reading and writing. More...

Typedefs
template<typename Scalar , int M>
using	Vector = Matrix< Scalar, M, 1 >
	template specialization for Vector as Nx1 matrix More...

template<typename Scalar >
using	Mat4 = Matrix< Scalar, 4, 4 >
	template specialization for 4x4 matrices More...

template<typename Scalar >
using	Mat3 = Matrix< Scalar, 3, 3 >
	template specialization for 3x3 matrices More...

template<typename Scalar >
using	Mat2 = Matrix< Scalar, 2, 2 >
	template specialization for 2x2 matrices More...

typedef Vector< float, 2 >	vec2
	template specialization for a vector of two float values More...

typedef Vector< double, 2 >	dvec2
	template specialization for a vector of two double values More...

typedef Vector< bool, 2 >	bvec2
	template specialization for a vector of two bool values More...

typedef Vector< int, 2 >	ivec2
	template specialization for a vector of two int values More...

typedef Vector< unsigned int, 2 >	uvec2
	template specialization for a vector of two unsigned int values More...

typedef Vector< float, 3 >	vec3
	template specialization for a vector of three float values More...

typedef Vector< double, 3 >	dvec3
	template specialization for a vector of three double values More...

typedef Vector< bool, 3 >	bvec3
	template specialization for a vector of three bool values More...

typedef Vector< int, 3 >	ivec3
	template specialization for a vector of three int values More...

typedef Vector< unsigned int, 3 >	uvec3
	template specialization for a vector of three unsigned int values More...

typedef Vector< float, 4 >	vec4
	template specialization for a vector of four float values More...

typedef Vector< double, 4 >	dvec4
	template specialization for a vector of four double values More...

typedef Vector< bool, 4 >	bvec4
	template specialization for a vector of four bool values More...

typedef Vector< int, 4 >	ivec4
	template specialization for a vector of four int values More...

typedef Vector< unsigned int, 4 >	uvec4
	template specialization for a vector of four unsigned int values More...

typedef Vector< float, 8 >	vec8
	template specialization for a vector of four float values More...

typedef Vector< double, 8 >	dvec8
	template specialization for a vector of four double values More...

typedef Vector< bool, 8 >	bvec8
	template specialization for a vector of four bool values More...

typedef Vector< int, 8 >	ivec8
	template specialization for a vector of four int values More...

typedef Vector< unsigned int, 8 >	uvec8
	template specialization for a vector of four unsigned int values More...

typedef Mat2< float >	mat2
	template specialization for a 2x2 matrix of float values More...

typedef Mat2< double >	dmat2
	template specialization for a 2x2 matrix of double values More...

typedef Mat3< float >	mat3
	template specialization for a 3x3 matrix of float values More...

typedef Mat3< double >	dmat3
	template specialization for a 3x3 matrix of double values More...

typedef Mat4< float >	mat4
	template specialization for a 4x4 matrix of float values More...

typedef Mat4< double >	dmat4
	template specialization for a 4x4 matrix of double values More...

typedef float	Scalar
	Scalar type. More...

typedef Vector< Scalar, 3 >	Point
	Point type. More...

typedef Vector< Scalar, 3 >	Normal
	Normal type. More...

typedef Vector< Scalar, 3 >	Color
	Color type. More...

typedef Vector< Scalar, 2 >	TexCoord
	Texture coordinate type. More...

