from_semipolar

auto kyosu::from_semipolar = eve::functor<from_semipolar_t>

inlineconstexpr

Callable object computing a quaternion from its semipolar representation.

This function build quaternions in a way similar to the way polar builds complex numbers from a polar representation of an \(\mathbb{R}^2\) element.

Header file

#include kyosu/module/quaternion.hpp>`

Callable Signatures

namespace kyosu
{
  auto from_semipolar(auto rho, auto alpha, auto theta1, auto theta2) const        noexcept;
  auto from_semipolar[radpi](auto rho, auto alpha, auto theta1, auto theta2) const noexcept;
}

Parameters

• r, alpha, theta1, theta2

Return value

• the quaternion value.
• If radpi is used alpha, theta1 and theta2must be given in \(\pi\) multiples else in radian.

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::from_semipolar;
 
  auto rho = 2.0;
  auto alpha = eve::pio_3(eve::as(rho));
  auto theta1 = eve::pio_4(eve::as(rho));
  auto theta2 = eve::pio_2(eve::as(rho));
  std::cout << " <- rho " << rho << std::endl;
  std::cout << " <- alpha " << alpha << std::endl;
  std::cout << " <- theta1 " << theta1 << std::endl;
  std::cout << " <- theta2 " << theta2 << std::endl;
  std::cout << " -> " << from_semipolar(rho, alpha, theta1, theta2) << "\n";
 
  return 0;
}