EasingFunctions.gd

#Terms of Use: Easing Functions (Equations)
#
#Open source under the MIT License and the 3-Clause BSD License.
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#MIT License
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#Copyright © 2001 Robert Penner
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#BSD License
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#Copyright © 2001 Robert Penner
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# easing functions

# t = elapsed time
# b = begin
# c = change = ending - beginning
# d = duration

# easing function make a value change from "b" to "b + c"
# in time from "t = 0" to "t = t + d"

class_name Easing

class Back:
# s = amplitude for "back" variation
	static func EaseIn(t: float, b: float, c: float, d: float, s: float = 1.70158) -> float:
		t = t / d
		return c * t * t * ((s + 1) * t - s) + b

	static func EaseOut(t: float, b: float, c: float, d: float, s: float = 1.70158) -> float:
		t = t / d - 1
		return c * (t * t * ((s + 1) * t + s) + 1) + b

	static func EaseInOut(t: float, b: float, c: float, d: float, s: float = 1.70158) -> float:
		t = t / d * 2
		s = s * 1.525
		if t < 1:
			return c / 2 * (t * t * ((s + 1) * t - s)) + b
		t = t - 2
		return c / 2 * (t * t * ((s + 1) * t + s) + 2) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float, s: float = 1.70158) -> float:
		return EaseOut(t * 2, b, c / 2, d, s) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d, s)

class Bounce:

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		if t < 1 / 2.75:
			return c * (7.5625 * t * t) + b
		elif t < 2 / 2.75:
			t = t - (1.5 / 2.75)
			return c * (7.5625 * t * t + 0.75) + b
		elif t < 2.5 / 2.75:
			t = t - (2.25 / 2.75)
			return c * (7.5625 * t * t + 0.9375) + b
		else:
			t = t - (2.625 / 2.75)
			return c * (7.5625 * t * t + 0.984375) + b

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		return c - EaseOut(d-t, 0, c, d) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		if (t < d/2):
			return EaseIn(t*2, 0, c, d) * 0.5 + b
		else:
			return EaseOut(t*2-d, 0, c, d) * 0.5 + c*0.5 + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Circ:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return -c * (sqrt(1 - t * t) - 1) + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d - 1
		return c * sqrt(1 - t * t) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d * 2
		if t < 1:
			return -c / 2 * (sqrt(1 - t * t) - 1) + b
		t = t - 2
		return c / 2 * (sqrt(1 - t * t) + 1) + b
		
	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Cubic:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return c * t * t * t + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d - 1
		return c * (t * t * t + 1) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d * 2
		if t < 1:
			return c / 2 * t * t * t + b
		t = t - 2
		return c / 2 * (t * t * t + 2) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Elastic:
# a = amplitude; p = period
	static func EaseIn(t: float, b: float, c: float, d: float, a: float = 0, p: float = 0) -> float:
		if t == 0:
			return b
		t = t / d
		if t == 1:
			return b + c

		if p == 0:
			p = d * 0.3

		var s: float
		if a == 0 or a < abs(c):
			a = c
			s = p / 4
		else:
			s = p / (2 * PI) * asin(c / a)

		t = t - 1
		return -(a * pow(2, 10 * t) * sin((t * d - s) * (2 * PI) / p)) + b

	static func EaseOut(t: float, b: float, c: float, d: float, a: float = 0, p: float = 0) -> float:
		if t == 0:
			return b
		t = t / d
		if t == 1:
			return b + c
			
		if p == 0:
			p = d * 0.3

		var s: float
		if a == 0:
			a = c
			s = p / 4
		else:
			s = p / (2 * PI) * asin(c / a)

		return a * pow(2, -10 * t) * sin((t * d - s) * (2 * PI) / p) + c + b

	static func EaseInOut(t: float, b: float, c: float, d: float, a: float = 0, p: float = 0) -> float:
		if t == 0:
			return b
		t = t / d * 2
		if t == 2:
			return b + c
			
		if p == 0:
			p = d * 0.3 * 1.5
			
		var s: float
		if a == 0 or a < abs(c):
			a = c
			s = p / 4
		else:
			s = p / (2 * PI) * asin( c / a)
		
		if t < 1:
			t = t - 1
			return -0.5 * (a * pow(2, 10 * t) * sin((t * d - s) * (2 * PI) / p)) + b
		else:
			t = t - 1
			return a * pow(2, -10 * t) * sin((t * d - s) * (2 * PI) / p ) * 0.5 + c + b

	static func EaseOutIn(t: float, b: float, c: float, d: float, a: float = 0, p: float = 0) -> float:
		return EaseOut(t * 2, b, c / 2, d, a, p) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d, a, p)


class Expo:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		return b if t==d else c * pow(2, 10 * (t / d - 1)) + b - c * 0.001

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		return b + c if t==d else c * 1.001 * (-pow(2, -10 * t / d) + 1) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		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
		t = t - 1
		return c / 2 * 1.0005 * (-pow(2, -10 * t) + 2) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Linear:

	static func EaseNone(t: float, b: float, c: float, d: float) -> float:
		return c * t / d + b

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		return c * t / d + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		return c * t / d + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		return c * t / d + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return c * t / d + b

class Quad:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return c * t * t + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return -c * t * (t - 2) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d * 2
		return c / 2 * t * t + b if t < 1 else -c / 2 * ((t - 1) * (t - 3) - 1) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Quart:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return c * t * t * t * t + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d - 1
		return -c * (t * t * t * t - 1) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d * 2
		if t < 1:
			return c / 2 * t * t * t * t + b
		else:
			t = t - 2
			return -c / 2 * (t * t * t * t - 2) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Quint:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		t = t / d
		return c * t * t * t * t * t + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d - 1
		return c*(t * t * t * t * t + 1) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		t = t / d * 2
		if t < 1:
			return c / 2 * t * t * t * t * t + b
		else:
			t = t - 2
			return c / 2 * (t * t * t * t * t + 2) + b
		
	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) - d, b + c / 2, c / 2, d)

class Sine:

	static func EaseIn(t: float, b: float, c: float, d: float) -> float:
		return -c * cos(t/d * (PI/2)) + c + b

	static func EaseOut(t: float, b: float, c: float, d: float) -> float:
		return c * sin(t/d * (PI/2)) + b

	static func EaseInOut(t: float, b: float, c: float, d: float) -> float:
		return -c/2 * (cos(PI*t/d) - 1) + b

	static func EaseOutIn(t: float, b: float, c: float, d: float) -> float:
		return EaseOut(t * 2, b, c / 2, d) if t < d / 2 else EaseIn((t * 2) -d, b + c / 2, c / 2, d)