Generic ND Transformations and their Generators. More...

#include <vsr_generic_op.h>

Static Public Member Functions
template<class A >
static auto	rot (const A &b) -> decltype(b+1)
	ND Rotor from Bivector b. More...

template<class A >
static auto	rotor (const A &b) -> decltype(b+1)
	ND Rotor from Bivector b. More...

template<class algebra >
static auto	log (const GARot< algebra > &r) -> GABiv< algebra >
	Get Bivector Generator from a Rotor (Conformal or Euclidean ) More...

template<class algebra >
static auto	log (const GABst< algebra > &r) -> GAPar< algebra >
	Get Pair Generator from a Conformal Boost. More...

template<class A >
static auto	pl (const GARot< A > &r) -> GABiv< A >
	Normalized plane of rotation from Rotor. More...

template<class A >
static auto	plane (const A &r) -> GABiv< A >
	Normalized plane of rotation from Rotor. More...

template<class A >
static VSR_PRECISION	iphi (const GARot< A > &r)
	Angle of Rotation from Rotor. More...

template<class A >
static auto	aa (const GARot< A > &r) -> GARot< A >
	Axis Angle from Rotor (WARNING NOT GENERIC) More...

template<class A >
static auto	axisAngle (const A &r) -> auto
	Axis Angle from Rotor (WARNING NOT GENERIC) More...

template<class A , class B >
static auto	trv (const Multivector< A, B > &a) -> auto
	Generate Local Boost at origin as exponential of a TangentVector vsr::GATnv<A> More...

template<class A >
static auto	transversor (const A &a) -> auto
	Generate Local Boost at origin as exponential of a Point Pair. More...

template<typename... T>
static auto	transversor (T...v) -> auto
	Generate nd transversor as exponential of a direction vector. More...

template<class A , class B >
static GATrs< A >	trs (const Multivector< A, B > &a)
	Generate translation from any type as exponential of a direction vector. More...

template<class A >
static auto	translator (const A &a) -> auto
	Generate translation as exponential of a direction vector. More...

template<typename... Ts>
static auto	trs (Ts...v) -> NTrs< sizeof...(Ts)+2 >
	Generate translation as exponential of a direction vector. More...

template<bits::type N, class T >
static constexpr auto	dil (T t) -> NDil< N >
	Generate translation as exponential of a direction vector. More...

template<class T >
static constexpr auto	dilator (T t) -> auto
	Generate a Dilation from Origin [[[ pass in ( log(t) * .5 ) ]]]. More...

template<class A , class T >
static auto	dil (const GAPnt< A > &p, T t) -> GATsd< A >
	Generate a Dilation from a point p by amt t. More...

template<class A , class T >
static constexpr auto	dilator (const A &p, T t) -> auto
	Generate a Dilation from a point p by amt t. More...

template<class A >
static auto	bst (const GAPar< A > &tp) -> decltype(tp+1)
	Generate Boost as exponential of a Point Pair Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011 e^B/2 = cosh(B/2) - sinh(B/2) More...

template<class A >
static auto	boost (const A &a) -> auto
	Generate Boost as exponential of a Point Pair Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011. More...

template<class A >
static auto	ratio (const GAVec< A > &a, const GAVec< A > &b) -> decltype((a *b))
	Generate general rotation as exponential of anonymous Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011. More...

Detailed Description

Generic ND Transformations and their Generators.

These can be used as-is, or put into a .cpp file for faster compilation (as is done, for example, in vsr_cga3D_op.cpp)

For instance, to create a quaternionic spin transformation nga::Gen::rotor will do the trick and be inlined, but if working in 3D conformal space cga::Gen::rotor will lead to faster compile times.

In keeping with the tendency throughout this library, functions can be written out in longform – e.g. Gen::translator – or Shorthand Syntax – e.g. Gen::trs

See also: vsr::cga::Gen for Operations documentation

Todo:: explain or fix multivector methods like .translate() that ONLY work in CGA

Member Function Documentation

template<class A >

static auto vsr::nga::Gen::aa ( const GARot< A > & r ) -> GARot<A>

inlinestatic

Axis Angle from Rotor (WARNING NOT GENERIC)

Parameters

r	vsr::cga::Rotor or vsr::ega::Rotor

template<class A >

static auto vsr::nga::Gen::axisAngle ( const A & r ) -> auto

static

Axis Angle from Rotor (WARNING NOT GENERIC)

Parameters

Rotor input

template<class A >

static auto vsr::nga::Gen::boost ( const A & a ) -> auto

static

Generate Boost as exponential of a Point Pair Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011.

Parameters

Point Pair generator

template<class A >

static auto vsr::nga::Gen::bst ( const GAPar< A > & tp ) -> decltype( tp + 1 )

inlinestatic

Generate Boost as exponential of a Point Pair Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011 e^B/2 = cosh(B/2) - sinh(B/2)

Parameters

Point Pair generator

template<bits::type N, class T >

static constexpr auto vsr::nga::Gen::dil ( T t ) -> NDil<N>

inlinestatic

Generate translation as exponential of a direction vector.

