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godot/scene/animation/easing_equations.h
Rémi Verschelde 1426cd3b3a
One Copyright Update to rule them all 
As many open source projects have started doing it, we're removing the
current year from the copyright notice, so that we don't need to bump
it every year.

It seems like only the first year of publication is technically
relevant for copyright notices, and even that seems to be something
that many companies stopped listing altogether (in a version controlled
codebase, the commits are a much better source of date of publication
than a hardcoded copyright statement).

We also now list Godot Engine contributors first as we're collectively
the current maintainers of the project, and we clarify that the
"exclusive" copyright of the co-founders covers the timespan before
opensourcing (their further contributions are included as part of Godot
Engine contributors).

Also fixed "cf." Frenchism - it's meant as "refer to / see".

Backported from #70885.
2023-01-10 15:26:54 +01:00

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/**************************************************************************/
/* 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. */
/**************************************************************************/
/*
* 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.
*/
#ifndef EASING_EQUATIONS_H
#define EASING_EQUATIONS_H
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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return out(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, 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);
}
return in(t * 2 - d, b + c / 2, c / 2, d);
}
}; // namespace back
#endif // EASING_EQUATIONS_H
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