vsr::cga::Gen Struct Reference

Generators and Logarithms Optimized for 3D Conformal Geometric Algebra. More...

#include <vsr_cga3D_op.h>

Static Public Member Functions
static Rot	rot (const Biv &b)
	vsr::cga::Rotor from vsr::cga::Bivector
static Rot	rotor (const Biv &b)
	vsr::cga::Rotor from vsr::cga::Bivector
static Bst	bst (const Pair &p)
	vsr::cga::Boost from vsr::cga::Pair
static Bst	boost (const Pair &p)
	vsr::cga::Boost from vsr::cga::Pair
static Tsd	dil (const Pnt &p, VSR_PRECISION t)
	vsr::cga::Dilator from vsr::cga::Point and amt t
static Tsd	dilator (const Pnt &p, VSR_PRECISION t)
	vsr::cga::Dilator from vsr::cga::Point and amt t
template<class A >
static Trs	trs (const A &a)
	vsr::cga::Translator from any type
template<class A >
static Trs	translator (const A &a)
	vsr::cga::Translator from any type
template<class A >
static Trv	trv (const A &a)
	vsr::cga::Transversor from any type
template<class A >
static Trv	transversor (const A &a)
	vsr::cga::Transversor from any type
static Rot	ratio (const Vec &v, const Vec &v2)
	vsr::cga::Rotor that takes one vec to another
static Biv	log (const Rot &r)
	vsr::cga::Bivector log of vsr::cga::Rotor
static Rot	rot (double theta, double phi)
	Generate a vsr::cga::Rotor from spherical coordinates. More...
static Rot	rot (double yaw, double pitch, double roll)
	Generate a vsr::cga::Rotor from Euler angles. More...
static Mot	mot (const Dll &dll)
	Generate a vsr::cga::Motor from a vsr::cga::DualLine Axis. More...
static Mot	motor (const Dll &dll)
	Generate a vsr::cga::Motor from a vsr::cga::DualLine Axis. More...
static Dll	log (const Mot &m)
	DualLine generator from a Motor. More...
static Dll	log (const Dll &a, const Dll &b, VSR_PRECISION t=1.0)
	DualLine generator of Motor That Twists DualLine a to DualLine b by amt t;. More...
static Mot	ratio (const vsr::cga::Dll &a, const vsr::cga::Dll &b, VSR_PRECISION t=1.0)
	Generate Motor that twists Dual Line a to Dual Line b;. More...
static Mot	ratio (const vsr::cga::Mot &a, const vsr::cga::Mot &b, VSR_PRECISION t)
	Generate Motor that twists Motor a to Motor b;. More...
template<class A , class T >
static Bst	bst (const A &tnv, const Vec &vec, T t)
	Generate a Translated Transversion. More...
static Bst	ratio (const DualSphere &a, const DualSphere &b, bool bFlip=true)
	Generate Simple Boost rotor from ratio of two dual spheres calculates SQUARE ROOT (normalizes 1+R)
static Pair	atanh2 (const Pair &p, VSR_PRECISION cs, bool bCW)
	atanh2 function for logarithm of general rotors, with clockwise boolean
static Pair	log (const Bst &b, bool bCW=false)
	Log of a simple rotor (uses atanh2)
static Con	ratio (const Circle &a, const Circle &b, bool bFlip=false, float theta=0)
	Generate Conformal Transformation from circle a to circle b uses square root method of Dorst et Valkenburg, 2011.
static Con	ratio (const Pair &a, const Pair &b, bool bFlip=false, float theta=0)
	Generate Conformal Transformation from pair a to pair b uses square root method of Dorst et Valkenburg, 2011.
static vector< Pair >	split (const Pair &par)
	Bivector Split Takes a general bivector and splits it into commuting pairs will give sinh(B+-)
static vector< Pair >	split (const Con &con)
	Bivector Split Takes a general ROTOR and splits it into commuting pairs will give sinh(B+-)
static vector< Pair >	log (const Con &rot)
	Split Log of General Conformal Rotor.
static vector< Pair >	log (const Circle &ca, const Circle &cb, bool bFlip=false, VSR_PRECISION theta=0)
	Split Log from a ratio of two Circles.
static vector< Pair >	log (const Pair &ca, const Pair &cb, bool bFlip=false, VSR_PRECISION theta=0)
	Split Log from a ratio of two Circles.
static Con	con (const vector< Pair > &log, VSR_PRECISION amt)
	General Conformal Transformation from a split log.
static Con	con (const vector< Pair > &log, VSR_PRECISION amtA, VSR_PRECISION amtB)
	General Conformal Transformation from a split log and two amts (one for each)
static Con	con (const Circle &ca, const Circle &cb, VSR_PRECISION amt)
static Con	con (const Circle &ca, const Circle &cb, VSR_PRECISION amtA, VSR_PRECISION amtB)
static Rotor	xf (const Biv &b)
	generates a Euclidean rotor transformation from a Euclidean vsr::cga::Bivector;
static Motor	xf (const DualLine &dll)
	generates a vsr::cga::Motor transformation from a vsr::cga::DualLine
static Dilator	xf (const FlatPoint &flp)
	generates a vsr::cga::Dilator transformation from a vsr::cga::FlatPoint
static Bst	xf (const Pair &p)
	generates a boost transformation from a point pair