Functions
template<typename Scalar , int M, int N>
std::ostream &	operator<< (std::ostream &os, const Matrix< Scalar, M, N > &m)
	output a matrix by printing its space-separated compontens More...

template<typename Scalar , int M, int N, int K>
Matrix< Scalar, M, N >	operator* (const Matrix< Scalar, M, K > &m1, const Matrix< Scalar, K, N > &m2)
	matrix-matrix multiplication More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	cmult (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	component-wise multiplication More...

template<typename Scalar , int M, int N>
Matrix< Scalar, N, M >	transpose (const Matrix< Scalar, M, N > &m)
	transpose MxN matrix to NxM matrix More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator+ (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	matrix addition: m1 + m2 More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator- (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	matrix subtraction: m1 - m2 More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator- (const Matrix< Scalar, M, N > &m)
	matrix negation: -m More...

template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator* (const Scalar2 s, const Matrix< Scalar, M, N > &m)
	scalar multiplication of matrix: s*m More...

template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator* (const Matrix< Scalar, M, N > &m, const Scalar2 s)
	scalar multiplication of matrix: m*s More...

template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator/ (const Matrix< Scalar, M, N > &m, const Scalar2 s)
	divide matrix by scalar: m/s More...

template<typename Scalar , int M, int N>
Scalar	norm (const Matrix< Scalar, M, N > &m)
	compute the Frobenius norm of a matrix (or Euclidean norm of a vector) More...

template<typename Scalar , int M, int N>
Scalar	sqrnorm (const Matrix< Scalar, M, N > &m)
	compute the squared Frobenius norm of a matrix (or squared Euclidean norm of a vector) More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	normalize (const Matrix< Scalar, M, N > &m)
	return a normalized copy of a matrix or a vector More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	min (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	return component-wise minimum More...

template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	max (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	return component-wise maximum More...

template<typename Scalar >
Mat4< Scalar >	viewport_matrix (Scalar l, Scalar b, Scalar w, Scalar h)
	OpenGL viewport matrix with parameters left, bottom, width, height. More...

template<typename Scalar >
Mat4< Scalar >	inverse_viewport_matrix (Scalar l, Scalar b, Scalar w, Scalar h)
	inverse of OpenGL viewport matrix with parameters left, bottom, width, height More...

template<typename Scalar >
Mat4< Scalar >	frustum_matrix (Scalar l, Scalar r, Scalar b, Scalar t, Scalar n, Scalar f)
	OpenGL frustum matrix with parameters left, right, bottom, top, near, far. More...

template<typename Scalar >
Mat4< Scalar >	inverse_frustum_matrix (Scalar l, Scalar r, Scalar b, Scalar t, Scalar n, Scalar f)
	inverse of OpenGL frustum matrix with parameters left, right, bottom, top, near, far More...

template<typename Scalar >
Mat4< Scalar >	perspective_matrix (Scalar fovy, Scalar aspect, Scalar zNear, Scalar zFar)
	OpenGL perspective matrix with parameters field of view in y-direction, aspect ratio, and distance of near and far planes. More...

template<typename Scalar >
Mat4< Scalar >	inverse_perspective_matrix (Scalar fovy, Scalar aspect, Scalar zNear, Scalar zFar)
	inverse of perspective matrix More...

template<typename Scalar >
Mat4< Scalar >	ortho_matrix (Scalar left, Scalar right, Scalar bottom, Scalar top, Scalar zNear=-1, Scalar zFar=1)
	OpenGL orthogonal projection matrix with parameters left, right, bottom, top, near, far. More...

template<typename Scalar >
Mat4< Scalar >	look_at_matrix (const Vector< Scalar, 3 > &eye, const Vector< Scalar, 3 > &center, const Vector< Scalar, 3 > &up)
	OpenGL look-at camera matrix with parameters eye position, scene center, up-direction. More...

template<typename Scalar >
Mat4< Scalar >	translation_matrix (const Vector< Scalar, 3 > &t)
	OpenGL matrix for translation by vector t. More...

template<typename Scalar >
Mat4< Scalar >	scaling_matrix (const Scalar s)
	OpenGL matrix for scaling x/y/z by s. More...

template<typename Scalar >
Mat4< Scalar >	scaling_matrix (const Vector< Scalar, 3 > &s)
	OpenGL matrix for scaling x/y/z by the components of s. More...

template<typename Scalar >
Mat4< Scalar >	rotation_matrix_x (Scalar angle)
	OpenGL matrix for rotation around x-axis by given angle (in degrees) More...

