to_euler

kyosu::to_euler = {}

inlineconstexpr

Callable object computing euler angles from a quaternion.

This function build euler angles from a quaternion. Template parameters I, J, K of type int are used to choose the euler order.

for instance I = 3, J = 2, K = 3 choose the ZYZ sequence. the values of I, J, and K must be in {1, 2, 3} ans satisfy I != J && J != K.

Defined in header

#include eve/module/quaternion.hpp>`

Callable Signatures

namespace eve
{
   template < int I, int J, int K >
   auto to_euler(auto q, axis<I> const & a1, axis<J> const & a2, axis<K> const & a3) noexcept
   requires(I != J && J != K)
}

Parameters

• q the rotation quaternion (not necesseraly normalized)
• a1, a2, a3: the axis parameters to be chosen between X_, Y_, Z_ (two consecutive axis cannot be the same)
• depending of the euler order

Template parameters

• I, J, K: actual parameters can be chosen between axis values X_, Y_, Z_ from which I, J and K are deduced

The computation method is taken from the article: "Quaternion to Euler angles conversion: A direct, general and computationally efficient method". PLoS ONE 17(11): e0276302. https://doi.org/10.1371/journal pone 0276302. Evandro Bernardes, and Stephane Viollet

Return value

kumi tuple of the three euler angles in radian. In case of singularity the first angle is 0.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::average;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
  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);
  e_t e1(2);
  std::cout << e0 << ", " << e1 << " -> "  << average(e0, e1) << "\n";
  std::cout << e0 << ", " << e0 << " -> "  << average(e0, e0) << "\n";
  we_t we0(e0);
  we_t we1(e1);
  std::cout << we0 << ", " << we1 << " -> " << average(we0, we1) << "\n";
 
  std::cout << "Complex:     "<< "\n";
  c_t c0(1, 5);
  c_t c1(5, 9);
  std::cout << c0 << ", " << c1 << " -> "  << average(c0, c1) << "\n";
  std::cout << c0 << ", " << c0 << " -> "  << average(c0, c0) << "\n";
  wc_t wc0(c0, c1);
  wc_t wc1(c1, c1);
  std::cout << wc0 << ", " << wc1 << " -> " << average(wc0, wc1) << "\n";
 
  std::cout << "Quaternion:  "<< "\n";
  q_t q0(1, 5, 2, 3);
  q_t q1(5, 9, 6, 7);
  std::cout << q0 << ", " << q1 << " -> "  << average(q0, q1) << "\n";
  std::cout << q0 << ", " << q0 << " -> "  << average(q0, q0) << "\n";
  wq_t wq0(q0, q1);
  wq_t wq1(q1, q1);
  std::cout << wq0 << ", " << wq1 << " -> " << average(wq0, wq1) << "\n";
 
  std::cout << "Mixed:  "<< "\n";
  std::cout << kyosu::average(c0, q1) << std::endl;
  std::cout << kyosu::average(e0, q1) << std::endl;
  std::cout << kyosu::average(c0, wq1) << std::endl;
  std::cout << kyosu::average(we0, q1) << std::endl;
 
  return 0;
}