vsr::cga Namespace Reference

3D Conformal Geometric Algebra Namespace More...

Classes
class	Bennett
	The bennett 4 bar linkage. More...
class	Chain
	A sequence of spatial Frames. More...
struct	Constrain
	Methods for Evaluating Constrained Points using Intersections of Sphere-based Distances. More...
struct	Construct
	constructive syntactic sugar for making geometric elements More...
class	CoupledTwist
	Coupled Twist Shape Generation x, y, z (after Rosenhahn et al) More...
struct	CyclideQuad
	Cylclidic Net (four tangent frames) More...
struct	Cylindrical
struct	DistancePtr
	Holds a pointer to a source, and has a radius t, the operator() generates a dual sphere at source with radius t. More...
struct	Flat
	3D operations on Flat types More...
struct	Fold
class	Frame
	Orthonormal Frame composed from a Position and Orientation. More...
struct	Gen
	Generators and Logarithms Optimized for 3D Conformal Geometric Algebra. More...
struct	Helical
class	HopfFiber
	Hopf Fibration More...
struct	Joint
struct	NCyclide
class	NTwist
	GENERIC n-TWIST mechanism. More...
struct	Op
	Extraction of axis-angle orientation and 3D position features from Multivectors. More...
class	Pantograph
	PANTOGRAPH for scissor-like kinematics. More...
struct	Planar
struct	Prismatic
struct	Revolute
struct	Rig
	Rig has n spherical constraints to satisfy (try using fabrik solver here) More...
struct	Rig2
	A Rigid Contraint Node set by Two Distance Pointers. More...
struct	Rig3
struct	Rigid
	A Rigid Constraint Node set by Three Distance Pointers. More...
struct	Rigid2
struct	RigidNode
	Generic Rigid Constraint Node. More...
struct	Round
	3D operations on Round types (Points, Point Pairs, Circles, Spheres) More...
struct	Shape
struct	Simplicial
struct	Simplicial2
struct	Spherical
struct	Tangent
	3D operations on Tangent types More...
struct	TangentFrame
	Frame Tangent to Surface. More...
struct	TorusKnot
class	Twist
	Decomposed Dual Line (As a Bivector and Direction Vector to it ) More...

Typedefs
using	Sca = NSca< 5 >
	Scalar
using	Vec = NVec< 5 >
	Vector
using	Biv = NBiv< 5 >
	Bivector
using	Rot = NRot< 5 >
	Rotor
using	Tri = NTri< 5 >
	Trivector
using	Ori = NOri< 5 >
	Origin
using	Inf = NInf< 5 >
	Infinity
using	Mnk = NMnk< 5 >
	Minkowski
using	Pss = NPss< 5 >
	Pseudoscalar
using	Pnt = NPnt< 5 >
	Point
using	Par = NPar< 5 >
	Pair
using	Cir = NCir< 5 >
	Circle
using	Sph = NSph< 5 >
	Sphere
using	Dls = NDls< 5 >
	DualSphere
using	Flp = NFlp< 5 >
	FlatPoint
using	Dll = NDll< 5 >
	DualLine
using	Lin = NLin< 5 >
	Line
using	Dlp = NDlp< 5 >
	DualPlane
using	Pln = NPln< 5 >
	Plane
using	Drv = NDrv< 5 >
	DirectionVector
using	Tnv = NTnv< 5 >
	TangentVector
using	Drb = NDrb< 5 >
	DirectionBivector
using	Tnb = NTnb< 5 >
	TangentBivector
using	Drt = NDrt< 5 >
	DirectionTrivector
using	Tnt = NTnt< 5 >
	TangentTrivector
using	Trs = NTrs< 5 >
	Translator
using	Mot = NMot< 5 >
	Motor
using	Trv = NTrv< 5 >
	Transversor
using	Bst = NBst< 5 >
	Boost
using	Con = NCon< 5 >
	ConformalRotor
using	Dil = NDil< 5 >
	Dilator
using	Tsd = NTsd< 5 >
	TranslatedDilator
typedef Sca	Scalar
	0-blade: \(s=1\) More...
typedef Vec	Vector
	Euclidean 1-blade: \(\boldsymbol{x}=\{e_1,e_2,e_3\}\)
typedef Biv	Bivector
	Euclidean 2-blade: \(\boldsymbol{B}=\{e_{12},e_{13},e_{23}\}\)
typedef Tri	Trivector
	Euclidean 3-blade: \(\boldsymbol{I_3}=\{e_{123}\}\)
typedef Rot	Rotor
	Euclidean Rotor (Quaternionic): \(R=\{1,e_{12},e_{13},e_{23}\}\)
typedef Ori	Origin
	Null Origin Blade: \(n_o\)
typedef Inf	Infinity
	Null Infinity Blade: \(n_\infty\)
typedef Mnk	Minkowski
	Minkowski Plane: \(E=n_o\wedge n_\infty\)
typedef Pss	Pseudoscalar
	Tangent Pseudoscalar 5-blade: \(I=e_{123} \wedge n_o \wedge n_\infty\)
typedef Pnt	Point
	Null Vector \(p=\{e_1,e_2,e_3,n_o,n_\infty\}\)
typedef Par	Pair
	Point Pair 2-blade \(\tau=p_a \wedge p_b=\{e_{12},e_{13},e_{23},e_{1}n_o,e_{2}n_o,e_{3}n_o,e_{1}n_\infty,e_{2}n_\infty,e_{3}n_\infty,n_{o}n_\infty\}\)
typedef Cir	Circle
	Direct Circle 3-blade \(\kappa=p_a \wedge p_b \wedge p_c\)
typedef Sph	Sphere
	Direct Sphere 4-blade \(\Sigma=p_a \wedge p_b \wedge p_c \wedge p_d\)
typedef Pnt	DualSphere
	Same Type as Point \(\sigma\)
typedef Drv	DirectionVector
	Direction Vector \(\boldsymbol{v}n_\infty\)
typedef Drb	DirectionBivector
	Direction Bivector \(\boldsymbol{B}n_\infty\)
typedef Drt	DirectionTrivector
	Direction Bivector \(\boldsymbol{I}n_\infty\)
typedef Tnv	TangentVector
	Tangent Vector \(\boldsymbol{x}n_o\)
typedef Tnb	TangentBivector
	Tangent Bivector \(\boldsymbol{B}n_o\)
typedef Tnt	TangentTrivector
	Tangent Trivector \(\boldsymbol{I}n_o\)
typedef Dll	DualLine
	Dual Line bivector \(\lambda=\boldsymbol{B}+\boldsymbol{x}n_\infty\)
typedef Lin	Line
	Direct Line Trivector \(p_a \wedge p_b \wedge n_\infty\)
typedef Flp	FlatPoint
	Flat Point \(p \wedge n_\infty\)
typedef Pln	Plane
	Direct Plane \(p_a \wedge p_b \wedge p_c \wedge n_\infty\)
typedef Dlp	DualPlane
	Dual Plane \(\boldsymbol{n}+n_\infty\)
typedef Trs	Translator
	Translating Rotor \(1-\boldsymbol{v}n_\infty\)
typedef Mot	Motor
	Twisting Rotor \(e^\lambda\)
typedef Trv	Transversor
	Transversion at the Origin \(1-\boldsymbol{v}n_o\)
typedef Bst	Boost
	Homogenous Transversion \(e^\tau=\mbox{cosh}(\tau)-\mbox{sinh}(\tau)\)
typedef Con	ConformalRotor
	General Conformal \(e^{\tau_a} e^{\tau_b}\);.
typedef Dil	Dilator
	Dilation relative to Origin \(1+E\)
typedef Tsd	TranslatedDilator
	Dilation relative to some point p \(e^{p \wedge n_\infty}\)

