versor  3.0
C++11 library for Geometric algebra

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


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,


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

0-blade: \(s=1\)

extract VSR_PRECISION value with operator []

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