template<typename Scalar >
Mat4< Scalar >	rotation_matrix_y (Scalar angle)
	OpenGL matrix for rotation around y-axis by given angle (in degrees) More...

template<typename Scalar >
Mat4< Scalar >	rotation_matrix_z (Scalar angle)
	OpenGL matrix for rotation around z-axis by given angle (in degrees) More...

template<typename Scalar >
Mat4< Scalar >	rotation_matrix (const Vector< Scalar, 3 > &axis, Scalar angle)
	OpenGL matrix for rotation around given axis by given angle (in degrees) More...

template<typename Scalar >
Mat4< Scalar >	rotation_matrix (const Vector< Scalar, 4 > &quat)
	OpenGL matrix for rotation specified by unit quaternion. More...

template<typename Scalar >
Mat3< Scalar >	linear_part (const Mat4< Scalar > &m)
	return upper 3x3 matrix from given 4x4 matrix, corresponding to the linear part of an affine transformation More...

template<typename Scalar >
Vector< Scalar, 3 >	projective_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	projective transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, divide by 4th component More...

template<typename Scalar >
Vector< Scalar, 3 >	affine_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	affine transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, do NOT divide by 4th component More...

template<typename Scalar >
Vector< Scalar, 3 >	linear_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	linear transformation of 3D vector v by a 4x4 matrix m: transform vector by upper-left 3x3 submatrix of m More...

template<typename Scalar >
Mat4< Scalar >	inverse (const Mat4< Scalar > &m)
	return the inverse of a 4x4 matrix More...

template<typename Scalar >
Scalar	determinant (const Mat3< Scalar > &m)
	return determinant of 3x3 matrix More...

template<typename Scalar >
Mat3< Scalar >	inverse (const Mat3< Scalar > &m)
	return the inverse of a 3x3 matrix More...

template<typename Scalar >
bool	symmetric_eigendecomposition (const Mat3< Scalar > &m, Scalar &eval1, Scalar &eval2, Scalar &eval3, Vector< Scalar, 3 > &evec1, Vector< Scalar, 3 > &evec2, Vector< Scalar, 3 > &evec3)
	compute eigenvector/eigenvalue decomposition of a 3x3 matrix More...

template<typename Scalar , int N>
std::istream &	operator>> (std::istream &is, Vector< Scalar, N > &vec)
	read the space-separated components of a vector from a stream More...

template<typename Scalar , int N>
std::ostream &	operator<< (std::ostream &os, const Vector< Scalar, N > &vec)
	output a vector by printing its space-separated compontens More...

template<typename Scalar , int N>
Scalar	dot (const Vector< Scalar, N > &v0, const Vector< Scalar, N > &v1)
	compute the dot product of two vectors More...

template<typename Scalar , int N>
Scalar	distance (const Vector< Scalar, N > &v0, const Vector< Scalar, N > &v1)
	compute the Euclidean distance between two points More...

template<typename Scalar >
Vector< Scalar, 2 >	perp (const Vector< Scalar, 2 > &v)
	compute perpendicular vector (rotate vector counter-clockwise by 90 degrees) More...

template<typename Scalar >
Vector< Scalar, 3 >	cross (const Vector< Scalar, 3 > &v0, const Vector< Scalar, 3 > &v1)
	compute the cross product of two vectors (only valid for 3D vectors) More...

std::ostream &	operator<< (std::ostream &os, Vertex v)
	output a Vertex to a stream More...

std::ostream &	operator<< (std::ostream &os, Halfedge h)
	output a Halfedge to a stream More...

std::ostream &	operator<< (std::ostream &os, Edge e)
	output an Edge to a stream More...

std::ostream &	operator<< (std::ostream &os, Face f)
	output a Face to a stream More...

static Matrix< Scalar, M, N >	identity ()
	return identity matrix (only for square matrices, N==M) More...

Detailed Description

Core data structure and utilities.

