to_semipolar

auto kyosu::to_semipolar = eve::functor<to_semipolar_t>

inlineconstexpr

Callable object computing the semipolar coordinates from a quaternion.

This function is the reciprocal of from_semipolar

Header file

#include kyosu/quaternion.hpp>`

Callable Signatures

namespace eve
{
  auto to_semipolar(auto q) const noexcept;
}

Parameters

q: quaternion

Return value

a tuple containing in this order rho, alpha, theta1, theta2: the components of the semipolar parametrisation of \f$\mathbb{R}^4\f$ coordinates. If the radpi is used alpha, theta1 and theta2 are given in \(\pi\) multiples else in radian.

---

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::complex_t;
  using kyosu::quaternion_t;
  using kyosu::to_semipolar;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using q_t = kyosu::quaternion_t<float>;
  using we_t = eve::wide<float, eve::fixed<2>>;
  using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
  using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
 
  std::cout << "Real:        " << "\n";
  e_t e0(1);
  std::cout << e0 << " -> " << to_semipolar(e0) << "\n";
  we_t we0(e0);
  std::cout << we0 << " -> " << to_semipolar(we0) << "\n";
 
  std::cout << "Complex:     " << "\n";
  c_t c0(1, 5);
  std::cout << c0 << " -> " << to_semipolar(c0) << "\n";
  wc_t wc0(c0);
  std::cout << wc0 << " -> " << to_semipolar(wc0) << "\n";
 
  std::cout << "Quaternion:  " << "\n";
  q_t q0(1, 5, 2, 3);
  std::cout << q0 << " -> " << to_semipolar(q0) << "\n";
  wq_t wq0(q0);
  std::cout << wq0 << " -> " << to_semipolar(wq0) << "\n";
 
  return 0;
}