slerp

kyosu::slerp = {}

inlineconstexpr

Computes the spherical interpolation between unitary quaternions.

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  constexpr auto slerp(auto z0, auto z1, floating_ordered_value t) noexcept;
}

Parameters

• z0, z1: unitary quaternions to process.
• t: floating value interpolation coefficient.

Return value

The value of the spherical interpolation (or extrapolation) between z0 and z1 is returned. The functions asserts if the quaternions are not unitary.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::slerp;
  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>>;
  using kyosu::sign;
 
  std::cout << "Real:        "<< "\n";
  e_t e0(1);
  e_t e1(-1);
  e_t t(0.3);
  std::cout << e0 << ", " << e1 << ", " << t << " -> "  << slerp(e0, e1, t) << "\n";
  std::cout << e0 << ", " << e0 << ", " << t << " -> "  << slerp(e0, e0, t) << "\n";
  we_t we0(e0);
  we_t we1(e1);
  std::cout << we0 << ", " << we1 << ", " << t<< " -> " << slerp(we0, we1, t) << "\n";
 
  std::cout << "Complex:     "<< "\n";
  c_t c0(1, 5);
  c_t c1(5, 9);
  c0 = sign(c0);
  c1 = sign(c1);
  std::cout << c0 << ", " << c1 << ", " << t << " -> "  << slerp(c0, c1, t) << "\n";
  std::cout << c0 << ", " << c0 << ", " << t << " -> "  << slerp(c0, c0, t) << "\n";
  wc_t wc0(c0, c1);
  wc_t wc1(c1, c1);
  std::cout << wc0 << ", " << wc1 << ", " << t << " -> " << slerp(wc0, wc1, t) << "\n";
 
  std::cout << "Quaternion:  "<< "\n";
  q_t q0(1, 5, 2, 3);
  q_t q1(5, 9, 6, 7);
  q0 = sign(q0);
  q1 = sign(q1);
  std::cout << q0 << ", " << q1 << ", " << t << " -> "  << slerp(q0, q1, t) << "\n";
  std::cout << q0 << ", " << q0 << ", " << t << " -> "  << slerp(q0, q0, t) << "\n";
  wq_t wq0(q0, q1);
  wq_t wq1(q1, q1);
  std::cout << wq0 << ", " << wq1 << ", " << t << " -> " << slerp(wq0, wq1, t) << "\n";
 
  std::cout << "Mixed:  "<< "\n";
  std::cout << c0 << ", " << q1 << ", " << t << " -> "  << kyosu::slerp(c0, q1, t) << std::endl;
  std::cout << e0 << ", " << q1 << ", " << t << " -> "  << kyosu::slerp(e0, q1, t) << std::endl;
  std::cout << c0 << ", " << wq1<< ", " << t << " -> "  << kyosu::slerp(c0, wq1, t) << std::endl;
  std::cout << we0<< ", " << wq1 << ", " << t << " -> " << kyosu::slerp(we0, wq1, t) << std::endl;
  std::cout << we0<< ", " << q1 << ", " << t << " -> "  << kyosu::slerp(we0, q1, t) << std::endl;
 
  return 0;
}