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Mathematic library for Multiplatform Kotlin 1.3
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package korlibs.math.interpolation
import korlibs.math.geom.*
import korlibs.math.geom.bezier.*
import korlibs.memory.*
import kotlin.math.*
private inline fun combine(it: Float, start: Easing, end: Easing) =
if (it < .5f) .5f * start(it * 2f) else .5f * end((it - .5f) * 2f) + .5f
private const val BOUNCE_FACTOR = 1.70158f
private const val HALF_PI = PI.toFloat() / 2f
@Suppress("unused")
fun interface Easing {
operator fun invoke(it: Float): Float
operator fun invoke(it: Double): Double = invoke(it.toFloat()).toDouble()
companion object {
operator fun invoke(name: () -> String, block: (Float) -> Float): Easing {
return object : Easing {
override fun invoke(it: Float): Float = block(it)
override fun toString(): String = name()
}
}
fun steps(steps: Int, easing: Easing): Easing = Easing({ "steps($steps, $easing)" }) {
easing((it * steps).toInt().toFloat() / steps)
}
fun cubic(x1: Float, y1: Float, x2: Float, y2: Float, name: String? = null): Easing = EasingCubic(x1, y1, x2, y2, name)
fun cubic(x1: Double, y1: Double, x2: Double, y2: Double, name: String? = null): Easing = EasingCubic(x1, y1, x2, y2, name)
fun cubic(f: (t: Float, b: Float, c: Float, d: Float) -> Float): Easing = Easing { f(it, 0f, 1f, 1f) }
fun combine(start: Easing, end: Easing) = Easing { combine(it, start, end) }
private val _ALL_LIST: List by lazy(LazyThreadSafetyMode.PUBLICATION) {
Easings.values().toList()
}
val ALL_LIST: List get() = _ALL_LIST
/**
* Retrieves a mapping of all standard easings defined directly in [Easing], for example "SMOOTH" -> Easing.SMOOTH.
*/
val ALL: Map by lazy(LazyThreadSafetyMode.PUBLICATION) {
_ALL_LIST.associateBy { it.name }
}
// Author's note:
// 1. Make sure new standard easings are added both here and in the Easings enum class
// 2. Make sure the name is the same, otherwise [ALL] will return confusing results
val SMOOTH: Easing get() = Easings.SMOOTH
val EASE_IN_ELASTIC: Easing get() = Easings.EASE_IN_ELASTIC
val EASE_OUT_ELASTIC: Easing get() = Easings.EASE_OUT_ELASTIC
val EASE_OUT_BOUNCE: Easing get() = Easings.EASE_OUT_BOUNCE
val LINEAR: Easing get() = Easings.LINEAR
val EASE: Easing get() = Easings.EASE
val EASE_IN: Easing get() = Easings.EASE_IN
val EASE_OUT: Easing get() = Easings.EASE_OUT
val EASE_IN_OUT: Easing get() = Easings.EASE_IN_OUT
val EASE_IN_OLD: Easing get() = Easings.EASE_IN_OLD
val EASE_OUT_OLD: Easing get() = Easings.EASE_OUT_OLD
val EASE_IN_OUT_OLD: Easing get() = Easings.EASE_IN_OUT_OLD
val EASE_OUT_IN_OLD: Easing get() = Easings.EASE_OUT_IN_OLD
val EASE_IN_BACK: Easing get() = Easings.EASE_IN_BACK
val EASE_OUT_BACK: Easing get() = Easings.EASE_OUT_BACK
val EASE_IN_OUT_BACK: Easing get() = Easings.EASE_IN_OUT_BACK
val EASE_OUT_IN_BACK: Easing get() = Easings.EASE_OUT_IN_BACK
val EASE_IN_OUT_ELASTIC: Easing get() = Easings.EASE_IN_OUT_ELASTIC
val EASE_OUT_IN_ELASTIC: Easing get() = Easings.EASE_OUT_IN_ELASTIC
val EASE_IN_BOUNCE: Easing get() = Easings.EASE_IN_BOUNCE
val EASE_IN_OUT_BOUNCE: Easing get() = Easings.EASE_IN_OUT_BOUNCE
val EASE_OUT_IN_BOUNCE: Easing get() = Easings.EASE_OUT_IN_BOUNCE
val EASE_IN_QUAD: Easing get() = Easings.EASE_IN_QUAD
val EASE_OUT_QUAD: Easing get() = Easings.EASE_OUT_QUAD
val EASE_IN_OUT_QUAD: Easing get() = Easings.EASE_IN_OUT_QUAD
val EASE_SINE: Easing get() = Easings.EASE_SINE
val EASE_CLAMP_START: Easing get() = Easings.EASE_CLAMP_START
val EASE_CLAMP_END: Easing get() = Easings.EASE_CLAMP_END
val EASE_CLAMP_MIDDLE: Easing get() = Easings.EASE_CLAMP_MIDDLE
}
}
// @TODO: We need to heavily optimize this. If we can have a formula instead of doing a bisect, this would be much faster.
