vsr::cga::Round Struct Reference

3D operations on Round types (Points, Point Pairs, Circles, Spheres) More...

#include <vsr_cga3D_round.h>

Static Public Member Functions
static DualSphere	surround (const Pair &s)
	Dual Surround of a Direct or Dual Pair. More...
static DualSphere	surround (const Circle &s)
	Dual Surround of a Direct or Dual Circle. More...
template<class A >
static DualSphere	sur (const A &s)
	Dual Surround of a Direct or Dual Round Element (Shorthand) More...
static Pair	produce (const DualSphere &dls, const Vec &v)
	Pair From DualSphere and Euclidean subspace Bivector Note: Result will be imaginary if input DualSphere is real . More...
static Circle	produce (const DualSphere &dls, const Biv &b)
	Circle From DualSphere and Euclidean subspace Bivector Note: Result will be imaginary if input DualSphere is real . More...
static DualSphere	at (const Point &c, const Point &p)
	Dual Round from Center and Point on Surface. More...
static Point	point (const DualSphere &dls, const Vec &flat)
	Direct Point From Dual Sphere and Euclidean Carrier Flat. More...
static Vec	vec (const Circle &c, VSR_PRECISION theta=0)
	Euclidean Vector of Circle at theta. More...
static Pair	pair (const Circle &c, VSR_PRECISION t)
	Point Pair on Direct Circle at angle t. More...
static Point	point (const Circle &c, VSR_PRECISION t)
	Point on Circle at angle t. More...
static Point	null (const Vec &v)
	Null Point from a vec.
static Point	null (const Point &v)
	Null Point from a Point.
static Point	null (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Or Null Point from Coordinates (x,y,z,...)
static Point	point (VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Null Point from Coordinates.
static DualSphere	dualSphere (VSR_PRECISION r, VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Dual Sphere from Coordinate Center. More...
static DualSphere	dls (VSR_PRECISION r, VSR_PRECISION x, VSR_PRECISION y, VSR_PRECISION z)
	Dual Sphere from Coordinate Center (shorthand) More...
static DualSphere	dls (const Vec &v, VSR_PRECISION r=1.0)
	Dual Sphere from Element FIRST and Radius. More...
static DualSphere	sphere (const Point &v, VSR_PRECISION r=1.0)
	Dual Sphere from Element FIRST and Radius. More...
static DualSphere	dls (const Point &p, VSR_PRECISION r=1.0)
	Dual Sphere from Point and Radius (faster) More...
static Point	center (const DualSphere &s)
	Simple Center of A Round (not normalized – use loc or location method instead) More...
static Point	center (const Pair &s)
	Simple Center of A Round (not normalized – use loc or location method instead) More...
static Point	center (const Circle &s)
	Simple Center of A Round (not normalized – use loc or location method instead) More...
static Point	center (const Sphere &s)
	Simple Center of A Round (not normalized – use loc or location method instead) More...
template<class A >
static Point	cen (const A &s)
	Simple Center of a Round Element (shorthand) More...
template<class A >
static Point	location (const A &s)
	Location (normalized) of A Round Element (normalized) (Shorthand) More...
template<class A >
static Point	loc (const A &s)
	Location (normalizd) of a Round Element (shorthand) More...
static VSR_PRECISION	size (const DualSphere &s, bool bDual=true)
	Squared Size of a DualSphere (result could be negative) More...
static VSR_PRECISION	size (const Pair &s, bool bDual=true)
	Squared Size of a Point Pair (result could be negative) More...
static VSR_PRECISION	size (const Circle &s, bool bDual=false)
	Squared Size of a Circle (result could be negative) More...
static VSR_PRECISION	size (const Sphere &s, bool bDual=false)
	Squared Size of a Sphere (result could be negative) More...
static VSR_PRECISION	dsize (const Point &dls)
	Squared Size of Normalized Dual Sphere (faster than general case) More...
static VSR_PRECISION	radius (const DualSphere &s)
	Radius of DualSphere.
static VSR_PRECISION	radius (const Pair &s)
	Radius of Pair.
static VSR_PRECISION	radius (const Circle &s)
	Radius of Circle.
static VSR_PRECISION	radius (const Sphere &s)
	Radius ofSphere.
template<class T >
static VSR_PRECISION	rad (const T &t)
	Squared Size of a DualSphere (result could be negative) More...
template<class A >
static VSR_PRECISION	curvature (const A &s)
	Curvature of Round. More...
template<class T >
static VSR_PRECISION	cur (const T &t)
	Curvature of Round. More...
static VSR_PRECISION	squaredDistance (const Point &a, const Point b)
	Squared distance between two points. More...
static VSR_PRECISION	sqd (const Point &a, const Point b)
	Squared distance between two points.
static VSR_PRECISION	distance (const Point &a, const Point b)
	Distance between points a and b.
static VSR_PRECISION	dist (const Point &a, const Point &b)
	Distance between points a and b (shorthand)
static std::vector< Point >	split (const Pair &pp)
	Split Points from Point Pair. More...
static std::vector< Point >	splitLocation (const Pair &pp)
	Split Points from Point Pair and normalize. More...
static Point	split (const Pair &pp, bool bFirst)
	Split a point pair and return one. More...
static std::vector< Point >	split (const Circle &nc)
	Split A Circle into its dual point pair poles.
static DirectionVector	direction (const Pair &p)
	Direction of a Pair. More...
static DirectionBivector	direction (const Circle &c)
	Direction of a Circle. More...
static DirectionBivector	direction (const Sphere &c)
	Direction of a Sphere. More...
template<class A >
static auto	dir (const A &s) -> decltype(direction(s))
	Direction of Round Element (shorthand) More...
static Line	carrier (const Pair &p)
	Carrier Flat of Pair. More...
static Plane	carrier (const Circle &c)
	Carrier Flat of Circle. More...
template<class A >
static auto	car (const A &s) -> decltype(carrier(s))
	Carrier Flat of Direct? Round Element (Shorthand) More...