Typedef Documentation

◆ bvec2

typedef Vector<bool, 2> bvec2

template specialization for a vector of two bool values

◆ bvec3

typedef Vector<bool, 3> bvec3

template specialization for a vector of three bool values

◆ bvec4

typedef Vector<bool, 4> bvec4

template specialization for a vector of four bool values

◆ bvec8

typedef Vector<bool, 8> bvec8

template specialization for a vector of four bool values

◆ Color

typedef Vector<Scalar, 3> Color

Color type.

◆ dmat2

typedef Mat2<double> dmat2

template specialization for a 2x2 matrix of double values

◆ dmat3

typedef Mat3<double> dmat3

template specialization for a 3x3 matrix of double values

◆ dmat4

typedef Mat4<double> dmat4

template specialization for a 4x4 matrix of double values

◆ dvec2

typedef Vector<double, 2> dvec2

template specialization for a vector of two double values

◆ dvec3

typedef Vector<double, 3> dvec3

template specialization for a vector of three double values

◆ dvec4

typedef Vector<double, 4> dvec4

template specialization for a vector of four double values

◆ dvec8

typedef Vector<double, 8> dvec8

template specialization for a vector of four double values

◆ ivec2

typedef Vector<int, 2> ivec2

template specialization for a vector of two int values

◆ ivec3

typedef Vector<int, 3> ivec3

template specialization for a vector of three int values

◆ ivec4

typedef Vector<int, 4> ivec4

template specialization for a vector of four int values

◆ ivec8

typedef Vector<int, 8> ivec8

template specialization for a vector of four int values

◆ Mat2

using Mat2 = Matrix<Scalar, 2, 2>

template specialization for 2x2 matrices

◆ mat2

typedef Mat2<float> mat2

template specialization for a 2x2 matrix of float values

◆ Mat3

using Mat3 = Matrix<Scalar, 3, 3>

template specialization for 3x3 matrices

◆ mat3

typedef Mat3<float> mat3

template specialization for a 3x3 matrix of float values

◆ Mat4

using Mat4 = Matrix<Scalar, 4, 4>

template specialization for 4x4 matrices

◆ mat4

typedef Mat4<float> mat4

template specialization for a 4x4 matrix of float values

◆ Normal

typedef Vector<Scalar, 3> Normal

Normal type.

◆ Point

typedef Vector<Scalar, 3> Point

Point type.

◆ Scalar

typedef float Scalar

Scalar type.

◆ TexCoord

typedef Vector<Scalar, 2> TexCoord

Texture coordinate type.

◆ uvec2

typedef Vector<unsigned int, 2> uvec2

template specialization for a vector of two unsigned int values

◆ uvec3

typedef Vector<unsigned int, 3> uvec3

template specialization for a vector of three unsigned int values

◆ uvec4

typedef Vector<unsigned int, 4> uvec4

template specialization for a vector of four unsigned int values

◆ uvec8

typedef Vector<unsigned int, 8> uvec8

template specialization for a vector of four unsigned int values

◆ vec2

typedef Vector<float, 2> vec2

template specialization for a vector of two float values

◆ vec3

typedef Vector<float, 3> vec3

template specialization for a vector of three float values

◆ vec4

typedef Vector<float, 4> vec4

template specialization for a vector of four float values

◆ vec8

typedef Vector<float, 8> vec8

template specialization for a vector of four float values

◆ Vector

using Vector = Matrix<Scalar, M, 1>

template specialization for Vector as Nx1 matrix

Function Documentation

◆ affine_transform()

Vector< Scalar, 3 > pmp::affine_transform	(	const Mat4< Scalar > &	m,
		const Vector< Scalar, 3 > &	v
	)

affine transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, do NOT divide by 4th component

◆ cmult()

Matrix< Scalar, M, N > pmp::cmult	(	const Matrix< Scalar, M, N > &	m1,
		const Matrix< Scalar, M, N > &	m2
	)

component-wise multiplication

◆ cross()

