/**************************************************************************/ /* easing_equations.h */ /**************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /**************************************************************************/ /* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */ /* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */ /* */ /* Permission is hereby granted, free of charge, to any person obtaining */ /* a copy of this software and associated documentation files (the */ /* "Software"), to deal in the Software without restriction, including */ /* without limitation the rights to use, copy, modify, merge, publish, */ /* distribute, sublicense, and/or sell copies of the Software, and to */ /* permit persons to whom the Software is furnished to do so, subject to */ /* the following conditions: */ /* */ /* The above copyright notice and this permission notice shall be */ /* included in all copies or substantial portions of the Software. */ /* */ /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ /* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */ /* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ /* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ /* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ /* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ /**************************************************************************/ #ifndef EASING_EQUATIONS_H #define EASING_EQUATIONS_H /* * Derived from Robert Penner's easing equations: http://robertpenner.com/easing/ * * Copyright (c) 2001 Robert Penner * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the "Software"), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in all * copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE * SOFTWARE. */ namespace linear { static real_t in(real_t t, real_t b, real_t c, real_t d) { return c * t / d + b; } }; // namespace linear namespace sine { static real_t in(real_t t, real_t b, real_t c, real_t d) { return -c * cos(t / d * (Math_PI / 2)) + c + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { return c * sin(t / d * (Math_PI / 2)) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { return -c / 2 * (cos(Math_PI * t / d) - 1) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace sine namespace quint { static real_t in(real_t t, real_t b, real_t c, real_t d) { return c * pow(t / d, 5) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { return c * (pow(t / d - 1, 5) + 1) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { t = t / d * 2; if (t < 1) { return c / 2 * pow(t, 5) + b; } return c / 2 * (pow(t - 2, 5) + 2) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace quint namespace quart { static real_t in(real_t t, real_t b, real_t c, real_t d) { return c * pow(t / d, 4) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { return -c * (pow(t / d - 1, 4) - 1) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { t = t / d * 2; if (t < 1) { return c / 2 * pow(t, 4) + b; } return -c / 2 * (pow(t - 2, 4) - 2) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace quart namespace quad { static real_t in(real_t t, real_t b, real_t c, real_t d) { return c * pow(t / d, 2) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { t /= d; return -c * t * (t - 2) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { t = t / d * 2; if (t < 1) { return c / 2 * pow(t, 2) + b; } return -c / 2 * ((t - 1) * (t - 3) - 1) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace quad namespace expo { static real_t in(real_t t, real_t b, real_t c, real_t d) { if (t == 0) { return b; } return c * pow(2, 10 * (t / d - 1)) + b - c * 0.001; } static real_t out(real_t t, real_t b, real_t c, real_t d) { if (t == d) { return b + c; } return c * 1.001 * (-pow(2, -10 * t / d) + 1) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { if (t == 0) { return b; } if (t == d) { return b + c; } t = t / d * 2; if (t < 1) { return c / 2 * pow(2, 10 * (t - 1)) + b - c * 0.0005; } return c / 2 * 1.0005 * (-pow(2, -10 * (t - 1)) + 2) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace expo namespace elastic { static real_t in(real_t t, real_t b, real_t c, real_t d) { if (t == 0) { return b; } t /= d; if (t == 1) { return b + c; } t -= 1; float p = d * 0.3f; float a = c * pow(2, 10 * t); float s = p / 4; return -(a * sin((t * d - s) * (2 * Math_PI) / p)) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { if (t == 0) { return b; } t /= d; if (t == 1) { return b + c; } float p = d * 0.3f; float s = p / 4; return (c * pow(2, -10 * t) * sin((t * d - s) * (2 * Math_PI) / p) + c + b); } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { if (t == 0) { return b; } if ((t /= d / 2) == 2) { return b + c; } float p = d * (0.3f * 1.5f); float a = c; float s = p / 4; if (t < 1) { t -= 1; a *= pow(2, 10 * t); return -0.5f * (a * sin((t * d - s) * (2 * Math_PI) / p)) + b; } t -= 1; a *= pow(2, -10 * t); return a * sin((t * d - s) * (2 * Math_PI) / p) * 0.5f + c + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace elastic namespace cubic { static real_t in(real_t t, real_t b, real_t c, real_t d) { t /= d; return c * t * t * t + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { t = t / d - 1; return c * (t * t * t + 1) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { t /= d / 2; if (t < 1) { return c / 2 * t * t * t + b; } t -= 2; return c / 2 * (t * t * t + 2) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace cubic namespace circ { static real_t in(real_t t, real_t b, real_t c, real_t d) { t /= d; return -c * (sqrt(1 - t * t) - 1) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { t = t / d - 1; return c * sqrt(1 - t * t) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { t /= d / 2; if (t < 1) { return -c / 2 * (sqrt(1 - t * t) - 1) + b; } t -= 2; return c / 2 * (sqrt(1 - t * t) + 1) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace circ namespace bounce { static real_t out(real_t t, real_t b, real_t c, real_t d) { t /= d; if (t < (1 / 2.75f)) { return c * (7.5625f * t * t) + b; } if (t < (2 / 2.75f)) { t -= 1.5f / 2.75f; return c * (7.5625f * t * t + 0.75f) + b; } if (t < (2.5 / 2.75)) { t -= 2.25f / 2.75f; return c * (7.5625f * t * t + 0.9375f) + b; } t -= 2.625f / 2.75f; return c * (7.5625f * t * t + 0.984375f) + b; } static real_t in(real_t t, real_t b, real_t c, real_t d) { return c - out(d - t, 0, c, d) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return in(t * 2, b, c / 2, d); } real_t h = c / 2; return out(t * 2 - d, b + h, h, d); } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace bounce namespace back { static real_t in(real_t t, real_t b, real_t c, real_t d) { float s = 1.70158f; t /= d; return c * t * t * ((s + 1) * t - s) + b; } static real_t out(real_t t, real_t b, real_t c, real_t d) { float s = 1.70158f; t = t / d - 1; return c * (t * t * ((s + 1) * t + s) + 1) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { float s = 1.70158f * 1.525f; t /= d / 2; if (t < 1) { return c / 2 * (t * t * ((s + 1) * t - s)) + b; } t -= 2; return c / 2 * (t * t * ((s + 1) * t + s) + 2) + b; } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace back namespace spring { static real_t out(real_t t, real_t b, real_t c, real_t d) { t /= d; real_t s = 1.0 - t; t = (sin(t * Math_PI * (0.2 + 2.5 * t * t * t)) * pow(s, 2.2) + t) * (1.0 + (1.2 * s)); return c * t + b; } static real_t in(real_t t, real_t b, real_t c, real_t d) { return c - out(d - t, 0, c, d) + b; } static real_t in_out(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return in(t * 2, b, c / 2, d); } real_t h = c / 2; return out(t * 2 - d, b + h, h, d); } static real_t out_in(real_t t, real_t b, real_t c, real_t d) { if (t < d / 2) { return out(t * 2, b, c / 2, d); } real_t h = c / 2; return in(t * 2 - d, b + h, h, d); } }; // namespace spring #endif // EASING_EQUATIONS_H