Multivector Types

3D CGA Instantiations of the Multivector Template class More...

Typedefs
typedef Sca	vsr::cga::Scalar
	0-blade: \(s=1\) More...
typedef Vec	vsr::cga::Vector
	Euclidean 1-blade: \(\boldsymbol{x}=\{e_1,e_2,e_3\}\)
typedef Biv	vsr::cga::Bivector
	Euclidean 2-blade: \(\boldsymbol{B}=\{e_{12},e_{13},e_{23}\}\)
typedef Tri	vsr::cga::Trivector
	Euclidean 3-blade: \(\boldsymbol{I_3}=\{e_{123}\}\)
typedef Rot	vsr::cga::Rotor
	Euclidean Rotor (Quaternionic): \(R=\{1,e_{12},e_{13},e_{23}\}\)
typedef Ori	vsr::cga::Origin
	Null Origin Blade: \(n_o\)
typedef Inf	vsr::cga::Infinity
	Null Infinity Blade: \(n_\infty\)
typedef Mnk	vsr::cga::Minkowski
	Minkowski Plane: \(E=n_o\wedge n_\infty\)
typedef Pss	vsr::cga::Pseudoscalar
	Tangent Pseudoscalar 5-blade: \(I=e_{123} \wedge n_o \wedge n_\infty\)
typedef Pnt	vsr::cga::Point
	Null Vector \(p=\{e_1,e_2,e_3,n_o,n_\infty\}\)
typedef Par	vsr::cga::Pair
	Point Pair 2-blade \(\tau=p_a \wedge p_b=\{e_{12},e_{13},e_{23},e_{1}n_o,e_{2}n_o,e_{3}n_o,e_{1}n_\infty,e_{2}n_\infty,e_{3}n_\infty,n_{o}n_\infty\}\)
typedef Cir	vsr::cga::Circle
	Direct Circle 3-blade \(\kappa=p_a \wedge p_b \wedge p_c\)
typedef Sph	vsr::cga::Sphere
	Direct Sphere 4-blade \(\Sigma=p_a \wedge p_b \wedge p_c \wedge p_d\)
typedef Pnt	vsr::cga::DualSphere
	Same Type as Point \(\sigma\)
typedef Drv	vsr::cga::DirectionVector
	Direction Vector \(\boldsymbol{v}n_\infty\)
typedef Drb	vsr::cga::DirectionBivector
	Direction Bivector \(\boldsymbol{B}n_\infty\)
typedef Drt	vsr::cga::DirectionTrivector
	Direction Bivector \(\boldsymbol{I}n_\infty\)
typedef Tnv	vsr::cga::TangentVector
	Tangent Vector \(\boldsymbol{x}n_o\)
typedef Tnb	vsr::cga::TangentBivector
	Tangent Bivector \(\boldsymbol{B}n_o\)
typedef Tnt	vsr::cga::TangentTrivector
	Tangent Trivector \(\boldsymbol{I}n_o\)
typedef Dll	vsr::cga::DualLine
	Dual Line bivector \(\lambda=\boldsymbol{B}+\boldsymbol{x}n_\infty\)
typedef Lin	vsr::cga::Line
	Direct Line Trivector \(p_a \wedge p_b \wedge n_\infty\)
typedef Flp	vsr::cga::FlatPoint
	Flat Point \(p \wedge n_\infty\)
typedef Pln	vsr::cga::Plane
	Direct Plane \(p_a \wedge p_b \wedge p_c \wedge n_\infty\)
typedef Dlp	vsr::cga::DualPlane
	Dual Plane \(\boldsymbol{n}+n_\infty\)
typedef Trs	vsr::cga::Translator
	Translating Rotor \(1-\boldsymbol{v}n_\infty\)
typedef Mot	vsr::cga::Motor
	Twisting Rotor \(e^\lambda\)
typedef Trv	vsr::cga::Transversor
	Transversion at the Origin \(1-\boldsymbol{v}n_o\)
typedef Bst	vsr::cga::Boost
	Homogenous Transversion \(e^\tau=\mbox{cosh}(\tau)-\mbox{sinh}(\tau)\)
typedef Con	vsr::cga::ConformalRotor
	General Conformal \(e^{\tau_a} e^{\tau_b}\);.
typedef Dil	vsr::cga::Dilator
	Dilation relative to Origin \(1+E\)
typedef Tsd	vsr::cga::TranslatedDilator
	Dilation relative to some point p \(e^{p \wedge n_\infty}\)

Detailed Description

3D CGA Instantiations of the Multivector Template class

These are the most Common 3D Conformal Geometric Algebra Types,

Naming

Types can be written in long form (as in Scalar or Pseudoscalar) or three-letter short form (as in Sca or Pss).

See also

Shorthand Syntax

Typedef Documentation

vsr::cga::Scalar

0-blade: \(s=1\)

extract VSR_PRECISION value with operator []

Scalar s(0);
float f = s[0];