8 #ifndef VSR_CGA3D_TYPES_INCLUDED
9 #define VSR_CGA3D_TYPES_INCLUDED
Con ConformalRotor
General Conformal \(e^{\tau_a} e^{\tau_b}\);.
Definition: vsr_cga3D_types.h:148
Dlp DualPlane
Dual Plane \(\boldsymbol{n}+n_\infty\)
Definition: vsr_cga3D_types.h:143
Dil Dilator
Dilation relative to Origin \(1+E\)
Definition: vsr_cga3D_types.h:149
Trv Transversor
Transversion at the Origin \(1-\boldsymbol{v}n_o\)
Definition: vsr_cga3D_types.h:146
Tsd TranslatedDilator
Dilation relative to some point p \(e^{p \wedge n_\infty}\)
Definition: vsr_cga3D_types.h:150
Par Pair
Point Pair 2-blade \(\tau=p_a \wedge p_b=\{e_{12},e_{13},e_{23},e_{1}n_o,e_{2}n_o,e_{3}n_o,e_{1}n_\infty,e_{2}n_\infty,e_{3}n_\infty,n_{o}n_\infty\}\)
Definition: vsr_cga3D_types.h:129
Tnb TangentBivector
Tangent Bivector \(\boldsymbol{B}n_o\)
Definition: vsr_cga3D_types.h:137
Rot Rotor
Euclidean Rotor (Quaternionic): \(R=\{1,e_{12},e_{13},e_{23}\}\)
Definition: vsr_cga3D_types.h:123
Generic Geometric Number Types (templated on an algebra and a basis )
Definition: vsr_algebra.h:69
Biv Bivector
Euclidean 2-blade: \(\boldsymbol{B}=\{e_{12},e_{13},e_{23}\}\)
Definition: vsr_cga3D_types.h:121
Inf Infinity
Null Infinity Blade: \(n_\infty\)
Definition: vsr_cga3D_types.h:125
Flp FlatPoint
Flat Point \(p \wedge n_\infty\)
Definition: vsr_cga3D_types.h:141
Mnk Minkowski
Minkowski Plane: \(E=n_o\wedge n_\infty\)
Definition: vsr_cga3D_types.h:126
Tnv TangentVector
Tangent Vector \(\boldsymbol{x}n_o\)
Definition: vsr_cga3D_types.h:136
Drt DirectionTrivector
Direction Bivector \(\boldsymbol{I}n_\infty\)
Definition: vsr_cga3D_types.h:135
Cir Circle
Direct Circle 3-blade \(\kappa=p_a \wedge p_b \wedge p_c\)
Definition: vsr_cga3D_types.h:130
Drv DirectionVector
Direction Vector \(\boldsymbol{v}n_\infty\)
Definition: vsr_cga3D_types.h:133
Vec Vector
Euclidean 1-blade: \(\boldsymbol{x}=\{e_1,e_2,e_3\}\)
Definition: vsr_cga3D_types.h:120
Tri Trivector
Euclidean 3-blade: \(\boldsymbol{I_3}=\{e_{123}\}\)
Definition: vsr_cga3D_types.h:122
Bst Boost
Homogenous Transversion \(e^\tau=\mbox{cosh}(\tau)-\mbox{sinh}(\tau)\)
Definition: vsr_cga3D_types.h:147
Pln Plane
Direct Plane \(p_a \wedge p_b \wedge p_c \wedge n_\infty\)
Definition: vsr_cga3D_types.h:142
Pnt Point
Null Vector \(p=\{e_1,e_2,e_3,n_o,n_\infty\}\)
Definition: vsr_cga3D_types.h:128
Trs Translator
Translating Rotor \(1-\boldsymbol{v}n_\infty\)
Definition: vsr_cga3D_types.h:144
Sca Scalar
0-blade: \(s=1\)
Definition: vsr_cga3D_types.h:119
Pnt DualSphere
Same Type as Point \(\sigma\)
Definition: vsr_cga3D_types.h:132
the versor library namespace
Definition: vsr_algebra.h:29
Drb DirectionBivector
Direction Bivector \(\boldsymbol{B}n_\infty\)
Definition: vsr_cga3D_types.h:134
Tnt TangentTrivector
Tangent Trivector \(\boldsymbol{I}n_o\)
Definition: vsr_cga3D_types.h:138
Dll DualLine
Dual Line bivector \(\lambda=\boldsymbol{B}+\boldsymbol{x}n_\infty\)
Definition: vsr_cga3D_types.h:139
Lin Line
Direct Line Trivector \(p_a \wedge p_b \wedge n_\infty\)
Definition: vsr_cga3D_types.h:140
Pss Pseudoscalar
Tangent Pseudoscalar 5-blade: \(I=e_{123} \wedge n_o \wedge n_\infty\)
Definition: vsr_cga3D_types.h:127
Mot Motor
Twisting Rotor \(e^\lambda\)
Definition: vsr_cga3D_types.h:145
generic multivector class, templated on a geometric algebra and a field
Sph Sphere
Direct Sphere 4-blade \(\Sigma=p_a \wedge p_b \wedge p_c \wedge p_d\)
Definition: vsr_cga3D_types.h:131
Ori Origin
Null Origin Blade: \(n_o\)
Definition: vsr_cga3D_types.h:124