Operations on Round types (Points, Point Pairs, Circles, Spheres, N-Spheres) More...

#include <vsr_generic_op.h>

Static Public Member Functions
template<class A , class B >
static constexpr GAPnt< A >	null (const Multivector< A, B > &v)
	Null Point from Arbitrary Multivector.

template<class... T>
static constexpr NPnt< sizeof...(T)+2 >	null (T...v)
	Or Null Point from Coordinates (x,y,z,...)

template<class... T>
static constexpr NPnt< sizeof...(T)+2 >	point (T...v)
	Null Point from Coordinates.

template<class... T>
static auto	dls (VSR_PRECISION r, T...v) -> NPnt< sizeof...(T)+2 >
	Dual Sphere from Radius FIRST and Coordinate Center. More...

template<class... T>
static auto	dualSphere (VSR_PRECISION r, T...v) -> auto

template<class A , class B >
static auto	dls (const Multivector< A, B > &v, VSR_PRECISION r=1.0) -> GAPnt< A >
	Dual Sphere from Element FIRST and Radius. More...

template<class T >
static auto	dualSphere (const T &t, VSR_PRECISION r=1.0) -> auto

template<class S >
static auto	sphere (const S &v, VSR_PRECISION r=1.0) -> auto
	Dual Sphere from Element FIRST and Radius. More...

template<class A >
static GADls< A >	dls_pnt (const GAPnt< A > &p, VSR_PRECISION r=1.0)
	Dual Sphere from Point and Radius (faster) More...

template<class A , class B >
static constexpr GAPnt< A >	center (const Multivector< A, B > &s)
	Simple Center of A Round Element (not normalized – use loc or location method)

template<class A , class B >
static constexpr GAPnt< A >	cen (const Multivector< A, B > &s)
	Simple Center of A Round Element (shorthand) More...

template<class A >
static constexpr A::space::point	location (const A &s)
	Location of A Round Element (normalized) (Shorthand)

template<class A >
static constexpr A::space::point	loc (const A &s)

template<class A >
static VSR_PRECISION	size (const A &r, bool dual)
	Squared Size of a General Round Element (could be negative) More...

template<class T >
static constexpr VSR_PRECISION	radius (const T &s)
	Radius of Round.

template<class T >
static constexpr VSR_PRECISION	rad (const T &t)

template<class A >
static VSR_PRECISION	curvature (const A &s)
	Curvature of Round. More...

template<class T >
static constexpr VSR_PRECISION	cur (const T &t)
	Curvature of Round. More...

template<class A >
static constexpr VSR_PRECISION	dsize (const GAPnt< A > &dls)
	Squared Size of Normalized Dual Sphere (faster than general case) More...

template<class A >
static constexpr VSR_PRECISION	squaredDistance (const GAPnt< A > &a, const GAPnt< A > b)
	Squared distance between two points.

template<class A >
static constexpr VSR_PRECISION	sqd (const A &a, const A &b)

template<class A >
static constexpr VSR_PRECISION	distance (const GAPnt< A > &a, const GAPnt< A > b)
	Distance between points a and b.

template<class A >
static constexpr VSR_PRECISION	dist (const A &a, const A &b)

template<class A >
static std::vector< GAPnt< A > >	split (const GAPar< A > &pp)
	Split Points from Point Pair. More...

template<class A >
static std::vector< GAPnt< A > >	splitLocation (const GAPar< A > &pp)
	Split Points from Point Pair and normalize. More...

template<class A >
static GAPnt< A >	split (const GAPar< A > &pp, bool bFirst)
	Split a point pair. More...

template<class A >
static std::vector< GAPnt< A > >	split (const GACir< A > &nc)
	Split A Circle into its dual point pair poles.

template<class A >
static constexpr auto	direction (const A &s) -> auto
	Direction of Direct Round Element. More...

template<class A >
static constexpr auto	dir (const A &s) -> auto
	Direction of Round Element (shorthand) More...

template<class A >
static constexpr auto	carrier (const A &s) -> auto
	Carrier Flat of Direct Round Element. More...

template<class A >
static constexpr auto	car (const A &s) -> auto
	Carrier Flat of Direct? Round Element (Shorthand)

template<class A >
static constexpr A::space::dual_sphere	surround (const A &s)
	Dual Surround of a Direct or Dual Round Element.

template<class A >
static constexpr auto	sur (const A &s) -> auto
	Dual Surround of a Direct or Dual Round Element (Shorthand)

template<class A , class S >
static constexpr auto	produce (const A &dls, const S &flat) -> auto
	Direct Round From Dual Sphere and Euclidean Bivector Note: round will be imaginary if dual sphere is real . More...

template<class A >
static constexpr auto	real (const A &s) -> auto
	Creates a real / imaginary round from an imaginary / real round.

template<class A >
static constexpr auto	imag (const A &s) -> auto
	Creates an imaginary round from an real round.

template<class A >
static constexpr GADls< A >	at (const GADls< A > &c, const GADls< A > &p)
	Dual Round from Center and Point on Surface. More...

template<class A >
static constexpr GAPnt< A >	pnt (const GADls< A > &dls, const GAVec< A > &flat)
	Direct Round From coordinates and Euclidean Bivector Note: round will be imaginary if dual sphere is real . More...

template<class A >
static GAVec< A >	vec (const GACir< A > &c, VSR_PRECISION theta=0)
	Direct Point From Dual Sphere and Euclidean Carrier Flat. More...

template<class A >
static GAPar< A >	par_cir (const GACir< A > &c, VSR_PRECISION t)
	Point Pair on Direct Circle at angle t.

template<class A >
static GAPnt< A >	pnt_cir (const GACir< A > &c, VSR_PRECISION t)
	Point on Circle at angle t.