Parameters

a	tangent vector

Generate a Dilation from Origin

pass in ( log(t) * .5 )

Parameters

Amt t

template<class A , class T >

static auto vsr::nga::Gen::dil	(	const GAPnt< A > &	p,
		T	t
	)		-> GATsd<A>

inlinestatic

Generate a Dilation from a point p by amt t.

Parameters

Point	p (or Vec)
Amt	t – to pass in a relative amt (i.e. t=.5 for half size or t=2 for VSR_PRECISION), pass in std::log(t)

template<class T >

static constexpr auto vsr::nga::Gen::dilator ( T t ) -> auto

static

Generate a Dilation from Origin [[[ pass in ( log(t) * .5 ) ]]].

Parameters

Amt t

template<class A , class T >

static constexpr auto vsr::nga::Gen::dilator	(	const A &	p,
		T	t
	)		-> auto

static

Generate a Dilation from a point p by amt t.

Parameters

Point	p (or Vec)
Amt	t – to pass in a relative amt (i.e. t=.5 for half size or t=2 for VSR_PRECISION), pass in std::log(t)

template<class A >

static VSR_PRECISION vsr::nga::Gen::iphi ( const GARot< A > & r )

inlinestatic

Angle of Rotation from Rotor.

Parameters

r	vsr::cga::Rotor or vsr::ega::Rotor

template<class algebra >

static auto vsr::nga::Gen::log ( const GARot< algebra > & r ) -> GABiv<algebra>

inlinestatic

Get Bivector Generator from a Rotor (Conformal or Euclidean )

Template Parameters

algebra ega or cga, auto deduced by argument type

Parameters

r	vsr::cga::Rotor or vsr::ega::Rotor

Returns: vsr::cga::Bivector or vsr::ega::Bivector

template<class algebra >

static auto vsr::nga::Gen::log ( const GABst< algebra > & r ) -> GAPar<algebra>

inlinestatic

Get Pair Generator from a Conformal Boost.

Parameters

r	vsr::cga::Boost

Todo:: test generic dimensionality of this log

template<class A >

static auto vsr::nga::Gen::pl ( const GARot< A > & r ) -> GABiv<A>

inlinestatic

Normalized plane of rotation from Rotor.

Parameters

r	vsr::cga::Rotor or vsr::ega::Rotor

template<class A >

static auto vsr::nga::Gen::plane ( const A & r ) -> GABiv<A>

inlinestatic

Normalized plane of rotation from Rotor.

Parameters

r	vsr::cga::Rotor or vsr::ega::Rotor

template<class A >

static auto vsr::nga::Gen::ratio	(	const GAVec< A > &	a,
		const GAVec< A > &	b
	)		-> decltype( (a*b) )

inlinestatic

Generate general rotation as exponential of anonymous Implemented from "Square Root and Logarithm of Rotors. . ." by Dorst and Valkenburg, 2011.

Parameters

Point Pair generator

Rotor Ratio of two Conformal vectors transforming a to b see dorst and valkenburg, basically this normalizes 1+R to give sqrt(ba)

template<class A >

static auto vsr::nga::Gen::rot ( const A & b ) -> decltype( b + 1 )

inlinestatic

ND Rotor from Bivector b.

Parameters

b	vsr::cga::Bivector or vsr::ega::Bivector

template<class A >

static auto vsr::nga::Gen::rotor ( const A & b ) -> decltype( b + 1 )

inlinestatic

ND Rotor from Bivector b.

Parameters

b Bivector

template<class A >

static auto vsr::nga::Gen::translator ( const A & a ) -> auto

static

Generate translation as exponential of a direction vector.

Parameters

a	a direction vector

template<class A >

static auto vsr::nga::Gen::transversor ( const A & a ) -> auto

static

Generate Local Boost at origin as exponential of a Point Pair.

Parameters

a	tangent vector

template<typename... T>

static auto vsr::nga::Gen::transversor ( T... v ) -> auto

static

Generate nd transversor as exponential of a direction vector.

Parameters

n	number of coordinates

template<class A , class B >

static GATrs<A> vsr::nga::Gen::trs ( const Multivector< A, B > & a )

inlinestatic

Generate translation from any type as exponential of a direction vector.

Parameters

any	multivector (will be copied, not cast, to direction vector)

template<typename... Ts>

static auto vsr::nga::Gen::trs ( Ts... v ) -> NTrs<sizeof...(Ts)+2>

inlinestatic

Generate translation as exponential of a direction vector.

Parameters

some	floats etc

template<class A , class B >

static auto vsr::nga::Gen::trv ( const Multivector< A, B > & a ) -> auto

static

Generate Local Boost at origin as exponential of a TangentVector vsr::GATnv<A>

Parameters

a	tangent vector in ND cga

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

/Users/wolftype/code/versor/vsr/detail/vsr_generic_op.h

Static Public Member Functions

Detailed Description

Member Function Documentation