Functions
vector< Point >	points (const Circle &k, int num, float theta=0, float phi=TWOPI)
ostream &	operator<< (ostream &os, const Twist &t)

Variables
auto	pointOnLine
	Point on line closest to another point v. More...
auto	pointOnCircle
	a single point on circle c at theta t More...
auto	pointsOnCircle
	n points on circle c More...
auto	pairOnSphere
	a pair on dual sphere More...
auto	pointOnSphere
	a single point on dual sphere s at theta t and phi p More...
auto	pointsOnSphere
	many points on sphere (could use map func from gfx::data) More...

Detailed Description

3D Conformal Geometric Algebra Namespace

Variable Documentation

auto vsr::cga::pairOnSphere

Initial value:

= [](const DualSphere& s, VSR_PRECISION t, VSR_PRECISION p){
     return Construct::pair(s, Vec::x.sp( Gen::rot(t,p) ) );
    }

a pair on dual sphere

auto vsr::cga::pointOnCircle

Initial value:

= [](const Circle& c, VSR_PRECISION t){
     return Construct::point(c,t);
    }

a single point on circle c at theta t

auto vsr::cga::pointOnLine

Initial value:

= []( const Line& lin, const Point& v){
      return Round::null( Flat::loc( lin, v, false) );
    }

Point on line closest to another point v.

auto vsr::cga::pointOnSphere

Initial value:

= [](const DualSphere& s, VSR_PRECISION t, VSR_PRECISION p){
      return Construct::pointA( pairOnSphere(s,t,p) ).null(); 
    }

a single point on dual sphere s at theta t and phi p

auto vsr::cga::pointsOnCircle

Initial value:

= [](const Circle& c, int num){
     vector<Point> out;
     for (int i=0;i<=num;++i){
       out.push_back(pointOnCircle(c, TWOPI*(float)i/num) );
     }
     return out;
    }

n points on circle c

auto vsr::cga::pointsOnSphere

Initial value:

= [](const DualSphere& s, int u, int v){
      vector<Point> out;
      for (int i = 0; i < u; ++i){
       for (int j = 0; j < v; ++j){

        float tu= TWOPI * i/u;
        float tv = -PIOVERTWO  + PI * j/v;

        out.push_back( pointOnSphere(s,tu,tv) );

      }
     }
     return out; 
    }

many points on sphere (could use map func from gfx::data)