Detailed Description

Operations on Round types (Points, Point Pairs, Circles, Spheres, N-Spheres)

Member Function Documentation

template<class A >

static constexpr GADls<A> vsr::nga::Round::at	(	const GADls< A > &	c,
		const GADls< A > &	p
	)

inlinestatic

Dual Round from Center and Point on Surface.

Parameters

Center
point	on surface

template<class A >

static constexpr auto vsr::nga::Round::carrier ( const A & s ) -> auto

static

Carrier Flat of Direct Round Element.

Parameters

Direct Round

template<class A , class B >

static constexpr GAPnt<A> vsr::nga::Round::cen ( const Multivector< A, B > & s )

inlinestatic

Simple Center of A Round Element (shorthand)

See also: cga::Round::cen

template<class T >

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

inlinestatic

Curvature of Round.

Parameters

t	a Round Element

template<class A >

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

inlinestatic

Curvature of Round.

Parameters

s	a Round Element

template<class A >

static constexpr auto vsr::nga::Round::dir ( const A & s ) -> auto

static

Direction of Round Element (shorthand)

Parameters

Direct Round

template<class A >

static constexpr auto vsr::nga::Round::direction ( const A & s ) -> auto

static

Direction of Direct Round Element.

Parameters

Direct Round

template<class... T>

static auto vsr::nga::Round::dls	(	VSR_PRECISION	r,
		T...	v
	)		-> NPnt< sizeof...(T) + 2 >

inlinestatic

Dual Sphere from Radius FIRST and Coordinate Center.

Parameters

Radius	(enter a negative radius for an imaginary sphere)
any	number of coordinates

Note that radius is the first argument in order to enable construction of a sphere in any dimension (depending upon how many coordinates are fed into this function)

template<class A , class B >

static auto vsr::nga::Round::dls	(	const Multivector< A, B > &	v,
		VSR_PRECISION	r = `1.0`
	)		-> GAPnt<A>

inlinestatic

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)

template<class A >

static GADls<A> vsr::nga::Round::dls_pnt	(	const GAPnt< A > &	p,
		VSR_PRECISION	r = `1.0`
	)

inlinestatic

Dual Sphere from Point and Radius (faster)

Parameters

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

template<class A >

static constexpr VSR_PRECISION vsr::nga::Round::dsize ( const GAPnt< A > & dls )

inlinestatic

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

Parameters

Normalized Dual Sphere

template<class A >

static constexpr GAPnt<A> vsr::nga::Round::pnt	(	const GADls< A > &	dls,
		const GAVec< A > &	flat
	)

inlinestatic

Direct Round From coordinates and Euclidean Bivector Note: round will be imaginary if dual sphere is real .

. .

Direct Point From Dual Sphere and Euclidean Carrier Flat

template<class A , class S >

static constexpr auto vsr::nga::Round::produce	(	const A &	dls,
		const S &	flat
	)		-> auto

static

Direct Round From Dual Sphere and Euclidean Bivector Note: round will be imaginary if dual sphere is real .

. .

template<class A >

static VSR_PRECISION vsr::nga::Round::size	(	const A &	r,
		bool	dual
	)

inlinestatic

Squared Size of a General Round Element (could be negative)

Parameters

r	input normalized round (dual sphere, point pair, circle, or direct sphere)
dual	duality flag

template<class S >

static auto vsr::nga::Round::sphere	(	const S &	v,
		VSR_PRECISION	r = `1.0`
	)		-> auto

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)

template<class A >

static std::vector< GAPnt<A> > vsr::nga::Round::split ( const GAPar< A > & pp )

inlinestatic

Split Points from Point Pair.

Parameters

PointPair input returns a vector<Pnt>

template<class A >

static GAPnt<A> vsr::nga::Round::split	(	const GAPar< A > &	pp,
		bool	bFirst
	)

inlinestatic

Split a point pair.

Parameters

Point	Pair
bool	which one

template<class A >

static std::vector< GAPnt<A> > vsr::nga::Round::splitLocation ( const GAPar< A > & pp )

inlinestatic

Split Points from Point Pair and normalize.

Parameters

PointPair input returns a vector<Pnt>

template<class A >

static GAVec<A> vsr::nga::Round::vec	(	const GACir< A > &	c,
		VSR_PRECISION	theta = `0`
	)

inlinestatic

Direct Point From Dual Sphere and Euclidean Carrier Flat.

Euclidean Vector of Circle at theta

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

/Users/wolftype/code/versor/vsr/detail/vsr_generic_op.h

Static Public Member Functions

Detailed Description

Member Function Documentation