from_spherical

kyosu::from_spherical = {}

inlineconstexpr

Callable object computing a quaternion from its spherical representation.

This function build quaternions in a way similar to the way polar builds complex numbers from a spherical representation of an \(\mathbb{R}^4\) element.

from_spherical takes as inputs a (positive) magnitude and a point on the hypersphere, given by three angles. The first of these, theta has a natural range of \(-\pi\) to \(+\pi\), and the other two have natural ranges of \(-\pi/2\) to \(+\pi/2\) (as is the case with the usual spherical coordinates in \(\mathbb{R}^3\)).

Defined in header

#include eve/module/quaternion.hpp>`

Callable Signatures

namespace eve
{
  auto from_spherical(auto rho, auto theta, auto phi1, auto phi2) const noexcept;
}

Parameters

• rho: the modulus
• theta, phi1, phi2: angles in radian

Return value

the quaternion value

---

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::from_spherical;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
 
  auto r = 2.0;
  auto theta  = eve::pio_3(eve::as(r));
  auto phi1   = eve::pio_4(eve::as(r));
  auto phi2   = eve::pio_2(eve::as(r));
  std::cout << " <- r     " << r << std::endl;
  std::cout << " <- theta " << theta<< std::endl;
  std::cout << " <- phi1  " << phi1<< std::endl;
  std::cout << " <- phi2  " << phi2<< std::endl;
  std::cout << " -> " << from_spherical(r, theta, phi1, phi2) << "\n";
 
  return 0;
}