#include <lds/lds.hpp>
Sphere3Hopf class
S(3) sequence generator by Hopf fibration.
| Template parameters | |
|---|---|
| Base0 | the base for the first van der Corput generator (phi coordinate) |
| Base1 | the base for the second van der Corput generator (psi coordinate) |
| Base2 | the base for the third van der Corput generator (eta coordinate) |
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) * \ / * '. .' * '-.....-' *
Public functions
- auto Sphere3Hopf() -> constexpr
- Construct a new Sphere 3 Hopf object.
- auto pop() -> std::array< double, 4 > -> constexpr auto
- Generate the next point on the 3-sphere using Hopf fibration.
- auto peek() -> std::array< double, 4 > -> constexpr auto
- Peek at the next value without advancing state.
- auto skip(unsigned long n) -> void -> constexpr auto
- Skip n values in the sequence.
- auto reseed(unsigned long seed) -> void -> constexpr auto
- Reset the state of the Sphere3Hopf sequence generator.
- auto get_index() const -> unsigned long -> constexpr auto
- Get current index.
- auto begin() -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > > -> constexpr auto
- Get iterator to beginning.
- auto end() const -> GeneratorIterator< Sphere3Hopf, std::array< double, 4 > > -> constexpr auto
- Get iterator to end (infinite sequence)
Function documentation
constexpr auto lds::
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.