dimension independent implementation of quadric error metrics More...

#include <qem.h>

Inheritance diagram for cgv::math::qem< T >:

Public Member Functions
	qem (int d=-1)
	standard constructor initializes qem based on dimension

	qem (const vec< T > &p, const vec< T > &n)
	construct from point and normal

	qem (const vec< T > &n, T d)
	construct from normal and distance to origin

void	set (const vec< T > &n, T d)
	set from normal and distance to origin

unsigned	dim () const
	number of elements

qem< T > &	operator= (const qem< T > &v)
	assignment of a vector v

const T &	scalar_part () const
	return the scalar part of the qem

vec< T >	vector_part () const
	return the vector part of the qem

mat< T >	matrix_part () const
	return matrix part

T	evaluate (const vec< T > &p) const
	evaluate the quadric error metric at given location

vec< T >	minarg (const vec< T > &p_ref, T relative_epsilon, T max_distance=-1, T epsilon=1e-10) const
	compute point that minimizes distance to qem and is inside the sphere of radius max_distance around p_ref.

template<typename S >
qem< T > &	operator+= (const qem< S > &v)
	in place qem addition

template<typename S >
qem< T > &	operator-= (const qem< S > &v)
	in place qem subtraction

template<typename S >
const qem< T >	operator+ (const qem< S > &v) const
	qem addition

template<typename S >
qem< T >	operator- (const qem< S > &v) const
	qem subtraction

qem< T >	operator- (void) const
	negates the qem

qem< T >	operator* (const T &s) const
	multiplication with scalar s

qem< T >	operator/ (const T &s) const
	divides vector by scalar s

void	resize (unsigned d)
	resize the vector

template<typename S >
bool	operator== (const qem< S > &v) const
	test for equality

template<typename S >
bool	operator!= (const qem< S > &v) const
	test for inequality

Public Member Functions inherited from cgv::math::vec< T >
iterator	begin ()

iterator	end ()

const_iterator	begin () const

const_iterator	end () const

reverse_iterator	rbegin ()

reverse_iterator	rend ()

const_reverse_iterator	rbegin () const

const_reverse_iterator	rend () const

unsigned	size () const
	number of elements

unsigned	dim () const
	number of elements

	vec ()
	standard constructor

	vec (unsigned dim, const T &value=T(0))
	creates a vector with dim elements

	vec (unsigned dim, const T *marray)
	creates a vector with dim elements from an array

	vec (const vec< T > &v)
	copy constructor for vectors with equal element type

template<typename S >
	vec (const vec< S > &v)
	copy constructor for vectors with different element type

	vec (const T &c0, const T &c1)
	creates a 2d vector (c0,c1)^T

	vec (const T &c0, const T &c1, const T &c2)
	creates a 3d vector (c0,c1,c2)^T

	vec (const T &c0, const T &c1, const T &c2, const T &c3)
	creates a 4d vector (c0,c1,c2,c3)^T

void	set (const T &c0, const T &c1)
	set entries of a 2d vector

void	set (const T &c0, const T &c1, const T &c2)
	set entries of a 3d vector

void	set (const T &c0, const T &c1, const T &c2, const T &c3)
	set entries of a 4d vector

void	set_extern_data (unsigned dim, T *data)
	set data pointer to an external data array

virtual	~vec ()
	destructor

void	destruct ()

T *	data ()
	cast into non const array

const T *	data () const
	cast into const array

vec< T > &	operator= (const vec< T > &v)
	assignment of a vector v

vec< T > &	operator= (const T &s)
	assignment of a scalar s

template<typename S >
vec< T > &	operator= (const vec< S > &v)
	assignment of a vector v

T &	operator() (unsigned i)
	element accessor

const T &	operator() (unsigned i) const
	const element accessor

T &	operator[] (unsigned i)
	element accessor

const T &	operator[] (unsigned i) const
	const element accessor

T &	first ()
	element accessor for the first element

const T &	first () const
	const element accessor for the first element

T &	last ()
	element accessor for the flast element

const T &	last () const
	const element accessor for the last element

T &	x ()
	element accessor for the first element

const T &	x () const
	const element accessor for the first element

T &	y ()
	element accessor for the second element

const T &	y () const
	const element accessor for the second element

T &	z ()
	element accessor for the third element

const T &	z () const
	const element accessor for the third element

T &	w ()
	element accessor for the fourth element

const T &	w () const
	const element accessor for the fourth element

vec< T > &	operator+= (const T &s)
	in place addition of a scalar s

vec< T > &	operator-= (const T &s)
	in place subtraction by scalar s

vec< T > &	operator*= (const T &s)
	in place multiplication with s

vec< T > &	operator/= (const T &s)
	in place division by scalar s

template<typename S >
vec< T > &	operator+= (const vec< S > &v)
	in place vector addition

template<typename S >
vec< T > &	operator-= (const vec< S > &v)
	in place vector subtraction

template<typename S >
vec< T > &	operator*= (const vec< S > &v)
	in place componentwise vector multiplication

