Generic Geometric Number Types (templated on an algebra and a basis ) More...

#include <vsr_multivector.h>

Public Types
using	algebra = algebra_type
	algebra (a metric and field)

using	basis = basis_type
	basis is an algebraic data type created with compile-time list processing

using	value_t = typename algebra::value_t
	the field over which the algebra is defined (e.g. float or double)

using	space = typename algebra::types
	<>::::<>

template<class B >
using	MultivectorB = Multivector< algebra, B >
	another Type within same algebra

using	Dual = typename algebra::template make_gp< typename blade< algebra::dim, algebra::dim >::type, basis >
	the Dual Type (product of this and algebra::types::pseudoscalar)

using	DualE = typename algebra::template make_gp< Basis< bits::pss(algebra::dim-2)>, basis >
	the Euclidan subspace Dual Type (product of this and algebra::types::euclidean_pseudoscalar)

typedef const value_t	array_type[Num]
	Data Array Type

Public Member Functions
array_type &	begin () const
	Pointer to first data.

constexpr value_t	operator[] (int idx) const
	Get value at idx

value_t &	operator[] (int idx)
	Set value at idx

template<typename... Args>
constexpr	Multivector (Args...v)
	Construct from list of args (cannot be longer than Num)

template<typename B >
constexpr	Multivector (const Multivector< algebra, B > &b)
	Construct from different Basis within same Algebra.

template<class alg , typename B >
constexpr	Multivector (const Multivector< alg, B > &b)
	Construct from different algebra signature and different basis.

template<bits::type IDX>
value_t	get () const
	Immutable get value of blade type IDX (. More...

template<bits::type IDX>
value_t &	get ()
	Mutable get value of blade type IDX.

template<bits::type IDX>
Multivector &	set (value_t v)
	Set value of blade type IDX

Multivector &	reset (value_t v=value_t())
	Reset.

Multivector	conjugation () const
	Conjugation Unary Operation.

Multivector	conj () const
	Conjugation Unary Operation Shorthand.

Multivector	involution () const
	Involution Unary Operation.

Multivector	inv () const
	Involution Unary Operation Shorthand.

template<class B >
B	cast () const
	Casting to type B.

template<class B >
B	copy () const
	Copying to type B.

bool	operator== (const Multivector &mv) const
	Comparison. More...

void	print ()
	Printing.

template<class B >
auto	operator* (const MultivectorB< B > &b) const -> decltype(algebra::gp(*this, b))
	Geometric Product \(a*b\)

template<class B >
Multivector &	operator*= (const MultivectorB< B > &b)
	Geometric Product in place Transformation.

template<class B >
auto	operator^ (const MultivectorB< B > &b) const -> decltype(algebra::op(*this, b))
	Outer Product \(a \wedge b\)

template<class B >
auto	operator<= (const MultivectorB< B > &b) const -> decltype(algebra::ip(*this, b))
	Inner Product \(a \cdot b \) Uses Hestenes Inner Contraction (a must be of lower grade than b)

template<class B >
auto	operator% (const MultivectorB< B > &b) const -> decltype(algebra::gp(*this, b))
	Commutator Product \(a \times b\)

template<typename B >
Multivector	spin (const MultivectorB< B > &b) const
	Rotor (even) transformation \(RA\tilde{R}\)

template<typename B >
Multivector	reflect (const MultivectorB< B > &b) const
	Versor (Odd) Transformation \(R\hat{A}\tilde{R}\)

template<typename B >
Multivector	sp (const MultivectorB< B > &b) const

template<typename B >
Multivector	re (const MultivectorB< B > &b) const

Multivector	operator~ () const
	Reversion \(\tilde{A}\)

Multivector	operator! () const
	Inversion \(\tilde{A}/A\tilde{A}\)

template<class B >
auto	operator/ (const MultivectorB< B > &b) const -> auto

Multivector< algebra, typename algebra::vector_basis >	null () const
	Conformal Mapping \(\boldsymbol(x)\to n_o + \boldsymbol{x} + \boldsymbol{x}^2n_\infty \)

template<class B >
Multivector	trs (const MultivectorB< B > &b) const

template<class B >
Multivector	translate (const MultivectorB< B > &b) const

template<class... Ts>
Multivector	trs (Ts...v) const

template<class... Ts>
Multivector	translate (Ts...v) const

template<class B >
Multivector	trv (const MultivectorB< B > &b) const

template<class B >
Multivector	transverse (const MultivectorB< B > &b) const

template<class... Ts>
Multivector	trv (Ts...v) const

template<class... Ts>
Multivector	transverse (Ts...v) const

template<class B >
Multivector	mot (const MultivectorB< B > &b) const

template<class B >
Multivector	motor (const MultivectorB< B > &b) const

template<class B >
Multivector	twist (const MultivectorB< B > &b) const

template<class B >
Multivector	bst (const MultivectorB< B > &b) const

template<class B >
Multivector	boost (const MultivectorB< B > &b) const

template<class B >
Multivector	dil (const MultivectorB< B > &b, VSR_PRECISION t) const

template<class B >
Multivector	dilate (const MultivectorB< B > &b, VSR_PRECISION t) const

auto	dual () const -> Dual

auto	undual () const -> Dual

auto	duale () const -> DualE

auto	unduale () const -> DualE

value_t	wt () const

value_t	rwt () const

value_t	norm () const

value_t	rnorm () const

Multivector	unit () const

Multivector	runit () const

Multivector	tunit () const

template<class B >
auto	operator+ (const MultivectorB< B > &b) -> decltype(algebra::sum(*this, b))