Vector< Scalar, 3 > pmp::cross	(	const Vector< Scalar, 3 > &	v0,
		const Vector< Scalar, 3 > &	v1
	)

inline

compute the cross product of two vectors (only valid for 3D vectors)

◆ determinant()

Scalar pmp::determinant ( const Mat3< Scalar > & m )

return determinant of 3x3 matrix

◆ distance()

Scalar pmp::distance	(	const Vector< Scalar, N > &	v0,
		const Vector< Scalar, N > &	v1
	)

inline

compute the Euclidean distance between two points

◆ dot()

Scalar pmp::dot	(	const Vector< Scalar, N > &	v0,
		const Vector< Scalar, N > &	v1
	)

inline

compute the dot product of two vectors

◆ frustum_matrix()

Mat4< Scalar > pmp::frustum_matrix	(	Scalar	l,
		Scalar	r,
		Scalar	b,
		Scalar	t,
		Scalar	n,
		Scalar	f
	)

OpenGL frustum matrix with parameters left, right, bottom, top, near, far.

◆ identity()

Matrix< Scalar, M, N > identity

static

return identity matrix (only for square matrices, N==M)

identity matrix (work only for square matrices)

◆ inverse() [1/2]

Mat3< Scalar > pmp::inverse ( const Mat3< Scalar > & m )

return the inverse of a 3x3 matrix

◆ inverse() [2/2]

Mat4< Scalar > pmp::inverse ( const Mat4< Scalar > & m )

return the inverse of a 4x4 matrix

◆ inverse_frustum_matrix()

Mat4< Scalar > pmp::inverse_frustum_matrix	(	Scalar	l,
		Scalar	r,
		Scalar	b,
		Scalar	t,
		Scalar	n,
		Scalar	f
	)

inverse of OpenGL frustum matrix with parameters left, right, bottom, top, near, far

See also: frustum_matrix

◆ inverse_perspective_matrix()

Mat4< Scalar > pmp::inverse_perspective_matrix	(	Scalar	fovy,
		Scalar	aspect,
		Scalar	zNear,
		Scalar	zFar
	)

inverse of perspective matrix

See also: perspective_matrix

◆ inverse_viewport_matrix()

Mat4< Scalar > pmp::inverse_viewport_matrix	(	Scalar	l,
		Scalar	b,
		Scalar	w,
		Scalar	h
	)

inverse of OpenGL viewport matrix with parameters left, bottom, width, height

See also: viewport_matrix

◆ linear_part()

Mat3< Scalar > pmp::linear_part ( const Mat4< Scalar > & m )

return upper 3x3 matrix from given 4x4 matrix, corresponding to the linear part of an affine transformation

◆ linear_transform()

Vector< Scalar, 3 > pmp::linear_transform	(	const Mat4< Scalar > &	m,
		const Vector< Scalar, 3 > &	v
	)

linear transformation of 3D vector v by a 4x4 matrix m: transform vector by upper-left 3x3 submatrix of m

◆ look_at_matrix()

Mat4< Scalar > pmp::look_at_matrix	(	const Vector< Scalar, 3 > &	eye,
		const Vector< Scalar, 3 > &	center,
		const Vector< Scalar, 3 > &	up
	)

OpenGL look-at camera matrix with parameters eye position, scene center, up-direction.

◆ max()

Matrix< Scalar, M, N > pmp::max	(	const Matrix< Scalar, M, N > &	m1,
		const Matrix< Scalar, M, N > &	m2
	)

inline

return component-wise maximum

◆ min()

Matrix< Scalar, M, N > pmp::min	(	const Matrix< Scalar, M, N > &	m1,
		const Matrix< Scalar, M, N > &	m2
	)

inline

return component-wise minimum

◆ norm()

Scalar pmp::norm ( const Matrix< Scalar, M, N > & m )

inline

compute the Frobenius norm of a matrix (or Euclidean norm of a vector)