Detailed Description

3D operations on Round types (Points, Point Pairs, Circles, Spheres)

3D CGA Template Specializations of ND functions found in vsr::nga::Round Note: the ND functions are inlined and can be used instead, but using these will speed up compile times since they are precompiled into libvsr.a

See also

Round for a list of Multivector Types on which these methods operate

vsr::nga::Round for the Generic n-dimensional implementation details

Member Function Documentation

static DualSphere vsr::cga::Round::at ( const Point &  c, const Point &  p  )

static

Dual Round from Center and Point on Surface.

Parameters

c	Point at center
p	Point on surface

static Line vsr::cga::Round::carrier ( const Pair &  p )

static

Carrier Flat of Pair.

Parameters

p	vsr::cga::Pair

See also

nga::Round::carrier for Generic implementation

static Plane vsr::cga::Round::carrier ( const Circle &  c )

static

Carrier Flat of Circle.

Parameters

c	vsr::cga::Circle

See also

nga::Round::carrier for Generic implementation

static Point vsr::cga::Round::center ( const DualSphere &  s )

static

Simple Center of A Round (not normalized – use loc or location method instead)

See also

nga::Round::center for Generic case

static Point vsr::cga::Round::center ( const Pair &  s )

static

Simple Center of A Round (not normalized – use loc or location method instead)

See also

nga::Round::center for Generic case

static Point vsr::cga::Round::center ( const Circle &  s )

static

Simple Center of A Round (not normalized – use loc or location method instead)

See also

nga::Round::center for Generic case

static Point vsr::cga::Round::center ( const Sphere &  s )

static

Simple Center of A Round (not normalized – use loc or location method instead)

See also

nga::Round::center for Generic case

template<class T >

static VSR_PRECISION vsr::cga::Round::cur ( const T &  t )

inlinestatic

Curvature of Round.

Parameters

Round

Element

template<class A >

static VSR_PRECISION vsr::cga::Round::curvature ( const A &  s )

inlinestatic

Curvature of Round.

Parameters

Round

Element

static DualSphere vsr::cga::Round::dls ( VSR_PRECISION  r, VSR_PRECISION  x, VSR_PRECISION  y, VSR_PRECISION  z  )

inlinestatic

Dual Sphere from Coordinate Center (shorthand)

static DualSphere vsr::cga::Round::dls ( const Vec &  v, VSR_PRECISION  r = 1.0  )

static

Dual Sphere from Element FIRST and Radius.

Parameters

v	vsr::cga::Vec (function will take first 3 weights)
Radius	(enter a negative radius for an imaginary sphere)

static DualSphere vsr::cga::Round::dls ( const Point &  p, VSR_PRECISION  r = 1.0  )

static

Dual Sphere from Point and Radius (faster)

Parameters

Point
Radius	(enter a negative radius for an imaginary sphere)

static VSR_PRECISION vsr::cga::Round::dsize ( const Point &  dls )

static

Squared Size of Normalized Dual Sphere (faster than general case)

Parameters

Normalized

Dual Sphere

See also

vsr::nga::dsize

static DualSphere vsr::cga::Round::dualSphere ( VSR_PRECISION  r, VSR_PRECISION  x, VSR_PRECISION  y, VSR_PRECISION  z  )

static

Dual Sphere from Coordinate Center.

note that radius is first argument

Parameters

r	Radius (enter a negative radius for an imaginary sphere)
3	of coordinates

See also

vsr::nga::dualSphere

template<class A >

static Point vsr::cga::Round::location ( const A &  s )

inlinestatic

Location (normalized) of A Round Element (normalized) (Shorthand)

See also

nga::Round::location for Generic implementation

static Pair vsr::cga::Round::pair ( const Circle &  c, VSR_PRECISION  t  )

static

Point Pair on Direct Circle at angle t.

