source/src/animation/easings.hpp

/*
 * 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_EASINGS_HPP
#define ANTKEEPER_EASINGS_HPP

#include <vmq/vmq.hpp>
#include <cmath>

template <typename T, typename S>
inline T ease_linear(const T& x, const T& y, S a)
{
	return (y - x) * a + x;
}

template <typename T, typename S>
T ease_in_sine(const T& x, const T& y, S a)
{
	return -(y - x) * std::cos(a * vmq::half_pi<S>) + (y - x) + x;
}

template <typename T, typename S>
T ease_out_sine(const T& x, const T& y, S a)
{
	return (y - x) * std::sin(a * vmq::half_pi<S>) + x;
}

template <typename T, typename S>
T ease_in_out_sine(const T& x, const T& y, S a)
{
	return -(y - x) * S(0.5) * (std::cos(vmq::pi<S> * a) - S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_quad(const T& x, const T& y, S a)
{
	return (y - x) * a * a + x;
}

template <typename T, typename S>
T ease_out_quad(const T& x, const T& y, S a)
{
	return -(y - x) * a * (a - S(2.0)) + x;
}

template <typename T, typename S>
T ease_in_out_quad(const T& x, const T& y, S a)
{
	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * a * a + x;
	}

	a -= S(1.0);
	return -(y - x) * S(0.5) * (a * (a - S(2.0)) - S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_cubic(const T& x, const T& y, S a)
{
	return (y - x) * a * a * a + x;
}

template <typename T, typename S>
T ease_out_cubic(const T& x, const T& y, S a)
{
	a -= S(1.0);
	return (y - x) * (a * a * a + S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_out_cubic(const T& x, const T& y, S a)
{
	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * a * a * a + x;
	}
	
	a -= S(2.0);
	return (y - x) * S(0.5) * (a * a * a + S(2.0)) + x;
}

template <typename T, typename S>
T ease_in_quart(const T& x, const T& y, S a)
{
	return (y - x) * a * a * a * a + x;
}

template <typename T, typename S>
T ease_out_quart(const T& x, const T& y, S a)
{
	a -= S(1.0);
	return -(y - x) * (a * a * a * a - S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_out_quart(const T& x, const T& y, S a)
{
	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * a * a * a * a + x;
	}
	
	a -= S(2.0);
	return -(y - x) * S(0.5) * (a * a * a * a - S(2.0)) + x;
}

template <typename T, typename S>
T ease_in_quint(const T& x, const T& y, S a)
{
	return (y - x) * a * a * a * a * a + x;
}

template <typename T, typename S>
T ease_out_quint(const T& x, const T& y, S a)
{
	a -= S(1.0);
	return (y - x) * (a * a * a * a * a + S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_out_quint(const T& x, const T& y, S a)
{
	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * a * a * a * a * a + x;
	}
	
	a -= S(2.0);
	return (y - x) * S(0.5) * (a * a * a * a * a + S(2.0)) + x;
}

template <typename T, typename S>
T ease_in_expo(const T& x, const T& y, S a)
{
	if (a == S(0.0))
	{
		return x;
	}

	return (y - x) * std::pow(S(2.0), S(10.0) * (a - S(1.0))) + x;
}

template <typename T, typename S>
T ease_out_expo(const T& x, const T& y, S a)
{
	if (a == S(1.0))
	{
		return y;
	}

	return (y - x) * (-std::pow(S(2.0), -S(10.0) * a) + S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_out_expo(const T& x, const T& y, S a)
{
	if (a == S(0.0))
	{
		return x;
	}
	else if (a == S(1.0))
	{
		return y;
	}

	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * std::pow(S(2.0), S(10.0) * (a - S(1.0))) + x;
	}

	a -= S(1.0);
	return (y - x) * S(0.5) * (-std::pow(S(2.0), -S(10.0) * a) + S(2.0)) + x;
}

template <typename T, typename S>
T ease_in_circ(const T& x, const T& y, S a)
{
	return -(y - x) * (std::sqrt(S(1.0) - a * a) - S(1.0)) + x;
}

template <typename T, typename S>
T ease_out_circ(const T& x, const T& y, S a)
{
	a -= S(1.0);
	return (y - x) * std::sqrt(S(1.0) - a * a) + x;
}

template <typename T, typename S>
T ease_in_out_circ(const T& x, const T& y, S a)
{
	a *= S(2.0);
	if (a < S(1.0))
	{
		return -(y - x) * S(0.5) * (std::sqrt(S(1.0) - a * a) - S(1.0)) + x;
	}
	
	a -= S(2.0);
	return (y - x) * S(0.5) * (std::sqrt(S(1.0) - a * a) + S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_back(const T& x, const T& y, S a)
{
	const S s = S(1.70158);
	return (y - x) * a * a * ((s + S(1.0)) * a - s) + x;
}

template <typename T, typename S>
T ease_out_back(const T& x, const T& y, S a)
{
	const S s = S(1.70158);
	a -= S(1.0);
	return (y - x) * (a * a * ((s + S(1.0)) * a + s) + S(1.0)) + x;
}

template <typename T, typename S>
T ease_in_out_back(const T& x, const T& y, S a)
{
	const S s = S(1.70158) * S(1.525f);

	a *= S(2.0);
	if (a < S(1.0))
	{
		return (y - x) * S(0.5) * (a * a * ((s + S(1.0)) * a - s)) + x;
	}

	a -= S(2.0);
	return (y - x) * S(0.5) * (a * a * ((s + S(1.0)) * a + s) + S(2.0)) + x;
}

#endif // ANTKEEPER_EASINGS_HPP