Move Penner easing equations to thirdparty/misc

It was Godot-ified and integrated into Tween originally (#628)
without mention that it was thirdparty code, but it's actually
derived from https://github.com/jesusgollonet/ofpennereasing.

It's also very bad quality code and should be replaced by a better,
properly-maintained library of easing equations.

1 files changed, 308 insertions, 0 deletions

diff --git a/thirdparty/misc/easing_equations.cpp b/thirdparty/misc/easing_equations.cpp
new file mode 100644
index 0000000000..bc84564b19
--- /dev/null
+++ b/thirdparty/misc/easing_equations.cpp
@@ -0,0 +1,308 @@
+/**
+ *  Adapted from Penner Easing equations' C++ port.
+ *  Source: https://github.com/jesusgollonet/ofpennereasing
+ *  License: BSD-3-clause
+ */
+
+#include "scene/animation/tween.h"
+
+const real_t pi = 3.1415926535898;
+
+///////////////////////////////////////////////////////////////////////////
+// linear
+///////////////////////////////////////////////////////////////////////////
+namespace linear {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	return c * t / d + b;
+}
+
+static real_t out(real_t t, real_t b, real_t c, real_t d) {
+	return c * t / d + b;
+}
+
+static real_t in_out(real_t t, real_t b, real_t c, real_t d) {
+	return c * t / d + b;
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return c * t / d + b;
+}
+}; // namespace linear
+///////////////////////////////////////////////////////////////////////////
+// sine
+///////////////////////////////////////////////////////////////////////////
+namespace sine {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	return -c * cos(t / d * (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 * (pi / 2)) + b;
+}
+
+static real_t in_out(real_t t, real_t b, real_t c, real_t d) {
+	return -c / 2 * (cos(pi * t / d) - 1) + b;
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace sine
+///////////////////////////////////////////////////////////////////////////
+// quint
+///////////////////////////////////////////////////////////////////////////
+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) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace quint
+///////////////////////////////////////////////////////////////////////////
+// quart
+///////////////////////////////////////////////////////////////////////////
+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) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace quart
+///////////////////////////////////////////////////////////////////////////
+// quad
+///////////////////////////////////////////////////////////////////////////
+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 = 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) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace quad
+///////////////////////////////////////////////////////////////////////////
+// expo
+///////////////////////////////////////////////////////////////////////////
+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) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace expo
+///////////////////////////////////////////////////////////////////////////
+// elastic
+///////////////////////////////////////////////////////////////////////////
+namespace elastic {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	if (t == 0) return b;
+	if ((t /= d) == 1) return b + c;
+	float p = d * 0.3f;
+	float a = c;
+	float s = p / 4;
+	float postFix = a * pow(2, 10 * (t -= 1)); // this is a fix, again, with post-increment operators
+	return -(postFix * sin((t * d - s) * (2 * pi) / p)) + b;
+}
+
+static real_t out(real_t t, real_t b, real_t c, real_t d) {
+	if (t == 0) return b;
+	if ((t /= d) == 1) return b + c;
+	float p = d * 0.3f;
+	float a = c;
+	float s = p / 4;
+	return (a * pow(2, -10 * t) * sin((t * d - s) * (2 * 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) {
+		float postFix = a * pow(2, 10 * (t -= 1)); // postIncrement is evil
+		return -0.5f * (postFix * sin((t * d - s) * (2 * pi) / p)) + b;
+	}
+	float postFix = a * pow(2, -10 * (t -= 1)); // postIncrement is evil
+	return postFix * sin((t * d - s) * (2 * pi) / p) * 0.5f + c + b;
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace elastic
+///////////////////////////////////////////////////////////////////////////