template<typename S >
vec< T > &	operator/= (const vec< S > &v)
	in place componentwise vector division

template<typename S >
const vec< T >	operator+ (const vec< S > &v) const
	vector addition

const vec< T >	operator+ (const T &s) const
	componentwise addition of scalar

const vec< T >	operator- (const T &s) const
	componentwise subtraction of scalar

template<typename S >
vec< T >	operator- (const vec< S > &v) const
	vector subtraction

template<typename S >
const vec< T >	operator* (const vec< S > &v) const
	componentwise vector multiplication

template<typename S >
const vec< T >	operator/ (const vec< S > &v) const
	componentwise vector division

vec< T >	operator- (void) const
	negates the vector

vec< T >	operator* (const T &s) const
	multiplication with scalar s

vec< T >	operator/ (const T &s) const
	divides vector by scalar s

void	fill (const T &v)
	fill elements of vector with scalar v

void	zeros ()
	fill the vector with zeros

void	ones ()
	fill the vector with ones

void	zeros (unsigned n)
	resize the vector to size n and fills the vector with zeros

void	ones (unsigned n)
	resize the vector to size n and fills thevector with ones

void	resize (unsigned dim)
	resize the vector

template<typename S >
bool	operator== (const vec< S > &v) const
	test for equality

template<typename S >
bool	operator!= (const vec< S > &v) const
	test for inequality

T	length () const
	length of the vector L2-Norm

void	abs ()
	componentwise absolute values

void	ceil ()
	ceil componentwise

void	floor ()
	floor componentwise

void	round ()
	round componentwise

T	sqr_length () const
	square length of vector

void	normalize ()
	normalize the vector using the L2-Norm

void	safe_normalize ()
	normalize the vector if length is not zero using the L2-Norm

vec< T >	sub_vec (unsigned ifrom, unsigned size) const
	extracts sub vector beginning at index ifrom with given size

void	copy (unsigned ifrom, unsigned s, vec< T > &subvec) const
	copy sub vector beginning at index ifrom with given size s into subvec

void	paste (unsigned ifrom, const vec< T > &v)
	paste v into vector beginning at index pos ifrom

Static Public Member Functions
static bool	inside (const vec< T > &p, const vec< T > &minp, const vec< T > &maxp)

Additional Inherited Members
Public Types inherited from cgv::math::vec< T >
typedef T	value_type

typedef T &	reference

typedef const T &	const_reference

typedef std::size_t	size_type

typedef std::ptrdiff_t	difference_type

typedef T *	pointer

typedef const T *	const_pointer

typedef T *	iterator

typedef const T *	const_iterator

typedef std::reverse_iterator< iterator >	reverse_iterator

typedef std::reverse_iterator< const_iterator >	const_reverse_iterator

Protected Attributes inherited from cgv::math::vec< T >
T *	_data
	pointer to _data storage

unsigned	_size
	number or elements

bool	data_is_external
	store whether data is not owned by vector

Detailed Description

template<typename T>
class cgv::math::qem< T >

dimension independent implementation of quadric error metrics

Definition at line 13 of file qem.h.

Constructor & Destructor Documentation

◆ qem() [1/3]

template<typename T >

cgv::math::qem< T >::qem ( int d = -1 )

inline

standard constructor initializes qem based on dimension

Definition at line 17 of file qem.h.

References cgv::math::vec< T >::zeros().

◆ qem() [2/3]

template<typename T >

cgv::math::qem< T >::qem	(	const vec< T > &	p,
		const vec< T > &	n
	)

inline

construct from point and normal

Definition at line 23 of file qem.h.

References cgv::math::qem< T >::set().

◆ qem() [3/3]

template<typename T >

cgv::math::qem< T >::qem	(	const vec< T > &	n,
		T	d
	)

inline

construct from normal and distance to origin

Definition at line 28 of file qem.h.

References cgv::math::qem< T >::set().

Member Function Documentation

◆ dim()

template<typename T >

unsigned cgv::math::qem< T >::dim ( ) const

inline

number of elements

Definition at line 44 of file qem.h.

References cgv::math::vec< T >::size().

Referenced by cgv::math::qem< T >::matrix_part(), cgv::math::qem< T >::minarg(), and cgv::math::qem< T >::vector_part().

◆ evaluate()

template<typename T >

T cgv::math::qem< T >::evaluate ( const vec< T > & p ) const

inline

evaluate the quadric error metric at given location

Definition at line 79 of file qem.h.

References cgv::math::qem< T >::matrix_part(), cgv::math::qem< T >::scalar_part(), and cgv::math::qem< T >::vector_part().

◆ inside()

template<typename T >

static bool cgv::math::qem< T >::inside	(	const vec< T > &	p,
		const vec< T > &	minp,
		const vec< T > &	maxp
	)

inlinestatic

Definition at line 83 of file qem.h.

◆ matrix_part()

template<typename T >

mat< T > cgv::math::qem< T >::matrix_part ( ) const

inline

return matrix part

Definition at line 68 of file qem.h.