class EasingCubic(val x1: Float, val y1: Float, val x2: Float, val y2: Float, val name: String? = null) : Easing {
constructor(x1: Double, y1: Double, x2: Double, y2: Double, name: String? = null) : this(x1.toFloat(), y1.toFloat(), x2.toFloat(), y2.toFloat(), name)
val cubic = Bezier(Point(0f, 0f), Point(x1.clamp(0f, 1f), y1), Point(x2.clamp(0f, 1f), y2), Point(1.0, 1.0))
override fun toString(): String = name ?: "cubic-bezier($x1, $y1, $x2, $y2)"
// @TODO: this doesn't work properly for `it` outside range [0, 1], and not in constant time
override fun invoke(it: Float): Float {
var pivotLeft = if (it < 0f) it * 10f else 0f
var pivotRight = if (it > 1f) it * 10f else 1f
//var pivot = (pivotLeft + pivotRight) * 0.5
var pivot = it
//println(" - x=$x, time=$time, pivotLeft=$pivotLeft, pivotRight=$pivotRight, pivot=$pivot")
var lastX = 0f
var lastY = 0f
var steps = 0
for (n in 0 until 50) {
steps++
val res = cubic.calc(pivot)
lastX = res.x
lastY = res.y
if ((lastX - it).absoluteValue < 0.001) break
if (it < lastX) {
pivotRight = pivot
pivot = (pivotLeft + pivot) * 0.5f
} else if (it > lastX) {
pivotLeft = pivot
pivot = (pivotRight + pivot) * 0.5f
} else {
break
}
}
//println("Requested steps=$steps, deviation=${(lastX - x).absoluteValue} requestedX=$x, lastX=$lastX, pivot=$pivot, pivotLeft=$pivotLeft, pivotRight=$pivotRight, lastY=$lastY")
return lastY
}
/*
override fun invoke(it: Double): Double {
val points = listOf(cubic.p0, cubic.p1, cubic.p2, cubic.p3)
val time = it
/** Step 0 */
val n = 5
val x = doubleArrayOf(0.0, points[0].x, points[1].x, points[2].x, points[3].x, 1.0)
val a = doubleArrayOf(0.0, points[0].y, points[1].y, points[2].y, points[3].y, 1.0)
val h = DoubleArray(n)
val A = DoubleArray(n)
val l = DoubleArray(n + 1)
val u = DoubleArray(n + 1)
val z = DoubleArray(n + 1)
val c = DoubleArray(n + 1)
val b = DoubleArray(n)
val d = DoubleArray(n)
/** Step 1 */
for (i in 0 until n) h[i] = x[i + 1] - x[i]
/** Step 2 */
for (i in 1 until n) A[i] = (3.0 * (a[i + 1] - a[i]) / h[i]) - (3.0 * (a[i] - a[i - 1]) / h[i - 1])
/** Step 3 */
l[0] = 1.0
u[0] = 0.0
z[0] = 0.0
/** Step 4 */
for (i in 1 until n) {
l[i] = 2.0 * (x[i + 1] - x[i - 1]) - (h[i - 1] * u[i - 1])
u[i] = h[i] / l[i]
z[i] = (A[i] - h[i - 1] * z[i - 1]) / l[i]
}
/** Step 5 */
l[n] = 1.0
z[n] = 0.0
c[n] = 0.0
/** Step 6 */
for (j in (n - 1) downTo 0) {
c[j] = z[j] - (u[j] * c[j + 1])
b[j] = ((a[j + 1] - a[j]) / h[j]) - (h[j] * (c[j + 1] + 2 * c[j]) / 3)
d[j] = (c[j + 1] - c[j]) / (3 * h[j])
}
// get t position
var result = 0.0
var t = time
for (i in 0 until n) {
if (t >= x[i] && t < x[i + 1]) {
t -= x[i]
result = a[i] + b[i] * t + c[i] * t * t + d[i] * t * t * t
}
}
return result
}
*/
}
private enum class Easings : Easing {
SMOOTH {
override fun invoke(it: Float): Float = it * it * (3 - 2 * it)
},
EASE_IN_ELASTIC {
override fun invoke(it: Float): Float =
if (it == 0f || it == 1f) {
it
} else {
val p = 0.3f
val s = p / 4.0f
val inv = it - 1
-1f * 2f.pow(10f * inv) * sin((inv - s) * (2f * PI.toFloat()) / p)
}
},
EASE_OUT_ELASTIC {
override fun invoke(it: Float): Float =
if (it == 0f || it == 1f) {
it
} else {
val p = 0.3f
val s = p / 4.0f
2.0f.pow(-10.0f * it) * sin((it - s) * (2.0f * PI.toFloat()) / p) + 1
}
},
EASE_OUT_BOUNCE {