Multivector	operator+ (const Multivector &a) const

Multivector	operator- (const Multivector &a) const

Multivector	operator- () const

Multivector &	operator-= (const Multivector &b)

Multivector &	operator+= (const Multivector &b)

Multivector	operator/ (VSR_PRECISION f) const

Multivector &	operator/= (VSR_PRECISION f)

Multivector	operator* (VSR_PRECISION f) const

Multivector &	*operator=** (VSR_PRECISION f)

auto	operator+ (VSR_PRECISION a) const -> decltype(algebra::sumv(a,*this))

template<class A >
Multivector< Algebra, B >	rot (const Multivector< Algebra, A > &t) const

template<class A >
Multivector< Algebra, B >	rotate (const Multivector< Algebra, A > &t) const

template<class A>
Multivector< Algebra, B >	trs (const Multivector< Algebra, A > &t) const

template<class A>
Multivector< Algebra, B >	translate (const Multivector< Algebra, A > &t) const

template<class... Ts>
Multivector< Algebra, B >	trs (Ts...v) const

template<class... Ts>
Multivector< Algebra, B >	translate (Ts...v) const

template<class A>
Multivector< Algebra, B >	trv (const Multivector< Algebra, A > &t) const

template<class A>
Multivector< Algebra, B >	transverse (const Multivector< Algebra, A > &t) const

template<class... Ts>
Multivector< Algebra, B >	trv (Ts...v) const

template<class... Ts>
Multivector< Algebra, B >	transverse (Ts...v) const

template<class A >
Multivector< Algebra, B >	dil (const Multivector< Algebra, A > &s, VSR_PRECISION t) const

template<class A >
Multivector< Algebra, B >	dilate (const Multivector< Algebra, A > &s, VSR_PRECISION t) const

template<class A >
Multivector< Algebra, B >	bst (const Multivector< Algebra, A > &t) const

template<class A >
Multivector< Algebra, B >	boost (const Multivector< Algebra, A > &t) const

template<class A >
A	cast () const

template<class A >
A	copy () const

template<bits::type IDX>
Algebra::value_t &	get ()

template<bits::type IDX>
Algebra::value_t	get () const

template<bits::type IDX>
Multivector< Algebra, B > &	set (typename Algebra::value_t v)

template<class A >
Multivector< Algebra, B >	mot (const Multivector< Algebra, A > &t) const

template<class A >
Multivector< Algebra, B >	motor (const Multivector< Algebra, A > &t) const

template<class A >
Multivector< Algebra, B >	twist (const Multivector< Algebra, A > &t) const


template<class B >
Multivector	rot (const MultivectorB< B > &b) const

template<class B >
Multivector	rotate (const MultivectorB< B > &b) const

Public Attributes
value_t	val [Num]
	Data Array

Static Public Attributes
static const int	Num = basis::Num
	number of bases

static Multivector	x = Multivector<Algebra,B>().template set<1>(1)

static Multivector	y = Multivector<Algebra,B>().template set<2>(1)

static Multivector	z = Multivector<Algebra,B>().template set<4>(1)

static Multivector	xy = Multivector<Algebra,B>().template set<3>(1)

static Multivector	xz = Multivector<Algebra,B>().template set<5>(1)

static Multivector	yz = Multivector<Algebra,B>().template set<6>(1)

Friends
ostream &	operator<< (ostream &os, const Multivector &m)

Detailed Description

template<typename algebra_type, typename basis_type>
struct vsr::Multivector< algebra_type, basis_type >

Generic Geometric Number Types (templated on an algebra and a basis )

Multivector is the main value-storing class. All Geometric Algebra Types are template instantiations of this class.

The types of values contained here (float, double, etc) are deterimined by the algebra. The way in which the data is combined with other methods is determined by their respective basis, in coordination with the algebra.

Member Function Documentation

template<typename algebra_type, typename basis_type>

template<bits::type IDX>

value_t vsr::Multivector< algebra_type, basis_type >::get ( ) const

Immutable get value of blade type IDX (.

Todo:: make blades user-defined literals?)

template<typename algebra_type, typename basis_type>

bool vsr::Multivector< algebra_type, basis_type >::operator== ( const Multivector< algebra_type, basis_type > & mv ) const

inline

Comparison.

Todo:: use dot product, see Group

template<typename algebra_type, typename basis_type>

template<class B >

Multivector vsr::Multivector< algebra_type, basis_type >::rot ( const MultivectorB< B > & b ) const

rotate in b plane

template<typename algebra_type, typename basis_type>

template<class B >

Multivector vsr::Multivector< algebra_type, basis_type >::rotate ( const MultivectorB< B > & b ) const

rotate in b plane

The documentation for this struct was generated from the following files:

/Users/wolftype/code/versor/vsr/detail/vsr_algebra.h
/Users/wolftype/code/versor/vsr/detail/vsr_multivector.h
/Users/wolftype/code/versor/vsr/detail/vsr_generic_op.h
/Users/wolftype/code/versor/vsr/space/vsr_cga3D_op.h

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

template<typename algebra_type, typename basis_type> struct vsr::Multivector< algebra_type, basis_type >

Member Function Documentation

template<typename algebra_type, typename basis_type>
struct vsr::Multivector< algebra_type, basis_type >