+// cubic
+///////////////////////////////////////////////////////////////////////////
+namespace cubic {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	return c * (t /= d) * 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) {
+	if ((t /= d / 2) < 1) return c / 2 * t * t * t + b;
+	return c / 2 * ((t -= 2) * t * t + 2) + b;
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace cubic
+///////////////////////////////////////////////////////////////////////////
+// circ
+///////////////////////////////////////////////////////////////////////////
+namespace circ {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	return -c * (sqrt(1 - (t /= d) * t) - 1) + b; // TODO: ehrich: operation with t is undefined
+}
+
+static real_t out(real_t t, real_t b, real_t c, real_t d) {
+	return c * sqrt(1 - (t = t / d - 1) * t) + b; // TODO: ehrich: operation with t is undefined
+}
+
+static real_t in_out(real_t t, real_t b, real_t c, real_t d) {
+	if ((t /= d / 2) < 1) return -c / 2 * (sqrt(1 - t * t) - 1) + b;
+	return c / 2 * (sqrt(1 - t * (t -= 2)) + 1) + b; // TODO: ehrich: operation with t is undefined
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace circ
+///////////////////////////////////////////////////////////////////////////
+// bounce
+///////////////////////////////////////////////////////////////////////////
+namespace bounce {
+static real_t out(real_t t, real_t b, real_t c, real_t d);
+
+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 out(real_t t, real_t b, real_t c, real_t d) {
+	if ((t /= d) < (1 / 2.75f)) {
+		return c * (7.5625f * t * t) + b;
+	} else if (t < (2 / 2.75f)) {
+		float postFix = t -= (1.5f / 2.75f);
+		return c * (7.5625f * (postFix)*t + .75f) + b;
+	} else if (t < (2.5 / 2.75)) {
+		float postFix = t -= (2.25f / 2.75f);
+		return c * (7.5625f * (postFix)*t + .9375f) + b;
+	} else {
+		float postFix = t -= (2.625f / 2.75f);
+		return c * (7.5625f * (postFix)*t + .984375f) + b;
+	}
+}
+
+static real_t in_out(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? in(t * 2, b, c / 2, d) : 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) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace bounce
+///////////////////////////////////////////////////////////////////////////
+// back
+///////////////////////////////////////////////////////////////////////////
+namespace back {
+static real_t in(real_t t, real_t b, real_t c, real_t d) {
+	float s = 1.70158f;
+	float postFix = t /= d;
+	return c * (postFix)*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;
+	return c * ((t = t / d - 1) * t * ((s + 1) * t + s) + 1) + b; // TODO: ehrich: operation with t is undefined
+}
+
+static real_t in_out(real_t t, real_t b, real_t c, real_t d) {
+	float s = 1.70158f;
+	if ((t /= d / 2) < 1) return c / 2 * (t * t * (((s *= (1.525f)) + 1) * t - s)) + b; // TODO: ehrich: operation with s is undefined
+	float postFix = t -= 2;
+	return c / 2 * ((postFix)*t * (((s *= (1.525f)) + 1) * t + s) + 2) + b; // TODO: ehrich: operation with s is undefined
+}
+
+static real_t out_in(real_t t, real_t b, real_t c, real_t d) {
+	return (t < d / 2) ? out(t * 2, b, c / 2, d) : in((t * 2) - d, b + c / 2, c / 2, d);
+}
+}; // namespace back
+
+Tween::interpolater Tween::interpolaters[Tween::TRANS_COUNT][Tween::EASE_COUNT] = {
+	{ &linear::in, &linear::out, &linear::in_out, &linear::out_in },
+	{ &sine::in, &sine::out, &sine::in_out, &sine::out_in },
+	{ &quint::in, &quint::out, &quint::in_out, &quint::out_in },
+	{ &quart::in, &quart::out, &quart::in_out, &quart::out_in },
+	{ &quad::in, &quad::out, &quad::in_out, &quad::out_in },
+	{ &expo::in, &expo::out, &expo::in_out, &expo::out_in },
+	{ &elastic::in, &elastic::out, &elastic::in_out, &elastic::out_in },
+	{ &cubic::in, &cubic::out, &cubic::in_out, &cubic::out_in },
+	{ &circ::in, &circ::out, &circ::in_out, &circ::out_in },
+	{ &bounce::in, &bounce::out, &bounce::in_out, &bounce::out_in },
+	{ &back::in, &back::out, &back::in_out, &back::out_in },
+};
+
+real_t Tween::_run_equation(TransitionType p_trans_type, EaseType p_ease_type, real_t t, real_t b, real_t c, real_t d) {
+
+	interpolater cb = interpolaters[p_trans_type][p_ease_type];
+	ERR_FAIL_COND_V(cb == NULL, b);
+	return cb(t, b, c, d);
+}