from_cylindrospherical

auto kyosu::from_cylindrospherical = eve::functor<from_cylindrospherical_t>

inlineconstexpr

Callable object computing a quaternion from its cylindrospherical representation.

cylindrospherical is specific to quaternions. It is often interesting to consider \(\mathbb{H}\) as the cartesian product of \(\mathbb{R}\) by \(\mathbb{R}^3\) (the quaternionic multiplication has then a special form, as given here). This function therefore builds a quaternion from this representation, with the \(\mathbb{R}^3\) component given in usual \(\mathbb{R}^3\) spherical coordinates.

Header file

#include kyosu/quaternion.hpp>`

Callable Signatures

namespace eve
{
  auto from_cylindrospherical(auto t, auto radius, auto longitude, auto latitude) const        noexcept;
  auto from_cylindrospherical[radpi](auto t, auto radius, auto longitude, auto latitude) const noexcept;
}

Parameters

• t, radius: the moduli
• longitude, latitude: angles. If radpi is present they are assumed expressed in \(\pi\) multiples else in radian.

Return value

the quaternion value

---

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::from_cylindrospherical;
  using kyosu::quaternion_t;
 
  auto radius = 2.0;
  auto t = eve::pio_3(eve::as(radius));
  auto longitude = eve::pio_4(eve::as(radius));
  auto latitude = eve::pio_2(eve::as(radius));
  std::cout << " <- radius     " << radius << std::endl;
  std::cout << " <- t          " << t << std::endl;
  std::cout << " <- longitude  " << longitude << std::endl;
  std::cout << " <- latitude   " << latitude << std::endl;
  std::cout << " -> " << from_cylindrospherical(radius, t, longitude, latitude) << "\n";
 
  return 0;
}

cylindrospherical is specific to quaternions. It is often interesting to consider \(\mathbb{H}\) as the cartesian product of \(\mathbb{R}\) by \(\mathbb{R}^3\) (the quaternionic multiplication has then a special form, as given here). This function therefore builds a quaternion from this representation, with the \(\mathbb{R}^3\) component given in usual \(\mathbb{R}^3\) spherical coordinates.

Header file

#include kyosu/quaternion.hpp>`

Callable Signatures

namespace eve
{
  auto from_cylindrospherical(auto t, auto radius, auto longitude, auto latitude) const noexcept;
}

Parameters

• t, radius: the moduli
• longitude, latitude: angles in radian

Return value

the quaternion value

---

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::from_cylindrospherical;
  using kyosu::quaternion_t;
 
  auto radius = 2.0;
  auto t = eve::pio_3(eve::as(radius));
  auto longitude = eve::pio_4(eve::as(radius));
  auto latitude = eve::pio_2(eve::as(radius));
  std::cout << " <- radius     " << radius << std::endl;
  std::cout << " <- t          " << t << std::endl;
  std::cout << " <- longitude  " << longitude << std::endl;
  std::cout << " <- latitude   " << latitude << std::endl;
  std::cout << " -> " << from_cylindrospherical(radius, t, longitude, latitude) << "\n";
 
  return 0;
}