References cgv::math::qem< T >::dim().

Referenced by cgv::math::qem< T >::evaluate(), and cgv::math::qem< T >::minarg().

◆ minarg()

template<typename T >

vec< T > cgv::math::qem< T >::minarg	(	const vec< T > &	p_ref,
		T	relative_epsilon,
		T	max_distance = `-1`,
		T	epsilon = `1e-10`
	)		const

inline

compute point that minimizes distance to qem and is inside the sphere of radius max_distance around p_ref.

If max_distance is -1, no sphere inclusion test is performed. relative_epsilon gives the absolute value of the fraction betweenan eigenvalue and the largest eigenvalue before it is set to zero. epsilon is a global limit on the absolute value of a singular value before accepted as non zero.

Definition at line 98 of file qem.h.

References cgv::math::qem< T >::dim(), cgv::math::qem< T >::matrix_part(), cgv::math::vec< T >::size(), cgv::math::vec< T >::sqr_length(), cgv::math::mat< T >::transpose(), cgv::math::qem< T >::vector_part(), and cgv::math::vec< T >::y().

Referenced by cgv::media::mesh::dual_contouring< X, T >::compute_cell_vertex().

◆ operator!=()

template<typename T >

template<typename S >

bool cgv::math::qem< T >::operator!= ( const qem< S > & v ) const

inline

test for inequality

Definition at line 196 of file qem.h.

References cgv::math::vec< T >::size().

◆ operator*()

template<typename T >

qem< T > cgv::math::qem< T >::operator* ( const T & s ) const

inline

multiplication with scalar s

Definition at line 165 of file qem.h.

◆ operator+()

template<typename T >

template<typename S >

const qem< T > cgv::math::qem< T >::operator+ ( const qem< S > & v ) const

inline

qem addition

Definition at line 144 of file qem.h.

◆ operator+=()

template<typename T >

template<typename S >

qem< T > & cgv::math::qem< T >::operator+= ( const qem< S > & v )

inline

in place qem addition

Definition at line 128 of file qem.h.

References cgv::math::vec< T >::size().

◆ operator-() [1/2]

template<typename T >

template<typename S >

qem< T > cgv::math::qem< T >::operator- ( const qem< S > & v ) const

inline

qem subtraction

Definition at line 151 of file qem.h.

◆ operator-() [2/2]

template<typename T >

qem< T > cgv::math::qem< T >::operator- ( void ) const

inline

negates the qem

Definition at line 157 of file qem.h.

◆ operator-=()

template<typename T >

template<typename S >

qem< T > & cgv::math::qem< T >::operator-= ( const qem< S > & v )

inline

in place qem subtraction

Definition at line 136 of file qem.h.

References cgv::math::vec< T >::size().

◆ operator/()

template<typename T >

qem< T > cgv::math::qem< T >::operator/ ( const T & s ) const

inline

divides vector by scalar s

Definition at line 172 of file qem.h.

◆ operator=()

template<typename T >

qem< T > & cgv::math::qem< T >::operator= ( const qem< T > & v )

inline

assignment of a vector v

Definition at line 49 of file qem.h.

◆ operator==()

template<typename T >

template<typename S >

bool cgv::math::qem< T >::operator== ( const qem< S > & v ) const

inline

test for equality

Definition at line 187 of file qem.h.

References cgv::math::vec< T >::size().

◆ resize()

template<typename T >

void cgv::math::qem< T >::resize ( unsigned d )

inline

resize the vector

Definition at line 180 of file qem.h.

References cgv::math::vec< T >::resize().

◆ scalar_part()

template<typename T >

const T & cgv::math::qem< T >::scalar_part ( ) const

inline

return the scalar part of the qem

Definition at line 55 of file qem.h.

References cgv::math::vec< T >::first().

Referenced by cgv::math::qem< T >::evaluate().

◆ set()

template<typename T >

void cgv::math::qem< T >::set	(	const vec< T > &	n,
		T	d
	)

inline

set from normal and distance to origin

Definition at line 33 of file qem.h.

References cgv::math::vec< T >::first(), and cgv::math::vec< T >::size().

Referenced by cgv::math::qem< T >::qem(), and cgv::math::qem< T >::qem().

◆ vector_part()

template<typename T >

vec< T > cgv::math::qem< T >::vector_part ( ) const

inline

return the vector part of the qem

Definition at line 60 of file qem.h.

References cgv::math::qem< T >::dim(), and cgv::math::vec< T >::size().

Referenced by cgv::math::qem< T >::evaluate(), and cgv::math::qem< T >::minarg().

The documentation for this class was generated from the following file:

cgv/math/qem.h

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ qem() [1/3]

◆ qem() [2/3]

◆ qem() [3/3]

Member Function Documentation

◆ dim()

◆ evaluate()

◆ inside()

◆ matrix_part()

◆ minarg()

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator=()

◆ operator==()

◆ resize()

◆ scalar_part()

◆ set()

◆ vector_part()