Detailed Description

Generators and Logarithms Optimized for 3D Conformal Geometric Algebra.

See also

vsr::nga::Gen for Generic implementation details

Member Function Documentation

template<class A , class T >

static Bst vsr::cga::Gen::bst ( const A &  tnv, const Vec &  vec, T  t  )

inlinestatic

Generate a Translated Transversion.

Parameters

tnv	TangentVector
vec	Vector position in space
t	scalar amt (typically 0 or 1)

static Dll vsr::cga::Gen::log ( const Mot &  m )

static

DualLine generator from a Motor.

Parameters

m	a vsr::cga::Motor (a concatenation of rotation and translation)

static Dll vsr::cga::Gen::log ( const Dll &  a, const Dll &  b, VSR_PRECISION  t = 1.0  )

static

DualLine generator of Motor That Twists DualLine a to DualLine b by amt t;.

Parameters

a	DualLine source
b	DualLine target
t	amt to transform in range [0,1]

Returns

vsr::cga::Motor

static Mot vsr::cga::Gen::mot ( const Dll &  dll )

static

Generate a vsr::cga::Motor from a vsr::cga::DualLine Axis.

Parameters

dll	a vsr::cga::DualLine generator axis of rotation

static Mot vsr::cga::Gen::motor ( const Dll &  dll )

static

Generate a vsr::cga::Motor from a vsr::cga::DualLine Axis.

Parameters

dll	a vsr::cga::DualLine generator axis of rotation

static Mot vsr::cga::Gen::ratio ( const vsr::cga::Dll &  a, const vsr::cga::Dll &  b, VSR_PRECISION  t = 1.0  )

static

Generate Motor that twists Dual Line a to Dual Line b;.

Parameters

a	DualLine source
b	DualLine target
t	amt to transform in range [0,1]

Returns

vsr::cga::Motor;

static Mot vsr::cga::Gen::ratio ( const vsr::cga::Mot &  a, const vsr::cga::Mot &  b, VSR_PRECISION  t  )

static

Generate Motor that twists Motor a to Motor b;.

Parameters

a	vsr::cga::Motor source
b	vsr::cga::Motor target
t	amt to transform in range [0,1]

Returns

vsr::cga::Motor

static Rot vsr::cga::Gen::rot ( double  theta, double  phi  )

static

Generate a vsr::cga::Rotor from spherical coordinates.

Parameters

theta	in xz plane from (1,0,0) in range [0,PI]
phi	in rotated xy plane in range [-PIOVERTWO, PIOVERTWO]

static Rot vsr::cga::Gen::rot ( double  yaw, double  pitch, double  roll  )

static

Generate a vsr::cga::Rotor from Euler angles.

Parameters

yaw	in xz plane
pitch	in (transformed) yz plane
roll	in (transformed) xy plane

---

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

• /Users/wolftype/code/versor/vsr/space/vsr_cga3D_op.h