coordinates.h

// Description: Conversion between coordinate systems
// Detail: Cartesian, cylinder, and spherical coordinate systems.

#ifndef PASTELMATH_COORDINATES_H
#define PASTELMATH_COORDINATES_H

#include "pastel/sys/mytypes.h"
#include "pastel/sys/vector.h"

namespace Pastel
{

    //! Converts cartesian coordinates to generalized cylinder coordinates.
    /*!
   Preconditions:
   k >= 0
   k <= cartesian.n()

   The generalized cylinder coordinates are computed as follows.
   Given a Cartesian coordinate vector (x, y) in R^n, with 
   x in R^k, and z in R^(n - k), the generalized cylinder coordinates 
   are given by (s, y), where s = spherical coordinates of x:
   
   s_1 = sqrt((x_1)^2 + ... + (x_k)^2)
   s_i = atan(sqrt((x_i)^2 + ... + (x_k)^2) / x_(i - 1)), for i in ]1, k[.
   s_k = atan(x_k / x_(k - 1))
   */
    template <typename Real, integer N>
    Vector<Real, N> cartesianToCylinder(
        const Vector<Real, N>& cartesian, integer k);

    //! Converts generalized cylinder coordinates to cartesian coordinates.
    /*!
   Preconditions:
   k >= 0
   k <= cylinder.n()

   Given generalized cylinder coordinates (s, y) in R^n
   (s in R^k), the Cartesian coordinates (x, y) in R^n
   (x in R^k) are computed by converting s from spherical 
   coordinates to Cartesian coordinates:

   x_1 = s_1 cos(s_2)
   x_i = s_1 sin(s_2) ... sin(s_i) cos(s_(i + 1)), for i in ]1, k[.
   x_k = s_1 sin(s_2) ... sin(s_(k - 1)) sin(s_(k))
   */

    template <typename Real, integer N>
    Vector<Real, N> cylinderToCartesian(
        const Vector<Real, N>& cylinder, integer k);

    //! Converts cartesian coordinates to cylinder coordinates.
    /*!
   This is a convenience function that calls
   cartesianToCylinder(cartesian, dimension - 1).
   */
    template <typename Real, integer N>
    Vector<Real, N> cartesianToCylinder(
        const Vector<Real, N>& cartesian);

    //! Converts cylinder coordinates to cartesian coordinates.
    /*!
   This is a convenience function that calls
   cylinderToCartesian(cartesian, dimension - 1).
   */
    template <typename Real, integer N>
    Vector<Real, N> cylinderToCartesian(
        const Vector<Real, N>& cylinder);

    //! Converts cartesian coordinates to spherical coordinates.
    /*!
   This is a convenience function that calls
   cartesianToCylinder(cartesian, dimension).
   */
    template <typename Real, integer N>
    Vector<Real, N> cartesianToSpherical(
        const Vector<Real, N>& cartesian);

    //! Converts spherical coordinates to cartesian coordinates.
    /*!
   This is a convenience function that calls
   cylinderToCartesian(cartesian, dimension).
   */
    template <typename Real, integer N>
    Vector<Real, N> sphericalToCartesian(
        const Vector<Real, N>& spherical);

}

#include "pastel/math/coordinate/coordinates.hpp"

#endif