◆ normalize()

Matrix< Scalar, M, N > pmp::normalize ( const Matrix< Scalar, M, N > & m )

inline

return a normalized copy of a matrix or a vector

◆ operator*() [1/3]

Matrix< Scalar, M, N > pmp::operator*	(	const Matrix< Scalar, M, K > &	m1,
		const Matrix< Scalar, K, N > &	m2
	)

matrix-matrix multiplication

◆ operator*() [2/3]

Matrix< Scalar, M, N > pmp::operator*	(	const Matrix< Scalar, M, N > &	m,
		const Scalar2	s
	)

inline

scalar multiplication of matrix: m*s

◆ operator*() [3/3]

Matrix< Scalar, M, N > pmp::operator*	(	const Scalar2	s,
		const Matrix< Scalar, M, N > &	m
	)

inline

scalar multiplication of matrix: s*m

◆ operator+()

Matrix< Scalar, M, N > pmp::operator+	(	const Matrix< Scalar, M, N > &	m1,
		const Matrix< Scalar, M, N > &	m2
	)

inline

matrix addition: m1 + m2

◆ operator-() [1/2]

Matrix< Scalar, M, N > pmp::operator- ( const Matrix< Scalar, M, N > & m )

inline

matrix negation: -m

◆ operator-() [2/2]

Matrix< Scalar, M, N > pmp::operator-	(	const Matrix< Scalar, M, N > &	m1,
		const Matrix< Scalar, M, N > &	m2
	)

inline

matrix subtraction: m1 - m2

◆ operator/()

Matrix< Scalar, M, N > pmp::operator/	(	const Matrix< Scalar, M, N > &	m,
		const Scalar2	s
	)

inline

divide matrix by scalar: m/s

◆ operator<<() [1/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		const Matrix< Scalar, M, N > &	m
	)

inline

output a matrix by printing its space-separated compontens

◆ operator<<() [2/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		const Vector< Scalar, N > &	vec
	)

inline

output a vector by printing its space-separated compontens

◆ operator<<() [3/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		Edge	e
	)

inline

output an Edge to a stream

◆ operator<<() [4/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		Face	f
	)

inline

output a Face to a stream

◆ operator<<() [5/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		Halfedge	h
	)

inline

output a Halfedge to a stream

◆ operator<<() [6/6]

std::ostream & pmp::operator<<	(	std::ostream &	os,
		Vertex	v
	)

inline

output a Vertex to a stream

◆ operator>>()

std::istream & pmp::operator>>	(	std::istream &	is,
		Vector< Scalar, N > &	vec
	)

inline

read the space-separated components of a vector from a stream

◆ ortho_matrix()

Mat4< Scalar > pmp::ortho_matrix	(	Scalar	left,
		Scalar	right,
		Scalar	bottom,
		Scalar	top,
		Scalar	zNear = `-1`,
		Scalar	zFar = `1`
	)

OpenGL orthogonal projection matrix with parameters left, right, bottom, top, near, far.

◆ perp()

Vector< Scalar, 2 > pmp::perp ( const Vector< Scalar, 2 > & v )

inline

compute perpendicular vector (rotate vector counter-clockwise by 90 degrees)

◆ perspective_matrix()

Mat4< Scalar > pmp::perspective_matrix	(	Scalar	fovy,
		Scalar	aspect,
		Scalar	zNear,
		Scalar	zFar
	)

OpenGL perspective matrix with parameters field of view in y-direction, aspect ratio, and distance of near and far planes.

◆ projective_transform()

Vector< Scalar, 3 > pmp::projective_transform	(	const Mat4< Scalar > &	m,
		const Vector< Scalar, 3 > &	v
	)

projective transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, divide by 4th component

◆ rotation_matrix() [1/2]

Mat4< Scalar > pmp::rotation_matrix	(	const Vector< Scalar, 3 > &	axis,
		Scalar	angle
	)

OpenGL matrix for rotation around given axis by given angle (in degrees)

◆ rotation_matrix() [2/2]

Mat4< Scalar > pmp::rotation_matrix ( const Vector< Scalar, 4 > & quat )

OpenGL matrix for rotation specified by unit quaternion.