override fun invoke(it: Float): Float {
val s = 7.5625f
val p = 2.75f
return when {
it < 1f / p -> s * it.pow(2f)
it < 2f / p -> s * (it - 1.5f / p).pow(2.0f) + 0.75f
it < 2.5f / p -> s * (it - 2.25f / p).pow(2.0f) + 0.9375f
else -> s * (it - 2.625f / p).pow(2.0f) + 0.984375f
}
}
},
//Easing.cubic(0.0, 0.0, 1.0, 1.0, "linear"),
LINEAR {
override fun invoke(it: Float): Float = it
},
// https://developer.mozilla.org/en-US/docs/Web/CSS/animation-timing-function
EASE {
val easing = EasingCubic(0.25f, 0.1f, 0.25f, 1.0f, "ease")
override fun invoke(it: Float): Float = easing.invoke(it)
},
EASE_IN {
val easing = EasingCubic(0.42f, 0.0f, 1.0f, 1.0f, "ease-in")
override fun invoke(it: Float): Float = easing.invoke(it)
},
EASE_OUT {
val easing = EasingCubic(0.0f, 0.0f, 0.58f, 1.0f, "ease-out")
override fun invoke(it: Float): Float = easing.invoke(it)
},
EASE_IN_OUT {
val easing = EasingCubic(0.42f, 0.0f, 0.58f, 1.0f, "ease-in-out")
override fun invoke(it: Float): Float = easing.invoke(it)
},
//EASE_OUT_IN {
// val easing = EasingCubic(-, "ease-out-in")
// override fun invoke(it: Double): Double = easing.invoke(it)
//},
EASE_IN_OLD {
override fun invoke(it: Float): Float = it * it * it
},
EASE_OUT_OLD {
override fun invoke(it: Float): Float =
(it - 1f).let { inv ->
inv * inv * inv + 1
}
},
EASE_IN_OUT_OLD {
override fun invoke(it: Float): Float = combine(it, EASE_IN_OLD, EASE_OUT_OLD)
},
EASE_OUT_IN_OLD {
override fun invoke(it: Float): Float = combine(it, EASE_OUT_OLD, EASE_IN_OLD)
},
EASE_IN_BACK {
override fun invoke(it: Float): Float = it.pow(2f) * ((BOUNCE_FACTOR + 1f) * it - BOUNCE_FACTOR)
},
EASE_OUT_BACK {
override fun invoke(it: Float): Float =
(it - 1f).let { inv ->
inv.pow(2f) * ((BOUNCE_FACTOR + 1f) * inv + BOUNCE_FACTOR) + 1f
}
},
EASE_IN_OUT_BACK {
override fun invoke(it: Float): Float = combine(it, EASE_IN_BACK, EASE_OUT_BACK)
},
EASE_OUT_IN_BACK {
override fun invoke(it: Float): Float = combine(it, EASE_OUT_BACK, EASE_IN_BACK)
},
EASE_IN_OUT_ELASTIC {
override fun invoke(it: Float): Float = combine(it, EASE_IN_ELASTIC, EASE_OUT_ELASTIC)
},
EASE_OUT_IN_ELASTIC {
override fun invoke(it: Float): Float = combine(it, EASE_OUT_ELASTIC, EASE_IN_ELASTIC)
},
EASE_IN_BOUNCE {
override fun invoke(it: Float): Float = 1f - EASE_OUT_BOUNCE(1f - it)
},
EASE_IN_OUT_BOUNCE {
override fun invoke(it: Float): Float = combine(it, EASE_IN_BOUNCE, EASE_OUT_BOUNCE)
},
EASE_OUT_IN_BOUNCE {
override fun invoke(it: Float): Float = combine(it, EASE_OUT_BOUNCE, EASE_IN_BOUNCE)
},
EASE_IN_QUAD {
override fun invoke(it: Float): Float = 1f * it * it
},
EASE_OUT_QUAD {
override fun invoke(it: Float): Float = -1f * it * (it - 2)
},
EASE_IN_OUT_QUAD {
override fun invoke(it: Float): Float =
(it * 2f).let { t ->
if (t < 1) {
+1f / 2 * t * t
} else {
-1f / 2 * ((t - 1) * ((t - 1) - 2) - 1)
}
}
},
EASE_SINE {
override fun invoke(it: Float): Float = sin(it * HALF_PI)
},
EASE_CLAMP_START {
override fun invoke(it: Float): Float = if (it <= 0f) 0f else 1f
},
EASE_CLAMP_END {
override fun invoke(it: Float): Float = if (it < 1f) 0f else 1f
},
EASE_CLAMP_MIDDLE {
override fun invoke(it: Float): Float = if (it < 0.5f) 0f else 1f
};
override fun toString(): String = super.toString().replace('_', '-').lowercase()
}