|
@ -0,0 +1,418 @@ |
|
|
|
|
|
/*
|
|
|
|
|
|
* Copyright (C) 2020 Christopher J. Howard |
|
|
|
|
|
* |
|
|
|
|
|
* This file is part of Antkeeper source code. |
|
|
|
|
|
* |
|
|
|
|
|
* Antkeeper source code is free software: you can redistribute it and/or modify |
|
|
|
|
|
* it under the terms of the GNU General Public License as published by |
|
|
|
|
|
* the Free Software Foundation, either version 3 of the License, or |
|
|
|
|
|
* (at your option) any later version. |
|
|
|
|
|
* |
|
|
|
|
|
* Antkeeper source code 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 General Public License for more details. |
|
|
|
|
|
* |
|
|
|
|
|
* You should have received a copy of the GNU General Public License |
|
|
|
|
|
* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
|
|
*/ |
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
|
* Easing Functions (Equations) |
|
|
|
|
|
* |
|
|
|
|
|
* Copyright (C) 2001 Robert Penner |
|
|
|
|
|
* |
|
|
|
|
|
* 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 author nor the names of 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 OWNER 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. |
|
|
|
|
|
*/ |
|
|
|
|
|
|
|
|
|
|
|
#ifndef ANTKEEPER_EASE_HPP
|
|
|
|
|
|
#define ANTKEEPER_EASE_HPP
|
|
|
|
|
|
|
|
|
|
|
|
#include <vmq/vmq.hpp>
|
|
|
|
|
|
#include <cmath>
|
|
|
|
|
|
#include <type_traits>
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
|
* Container for templated easing functions. |
|
|
|
|
|
* |
|
|
|
|
|
* All easing functions require the following operators to be defined: |
|
|
|
|
|
* |
|
|
|
|
|
* value_type operator+(const value_type&, const value_type&); |
|
|
|
|
|
* value_type operator-(const value_type&, const value_type&); |
|
|
|
|
|
* value_type operator*(const value_type&, scalar_type) const; |
|
|
|
|
|
* |
|
|
|
|
|
* @tparam T Value type. |
|
|
|
|
|
* @tparam S Scalar type. |
|
|
|
|
|
*/ |
|
|
|
|
|
template <typename T, typename S = float> |
|
|
|
|
|
struct ease |
|
|
|
|
|
{ |
|
|
|
|
|
typedef T value_type; |
|
|
|
|
|
typedef S scalar_type; |
|
|
|
|
|
|
|
|
|
|
|
/// Linearly interpolates between @p x and @p y.
|
|
|
|
|
|
static T linear(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
/// Logarithmically interpolates between @p x and @p y.
|
|
|
|
|
|
static T log(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_sine(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_sine(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_sine(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_quad(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_quad(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_quad(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_cubic(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_cubic(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_cubic(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_quart(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_quart(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_quart(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_quint(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_quint(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_quint(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_expo(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_expo(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_expo(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_circ(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_circ(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_circ(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_back(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_back(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_back(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_elastic(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_elastic(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_elastic(const T& x, const T& y, S a); |
|
|
|
|
|
|
|
|
|
|
|
static T in_bounce(const T& x, const T& y, S a); |
|
|
|
|
|
static T out_bounce(const T& x, const T& y, S a); |
|
|
|
|
|
static T in_out_bounce(const T& x, const T& y, S a); |
|
|
|
|
|
}; |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
inline T ease<T, S>::linear(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return (y - x) * a + x; |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
inline T ease<T, S>::log(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
//return std::exp(linear(std::log(x), std::log(y), a));
|
|
|
|
|
|
return x * std::pow(y / x, a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_sine(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(y, x, std::cos(a * vmq::half_pi<S>)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_sine(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, std::sin(a * vmq::half_pi<S>)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_sine(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, -(std::cos(a * vmq::pi<S>) - S(1)) * S(0.5)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_quad(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_quad(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (S(2) - a) * a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_quad(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (a < S(0.5)) ? S(2) * a * a : -(S(2) * a * a - S(4) * a + S(1))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_cubic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * a * a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_cubic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * ((a - S(3)) * a + S(3))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_cubic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (a < S(0.5)) ? S(4) * a * a * a : S(4) * a * a * a - S(12) * a * a + S(12) * a - 3); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_quart(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * a * a * a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_quart(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * (a * ((S(4) - a) * a - S(6)) + S(4))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_quart(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (a < S(0.5)) ? S(8) * a * a * a * a : a * (a * ((S(32) - S(8) * a) * a - S(48)) + S(32)) - S(7)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_quint(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * a * a * a * a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_quint(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * (a * (a * ((a - S(5)) * a + S(10)) - S(10)) + S(5))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_quint(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a < S(0.5)) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, S(16) * a * a * a * a * a); |
