al_Spherical.hpp

#ifndef INCLUDE_AL_SPHERICAL_HPP
#define INCLUDE_AL_SPHERICAL_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  A collection of classes related to spherical geometry
 
  File author(s):
  Lance Putnam, 2011, putnam.lance@gmail.com
*/
 
#include "al/math/al_Complex.hpp"
#include "al/math/al_Functions.hpp"
#include "al/math/al_Vec.hpp"
 
namespace al {
 
template <class T>
class SphereCoord;
 
typedef SphereCoord<float> SphereCoordf;   
typedef SphereCoord<double> SphereCoordd;  
 
 
template <class T>
void sphericalToCart(T& r2x, T& t2y, T& p2z);
 
template <class T>
void sphericalToCart(T* vec3);
 
 
template <class T>
void cartToSpherical(T& x2r, T& y2t, T& z2p);
 
template <class T>
void cartToSpherical(T* vec3);
 
 
template <int N, class T>
Vec<N - 1, T> sterProj(const Vec<N, T>& v);
 
 
template <class T>
class SphereCoord {
 public:
  typedef Complex<T> C;
 
  C t;  
  C p;  
 
  SphereCoord(const C& theta = C(1, 0), const C& phi = C(1, 0))
      : t(theta), p(phi) {}
 
  template <class U>
  SphereCoord(const Vec<3, U>& v) {
    fromCart(v);
  }
 
  SphereCoord operator-() const { return SphereCoord(t, -p); }
  SphereCoord& operator*=(T v) {
    p *= v;
    return *this;
  }
  SphereCoord operator*(T v) const { return SphereCoord(t, p * v); }
 
  T radius() const { return p.mag(); }
 
  Vec<3, T> toCart() const { return Vec<3, T>(t.r * p.i, t.i * p.i, p.r); }
 
 
  SphereCoord& fromAngle(const T& theta, const T& phi, const T& radius = T(1)) {
    t.fromPolar(theta);
    p.fromPolar(radius, phi);
    return *this;
  }
 
  template <class U>
  SphereCoord& fromCart(const Vec<3, U>& v) {
    t.set(v[0], v[1]);
    T tmag = t.mag();
    p.set(v[2], tmag);
    tmag != 0 ? t *= (1. / tmag) : t.set(1, 0);
    return *this;
  }
};
 
 
template <int L_MAX = 16>
class SphericalHarmonic {
 public:
  SphericalHarmonic() { createLUT(); }
 
 
  template <class T>
  Complex<T> operator()(int l, int m, const Complex<T>& ctheta,
                        const Complex<T>& cphi) const {
    return coef(l, m) * al::legendreP(l, std::abs(m), cphi.r, cphi.i) *
           expim(m, ctheta);
  }
 
  template <class T>
  static Complex<T> expim(int m, const Complex<T>& ctheta) {
    Complex<T> res = al::powN(ctheta, std::abs(m));
    if (m < 0) res.i = -res.i;
    return res;
  }
 
  static double coef(int l, int m) {
    return l <= L_MAX ? coefTab(l, m) : coefCalc(l, m);
  }
 
  static const double& coefTab(int l, int m) { return LUT(l, m); }
 
  static double coefCalc(int l, int m) {
    int M = std::abs(m);
    double res = ::sqrt((2 * l + 1) / M_4PI) * al::factorialSqrt(l - M) /
                 al::factorialSqrt(l + M);
    return (m < 0 && al::odd(M)) ? -res : res;
  }
 
 private:
  // this holds precomputed coefficients for each basis
  static double& LUT(int l, int m) {
    static double t[L_MAX + 1][L_MAX * 2 + 1];
    return t[l][m + L_MAX];
  }
 
  static void createLUT() {
    static bool make = true;
    if (make) {
      make = false;
      for (int l = 0; l <= L_MAX; ++l) {
        for (int m = -L_MAX; m <= L_MAX; ++m) {
          double c = 0;
          // m must be in [-l,l]
          if (std::abs(m) <= l) c = coefCalc(l, m);
          LUT(l, m) = c;
        }
      }
    }
  }
};
 
static SphericalHarmonic<> spharm;
 
// Implementation
//------------------------------------------------------------------------------
 
template <class T>
void sphericalToCart(T& r, T& t, T& p) {
  T rsinp = r * sin(p);
  T rcosp = r * cos(p);
  r = rsinp * cos(t);
  t = rsinp * sin(t);
  p = rcosp;
}
 
template <class T>
inline void sphericalToCart(T* vec3) {
  sphericalToCart(vec3[0], vec3[1], vec3[2]);
}
 
template <class T>
void cartToSpherical(T& x, T& y, T& z) {
  T r = sqrt(x * x + y * y + z * z);
  T t = atan2(y, x);
  z = acos(z / r);
  y = t;
  x = r;
}
 
template <class T>
inline void cartToSpherical(T* vec3) {
  cartToSpherical(vec3[0], vec3[1], vec3[2]);
}
 
template <int N, class T>
inline Vec<N - 1, T> sterProj(const Vec<N, T>& v) {
  return sub<N - 1>(v) * (T(1) / v[N - 1]);
}
 
}  // namespace al
 
#endif