See also

vsr::nga::par_cir for the Generic implementation

static Point vsr::cga::Round::point ( const DualSphere &  dls, const Vec &  flat  )

static

Direct Point From Dual Sphere and Euclidean Carrier Flat.

See also

vsr::nga::pnt for the Generic implementation

static Point vsr::cga::Round::point ( const Circle &  c, VSR_PRECISION  t  )

static

Point on Circle at angle t.

See also

vsr::nga::pnt_cir for the Generic implementation

static Pair vsr::cga::Round::produce ( const DualSphere &  dls, const Vec &  v  )

static

Pair From DualSphere and Euclidean subspace Bivector Note: Result will be imaginary if input DualSphere is real .

Parameters

dls	DualSphere
v	Vector

Returns

Pair

See also

nga::Round::produce for Generic implementation

static Circle vsr::cga::Round::produce ( const DualSphere &  dls, const Biv &  b  )

static

Circle From DualSphere and Euclidean subspace Bivector Note: Result will be imaginary if input DualSphere is real .

Parameters

dls	DualSphere
b	Bivector

Returns

Circle

See also

nga::Round::produce for Generic implementation

template<class T >

static VSR_PRECISION vsr::cga::Round::rad ( const T &  t )

inlinestatic

Squared Size of a DualSphere (result could be negative)

Parameters

input

normalized dual sphere

See also

vsr::nga::size for general case

static VSR_PRECISION vsr::cga::Round::size ( const DualSphere &  s, bool  bDual = true  )

static

Squared Size of a DualSphere (result could be negative)

Parameters

input

normalized dual sphere

See also

vsr::nga::size for general case

static VSR_PRECISION vsr::cga::Round::size ( const Pair &  s, bool  bDual = true  )

static

Squared Size of a Point Pair (result could be negative)

Parameters

input

normalized vsr::cga::Pair

See also

vsr::nga::size for general case

static VSR_PRECISION vsr::cga::Round::size ( const Circle &  s, bool  bDual = false  )

static

Squared Size of a Circle (result could be negative)

Parameters

input

normalized vsr::cga::Circle

See also

vsr::nga::size for general case

static VSR_PRECISION vsr::cga::Round::size ( const Sphere &  s, bool  bDual = false  )

static

Squared Size of a Sphere (result could be negative)

Parameters

input

normalized vsr::cga::Sphere

See also

vsr::nga::size for general case

static DualSphere vsr::cga::Round::sphere ( const Point &  v, VSR_PRECISION  r = 1.0  )

static

Dual Sphere from Element FIRST and Radius.

Parameters

Any	input Multivector v (function will take first 3 weights)
Radius	(enter a negative radius for an imaginary sphere)

static std::vector<Point> vsr::cga::Round::split ( const Pair &  pp )

static

Split Points from Point Pair.

Parameters

PointPair

input returns a vector<Pnt>

static Point vsr::cga::Round::split ( const Pair &  pp, bool  bFirst  )

static

Split a point pair and return one.

Parameters

pp	Point Pair
bFirst	which one to return

static std::vector<Point> vsr::cga::Round::splitLocation ( const Pair &  pp )

static

Split Points from Point Pair and normalize.

Parameters

PointPair

input returns a vector<Pnt>

static VSR_PRECISION vsr::cga::Round::squaredDistance ( const Point &  a, const Point  b  )

static

Squared distance between two points.

See also

vsr::nga::squaredDistance

static DualSphere vsr::cga::Round::surround ( const Pair &  s )

static

Dual Surround of a Direct or Dual Pair.

See also

nga::Round::surround for Generic implementation

static DualSphere vsr::cga::Round::surround ( const Circle &  s )

static

Dual Surround of a Direct or Dual Circle.

See also

nga::Round::surround for Generic implementation

static Vec vsr::cga::Round::vec ( const Circle &  c, VSR_PRECISION  theta = 0  )

static

Euclidean Vector of Circle at theta.

See also

vsr::nga::vec for the Generic implementation

---

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

• /Users/wolftype/code/versor/vsr/space/vsr_cga3D_round.h