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
a = S(2) * (S(1) - a); |
|
|
|
|
|
return linear(x, y, S(0.5) * (S(2) - a * a * a * a * a)); |
|
|
|
|
|
} |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_expo(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return (a == S(0)) ? x : linear(x, y, std::pow(S(1024), a - S(1))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_expo(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return (a == S(1)) ? y : linear(y, x, std::pow(S(2), S(-10) * a)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_expo(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a == S(0)) |
|
|
|
|
|
{ |
|
|
|
|
|
return x; |
|
|
|
|
|
} |
|
|
|
|
|
else if (a == S(1)) |
|
|
|
|
|
{ |
|
|
|
|
|
return y; |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
return linear(x, y, (a < S(0.5)) ? std::pow(S(2), S(20) * a - S(11)) : S(1) - std::pow(S(2), S(9) - S(20) * a)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_circ(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(y, x, std::sqrt(S(1) - a * a)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_circ(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, std::sqrt(-(a - S(2)) * a)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_circ(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a < S(0.5)) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, S(0.5) - S(0.5) * std::sqrt(S(1) - S(4) * a * a)); |
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, S(0.5) * (std::sqrt(S(-4) * (a - S(2)) * a - S(3)) + S(1))); |
|
|
|
|
|
} |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_back(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
const S c = S(1.70158); |
|
|
|
|
|
return linear(x, y, a * a * (a * c + a - c)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_back(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
const S c = S(1.70158); |
|
|
|
|
|
a -= S(1); |
|
|
|
|
|
return linear(x, y, a * a * (a * c + a + c) + S(1)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_back(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
const S c = S(1.70158) * S(1.525f); |
|
|
|
|
|
|
|
|
|
|
|
if (a < S(0.5)) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, a * a * (a * (S(4) * c + S(4)) - S(2) * c)); |
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
S b = S(1) - S(2) * a; |
|
|
|
|
|
return linear(x, y, b * b * (a * c + a - c * S(0.5) - S(1)) + S(1)); |
|
|
|
|
|
} |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_elastic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a == S(0)) |
|
|
|
|
|
{ |
|
|
|
|
|
return x; |
|
|
|
|
|
} |
|
|
|
|
|
else if (a == S(1)) |
|
|
|
|
|
{ |
|
|
|
|
|
return y; |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
return linear(x, y, -std::pow(S(1024), a - S(1)) * std::sin(S(20.944) * (a - S(1.075)))); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_elastic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a == S(0)) |
|
|
|
|
|
{ |
|
|
|
|
|
return x; |
|
|
|
|
|
} |
|
|
|
|
|
else if (a == S(1)) |
|
|
|
|
|
{ |
|
|
|
|
|
return y; |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
return linear(x, y, std::pow(S(2), S(-10) * a) * std::sin(S(20.944) * (a - S(0.075))) + S(1)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_elastic(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a == S(0)) |
|
|
|
|
|
{ |
|
|
|
|
|
return x; |
|
|
|
|
|
} |
|
|
|
|
|
else if (a == S(1)) |
|
|
|
|
|
{ |
|
|
|
|
|
return y; |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
if (a < S(0.5)) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, std::pow(S(2), S(20) * a - S(11)) * std::sin(S(15.5334) - S(27.5293) * a)); |
|
|
|
|
|
|
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(y, x, std::pow(2, S(9) - S(20) * a) * std::sin(S(15.5334) - S(27.5293) * a)); |
|
|
|
|
|
} |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_bounce(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, S(1) - ease<S, S>::out_bounce(S(0), S(1), S(1) - a)); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::out_bounce(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
const S n = S(7.5625); |
|
|
|
|
|
const S d = S(2.75); |
|
|
|
|
|
|
|
|
|
|
|
if (a < S(1) / d) |
|
|
|
|
|
{ |
|
|
|
|
|
a = n * a * a; |
|
|
|
|
|
} |
|
|
|
|
|
else if (a < S(2) / d) |
|
|
|
|
|
{ |
|
|
|
|
|
a -= S(1.5) / d; |
|
|
|
|
|
a = n * a * a + S(0.75); |
|
|
|
|
|
} |
|
|
|
|
|
else if (a < S(2.5) / d) |
|
|
|
|
|
{ |
|
|
|
|
|
a -= S(2.25) / d; |
|
|
|
|
|
a = n * a * a + S(0.9375); |
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
a -= S(2.625) / d; |
|
|
|
|
|
a = n * a * a + S(0.984375); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
return linear(x, y, a); |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
template <typename T, typename S> |
|
|
|
|
|
T ease<T, S>::in_out_bounce(const T& x, const T& y, S a) |
|
|
|
|
|
{ |
|
|
|
|
|
if (a < S(0.5)) |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (S(1) - ease<S, S>::out_bounce(S(0), S(1), S(1) - S(2) * a)) * S(0.5)); |
|
|
|
|
|
} |
|
|
|
|
|
else |
|
|
|
|
|
{ |
|
|
|
|
|
return linear(x, y, (S(1) + ease<S, S>::out_bounce(S(0), S(1), S(2) * a - S(1))) * S(0.5)); |
|
|
|
|
|
} |
|
|
|
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
#endif // ANTKEEPER_EASE_HPP
|