◆ rotation_matrix_x()

Mat4< Scalar > pmp::rotation_matrix_x ( Scalar angle )

OpenGL matrix for rotation around x-axis by given angle (in degrees)

◆ rotation_matrix_y()

Mat4< Scalar > pmp::rotation_matrix_y ( Scalar angle )

OpenGL matrix for rotation around y-axis by given angle (in degrees)

◆ rotation_matrix_z()

Mat4< Scalar > pmp::rotation_matrix_z ( Scalar angle )

OpenGL matrix for rotation around z-axis by given angle (in degrees)

◆ scaling_matrix() [1/2]

Mat4< Scalar > pmp::scaling_matrix ( const Scalar s )

OpenGL matrix for scaling x/y/z by s.

◆ scaling_matrix() [2/2]

Mat4< Scalar > pmp::scaling_matrix ( const Vector< Scalar, 3 > & s )

OpenGL matrix for scaling x/y/z by the components of s.

◆ sqrnorm()

Scalar pmp::sqrnorm ( const Matrix< Scalar, M, N > & m )

inline

compute the squared Frobenius norm of a matrix (or squared Euclidean norm of a vector)

◆ symmetric_eigendecomposition()

bool pmp::symmetric_eigendecomposition	(	const Mat3< Scalar > &	m,
		Scalar &	eval1,
		Scalar &	eval2,
		Scalar &	eval3,
		Vector< Scalar, 3 > &	evec1,
		Vector< Scalar, 3 > &	evec2,
		Vector< Scalar, 3 > &	evec3
	)

compute eigenvector/eigenvalue decomposition of a 3x3 matrix

◆ translation_matrix()

Mat4< Scalar > pmp::translation_matrix ( const Vector< Scalar, 3 > & t )

OpenGL matrix for translation by vector t.

◆ transpose()

Matrix< Scalar, N, M > pmp::transpose ( const Matrix< Scalar, M, N > & m )

transpose MxN matrix to NxM matrix

◆ viewport_matrix()

Mat4< Scalar > pmp::viewport_matrix	(	Scalar	l,
		Scalar	b,
		Scalar	w,
		Scalar	h
	)

OpenGL viewport matrix with parameters left, bottom, width, height.

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ bvec2

◆ bvec3

◆ bvec4

◆ bvec8

◆ Color

◆ dmat2

◆ dmat3

◆ dmat4

◆ dvec2

◆ dvec3

◆ dvec4

◆ dvec8

◆ ivec2

◆ ivec3

◆ ivec4

◆ ivec8

◆ Mat2

◆ mat2

◆ Mat3

◆ mat3

◆ Mat4

◆ mat4

◆ Normal

◆ Point

◆ Scalar

◆ TexCoord

◆ uvec2

◆ uvec3

◆ uvec4

◆ uvec8

◆ vec2

◆ vec3

◆ vec4

◆ vec8

◆ Vector

Function Documentation

◆ affine_transform()

◆ cmult()

◆ cross()

◆ determinant()

◆ distance()

◆ dot()

◆ frustum_matrix()

◆ identity()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ inverse_frustum_matrix()

◆ inverse_perspective_matrix()

◆ inverse_viewport_matrix()

◆ linear_part()

◆ linear_transform()

◆ look_at_matrix()

◆ max()

◆ min()

◆ norm()

◆ normalize()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ operator<<() [1/6]

◆ operator<<() [2/6]

◆ operator<<() [3/6]

◆ operator<<() [4/6]

◆ operator<<() [5/6]

◆ operator<<() [6/6]

◆ operator>>()

◆ ortho_matrix()

◆ perp()

◆ perspective_matrix()

◆ projective_transform()

◆ rotation_matrix() [1/2]