ldsgen::Sphere3Hopf class
#include <ldsgen/lds.hpp>

S(3) sequence generator by Hopf fibration.

The Sphere3Hopf class is a sequence generator that generates points on a 3-sphere using the Hopf fibration. It uses three instances of the VdCorput class to generate the sequence values and maps them to points on the 3-sphere. The pop() method returns the next point on the 3-sphere as a std::array<double, 4>, where the first three elements represent the x, y, and z coordinates of the point, and the fourth element represents the w coordinate. The reseed() method is used to reset the state of the sequence generator to a specific seed value.

*     3-Sphere (S3) visualization:
*     A 4D hypersphere where points (x,y,z,w)
*     satisfy x²+y²+z²+w² = 1
*
*         4D hypersurface
*            _____
*         .-'     '-.
*       ,'           ',
*      /               \
*     |        O        |  (4D analog of sphere)
*      \               /
*       '.           .'
*         '-.....-'
*

Constructors, destructors, conversion operators

Sphere3Hopf(const unsigned long base0, const unsigned long base1, const unsigned long base2): Construct a new Sphere 3 Hopf object.

Public functions

auto pop() -> std::array< double, 4 > -> auto: Generate the next point on the 3-sphere using Hopf fibration.
auto peek() -> std::array< double, 4 > -> auto: Peek at the next value without advancing state.
auto skip(unsigned int n) -> void -> auto: Skip n values in the sequence.
auto reseed(unsigned long seed) -> void -> auto: Reset the state of the Sphere3Hopf sequence generator.
auto get_index() const -> unsigned long -> auto: Get current index.
auto begin() -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > > -> auto: Get iterator to beginning.
auto end() const -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > > -> auto: Get iterator to end (infinite sequence)

Function documentation

ldsgen::Sphere3Hopf::Sphere3Hopf(const unsigned long base0, const unsigned long base1, const unsigned long base2)

Construct a new Sphere 3 Hopf object.

Parameters
base0 in	the base for the first Van der Corput generator (phi coordinate)
base1 in	the base for the second Van der Corput generator (psi coordinate)
base2 in	the base for the third Van der Corput generator (eta coordinate)

Constructs a 3-sphere sequence generator using the Hopf fibration with the specified bases.

auto ldsgen::Sphere3Hopf::pop() -> std::array< double, 4 >

Generate the next point on the 3-sphere using Hopf fibration.

Returns	std::array<double, 4> the next point on the 3-sphere

Returns the next point on the 3-sphere using the Hopf fibration as an array of four double values.

auto ldsgen::Sphere3Hopf::peek() -> std::array< double, 4 >

Peek at the next value without advancing state.

Returns	std::array<double, 4> next point on the 3-sphere

auto ldsgen::Sphere3Hopf::skip(unsigned int n) -> void

Skip n values in the sequence.

Parameters
n in	number of values to skip

auto ldsgen::Sphere3Hopf::reseed(unsigned long seed) -> void

Reset the state of the Sphere3Hopf sequence generator.

Parameters
seed in	the seed value to reset the sequence generator to

Resets the state of the sequence generator to a specific seed value.

auto ldsgen::Sphere3Hopf::get_index() const -> unsigned long

Get current index.

Returns	unsigned long current index in sequence

auto ldsgen::Sphere3Hopf::begin() -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > >

Get iterator to beginning.

Returns	GeneratorIterator<Sphere3Hopf, std::array<double, 4>>

auto ldsgen::Sphere3Hopf::end() const -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > >

Get iterator to end (infinite sequence)

Returns	GeneratorIterator<Sphere3Hopf, std::array<double, 4>>

ldsgen::Sphere3Hopf class #include <ldsgen/lds.hpp>