periodic.hpp

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// This file is part of the Acts project.
//
// Copyright (C) 2016-2020 CERN for the benefit of the Acts project
//
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.

#pragma once

#include <cmath>

namespace Acts {
namespace detail {

template <typename T>
inline T wrap_periodic(T value, T start, T range) {
  using std::floor;
  // only wrap if really necessary
  T diff = value - start;
  return ((0 <= diff) && (diff < range))
             ? value
             : (value - range * floor(diff / range));
}

template <typename T>
inline T difference_periodic(T lhs, T rhs, T range) {
  using std::fmod;
  T delta = fmod(lhs - rhs, range);
  // check if |delta| is larger than half the range. if that is the case, we
  // can move either rhs/lhs by one range/period to get a smaller |delta|.
  if ((2 * delta) < -range) {
    delta += range;
  } else if (range <= (2 * delta)) {
    delta -= range;
  }
  return delta;
}

template <typename T>
inline T radian_pos(T x) {
  return wrap_periodic<T>(x, T(0), T(2 * M_PI));
}

template <typename T>
inline T radian_sym(T x) {
  return wrap_periodic<T>(x, T(-M_PI), T(2 * M_PI));
}

template <typename T>
inline std::pair<T, T> normalizePhiTheta(T phi, T theta) {
  // wrap to [0,2pi). while the nominal range of theta is [0,pi], it is
  // periodic, i.e. describes identical positions, in the full [0,2pi) range.
  // moving it first to the periodic range simplifies further steps as the
  // possible range of theta becomes fixed.
  theta = radian_pos(theta);
  if (M_PI < theta) {
    // theta is in the second half of the great circle and outside its nominal
    // range. need to change both phi and theta to be within range.
    phi += M_PI;
    theta = 2 * M_PI - theta;
  }
  return {radian_sym(phi), theta};
}

}  // namespace detail
}  // namespace Acts