simgear/simgear/props/easing_functions.cxx

///@file
/// Easing functions for property interpolation.
///
/// Based on easing functions by Robert Penner
/// (http://www.robertpenner.com/easing)
//
// Copyright (C) 2013  Thomas Geymayer <tomgey@gmail.com>
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public
// License as published by the Free Software Foundation; either
// version 2 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA

#include "easing_functions.hxx"
#include <simgear/math/SGMath.hxx>


namespace simgear
{

  /// Simple linear easing.
  double easingLinear(double t)
  {
    return t;
  }

  /// http://easings.net/#easeInSine
  double easeInSine(double t)
  {
    return 1 - std::cos(t * M_PI_2);
  }

  /// http://easings.net/#easeOutSine
  double easeOutSine(double t)
  {
    return std::sin(t * M_PI_2);
  }

  /// http://easings.net/#easeInOutSine
  double easeInOutSine(double t)
  {
    return 0.5 - 0.5 * std::cos(t * M_PI);
  }

  template<easing_func_t easeIn, easing_func_t easeOut>
  double easeInOut(double t)
  {
    if( (t *= 2) < 1 )
      return 0.5 * (*easeIn)(t);
    else
      return 0.5 + 0.5 * (*easeOut)(t - 1);
  }

  /**
   * Helper for exponential ease out with integer exponent.
   *
   * @tparam N      Exponent.
   * @tparam is_odd If the exponent is odd.
   */
  template<size_t N, bool is_odd>
  struct easeOutImpl;

  /**
   * Ease out with odd integer exponent.
   *
   * @tparam N Exponent.
   * @see http://easings.net/#easeOutCubic (N = 3)
   * @see http://easings.net/#easeOutQuint (N = 5)
   */
  template<size_t N>
  struct easeOutImpl<N, true>
  {
    static double calc(double t)
    {
      return SGMiscd::pow<N>(t - 1) + 1;
    }
  };

  /**
   * Ease out with even integer exponent.
   *
   * @tparam N Exponent.
   * @see http://easings.net/#easeOutQuad  (N = 2)
   * @see http://easings.net/#easeOutQuart (N = 4)
   */
  template<size_t N>
  struct easeOutImpl<N, false>
  {
    static double calc(double t)
    {
      return -SGMiscd::pow<N>(t - 1) + 1;
    }
  };

  /**
   * Exponential ease out with integer exponent.
   *
   * @see http://easings.net/#easeOutQuad  (N = 2)
   * @see http://easings.net/#easeOutCubic (N = 3)
   * @see http://easings.net/#easeOutQuart (N = 4)
   * @see http://easings.net/#easeOutQuint (N = 5)
   * @see easeOutImpl
   */
  template<size_t N>
  double easeOutPow(double t)
  {
    return easeOutImpl<N, N & 1>::calc(t);
  }

  /// http://easings.net/#easeInOutQuad  (N = 2)
  /// http://easings.net/#easeInOutCubic (N = 3)
  /// http://easings.net/#easeInOutQuart (N = 4)
  /// http://easings.net/#easeInOutQuint (N = 5)
  template<size_t N>
  double easeInOutPow(double t)
  {
    return easeInOut<&SGMiscd::pow<N>, &easeOutPow<N> >(t);
  }

  /// http://easings.net/#easeInExpo
  double easeInExpo(double t)
  {
    return (t == 0) ? 0 : std::pow(2, 10 * (t - 1));
  }

  /// http://easings.net/#easeOutExpo
  double easeOutExpo(double t)
  {
    return (t == 1) ? 1 : 1 - std::pow(2, -10 * t);
  }

  /// http://easings.net/#easeInCirc
  double easeInCirc(double t)
  {
    return 1 - std::sqrt(1 - SGMiscd::pow<2>(t));
  }

  /// http://easings.net/#easeOutCirc
  double easeOutCirc(double t)
  {
    return std::sqrt(1 - SGMiscd::pow<2>(t - 1));
  }

  static const double ease_s = 1.70158;

  /// http://easings.net/#easeInBack
  double easeInBack(double t)
  {

    return SGMiscd::pow<2>(t) * ((ease_s + 1) * t - ease_s);
  }

  /// http://easings.net/#easeOutBack
  double easeOutBack(double t)
  {
    t -= 1;
    return SGMiscd::pow<2>(t) * ((ease_s + 1) * t + ease_s) + 1;
  }

  /// http://easings.net/#easeOutBack
  double easeInElastic(double t)
  {
    if( t == 0 )
      return 0;
    if( t == 1 )
      return 1;

    t -= 1;
    const double p = .3;
    const double s = p * 0.25;

    return -std::pow(2, 10 * t) * std::sin((t - s) * 2 * M_PI / p);
  }

  /// http://easings.net/#easeOutBack
  double easeOutElastic(double t)
  {
    if( t == 0 )
      return 0;
    if( t == 1 )
      return 1;

    const double p = .3;
    const double s = p * 0.25;

    return std::pow(2, -10 * t) * std::sin((t - s) * 2 * M_PI / p) + 1;
  }

  /// http://easings.net/#easeOutBounce
  double easeOutBounce(double t)
  {
    if( t < 1/2.75 )
      return 7.5625 * SGMiscd::pow<2>(t);
    else if( t < 2/2.75 )
      return 7.5625 * SGMiscd::pow<2>(t - 1.5/2.75) + .75;
    else if( t < 2.5/2.75 )
      return 7.5625 * SGMiscd::pow<2>(t - 2.25/2.75) + .9375;
    else
      return 7.5625 * SGMiscd::pow<2>(t - 2.625/2.75) + .984375;
  }

  /// http://easings.net/#easeInBounce
  double easeInBounce(double time)
  {
    return 1 - easeOutBounce(1 - time);
  }

#define SG_ADD_EASING(name) {#name, &name},
#define SG_STR(str) #str
#define SG_ADD_EASING_IN_OUT(name)\
          SG_ADD_EASING(easeIn##name)\
          SG_ADD_EASING(easeOut##name)\
          {SG_STR(easeInOut##name), &easeInOut<&easeIn##name, &easeOut##name>},

  const EasingMapEntry easing_functions[] = {
    {"linear", &easingLinear},
    {"swing", &easeInOutSine},
    SG_ADD_EASING_IN_OUT(Sine)
    {"easeInQuad",    &SGMiscd::pow<2>},
    {"easeInCubic",   &SGMiscd::pow<3>},
    {"easeInQuart",   &SGMiscd::pow<4>},
    {"easeInQuint",   &SGMiscd::pow<5>},
    {"easeOutQuad",   &easeOutPow<2>},
    {"easeOutCubic",  &easeOutPow<3>},
    {"easeOutQuart",  &easeOutPow<4>},
    {"easeOutQuint",  &easeOutPow<5>},
    {"easeInOutQuad", &easeInOutPow<2>},
    {"easeInOutCubic",&easeInOutPow<3>},
    {"easeInOutQuart",&easeInOutPow<4>},
    {"easeInOutQuint",&easeInOutPow<5>},
    SG_ADD_EASING_IN_OUT(Expo)
    SG_ADD_EASING_IN_OUT(Circ)
    SG_ADD_EASING_IN_OUT(Back)
    SG_ADD_EASING_IN_OUT(Elastic)
    SG_ADD_EASING_IN_OUT(Bounce)
    {0, 0}
  };

#undef SG_ADD_EASING
#undef SG_STR
#undef SG_ADD_EASING_IN_OUT

} // namespace simgear