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reverting akima intp: derivatives are not being preserved at the sample points

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minjaesong
2023-09-02 23:43:50 +09:00
parent 1e98353b50
commit 6a78cf6a41
1 changed files with 106 additions and 61 deletions
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167
src/net/torvald/terrarum/weather/Weatherbox.kt
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@@ -1,15 +1,13 @@
package net.torvald.terrarum.weather package net.torvald.terrarum.weather
import com.jme3.math.FastMath import com.jme3.math.FastMath
import net.torvald.terrarum.App.printdbg
import net.torvald.terrarum.floorToInt import net.torvald.terrarum.floorToInt
import net.torvald.terrarum.gameworld.GameWorld import net.torvald.terrarum.gameworld.GameWorld
import net.torvald.terrarum.gameworld.fmod import net.torvald.terrarum.gameworld.fmod
import org.apache.commons.math3.analysis.interpolation.AkimaSplineInterpolator import org.apache.commons.math3.analysis.UnivariateFunction
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction import org.apache.commons.math3.analysis.interpolation.NevilleInterpolator
import org.apache.commons.math3.analysis.interpolation.SplineInterpolator
import java.util.* import java.util.*
import kotlin.math.max
import kotlin.math.pow
data class WeatherSchedule(val weather: BaseModularWeather = WeatherMixer.DEFAULT_WEATHER, val duration: Long = 3600) data class WeatherSchedule(val weather: BaseModularWeather = WeatherMixer.DEFAULT_WEATHER, val duration: Long = 3600)
@@ -93,22 +91,37 @@ open class WeatherStateBox(
// pM1 and p4 only exists for the sake of better weather forecasting // pM1 and p4 only exists for the sake of better weather forecasting
// - removing p4 and beyond: for faster response to the changing weather schedule and make the forecasting less accurate like irl // - removing p4 and beyond: for faster response to the changing weather schedule and make the forecasting less accurate like irl
) { ) {
// protected lateinit var polynomial: UnivariateFunction
protected lateinit var polynomial: PolynomialSplineFunction // protected val interpolator = SplineInterpolator()
protected val interpolator = AkimaSplineInterpolator()
open val value: Float; get() = valueAt(x) open val value: Float; get() = valueAt(x)
open fun valueAt(x: Float) = polynomial.value(x + 1.0).toFloat() open fun valueAt(x: Float) = when (x.floorToInt()) {
-2 -> interpolate(x + 2, pM2,pM1, p0, p1)
-1 -> interpolate(x + 1, pM1, p0, p1, p2)
0 -> interpolate(x - 0, p0, p1, p2, p3)
1 -> interpolate(x - 1, p1, p2, p3, p3)
2 -> interpolate(x - 2, p2, p3, p3, p3)
3 -> interpolate(x - 3, p3, p3, p3, p3)
else -> throw IllegalArgumentException()
}
open protected fun extrapolate(): Float {
val d1 = p2 - p1
val d2 = p3 - p2
// if two slopes are monotonic
return if (d1 * d2 >= 0f)
(d2 + d1) / 2f + p3
else
(d2 + d1) / 2f + p3
}
open protected fun updatePolynomials() { open protected fun updatePolynomials() {
polynomial = interpolator.interpolate(
doubleArrayOf(-2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0),
doubleArrayOf(pM2.toDouble(), pM1.toDouble(), p0.toDouble(), p1.toDouble(), p2.toDouble(), p3.toDouble(), p3.toDouble())
)
} }
open fun update(xdelta: Float, next: () -> Float) { open fun update(xdelta: Float, next: () -> Float) {
if (!::polynomial.isInitialized) updatePolynomials() // if (!::polynomial.isInitialized) updatePolynomials()
synchronized(WeatherMixer.RNG) { synchronized(WeatherMixer.RNG) {
x += xdelta x += xdelta
@@ -121,9 +134,21 @@ open class WeatherStateBox(
p2 = p3 p2 = p3
p3 = next() p3 = next()
} }
updatePolynomials() // updatePolynomials()
} }
} }
protected fun interpolate(u: Float, p0: Float, p1: Float, p2: Float, p3: Float): Float {
val T = FastMath.interpolateLinear(u, p1, p2).div(maxOf(p0, p3).coerceAtLeast(1f)).toDouble().coerceIn(0.0, 0.5)
// if (u == x) printdbg(this, "u=$u, p1=$p1, p2=$p2; T=$T")
val c1 = p1.toDouble()
val c2 = -1.0 * T * p0 + T * p2
val c3 = 2 * T * p0 + (T - 3) * p1 + (3 - 2 * T) * p2 + -T * p3
val c4 = -T * p0 + (2 - T) * p1 + (T - 2) * p2 + T * p3
return (((c4 * u + c3) * u + c2) * u + c1).toFloat()
}
} }
/** /**
@@ -138,9 +163,8 @@ class WeatherDirBox(
p2: Float = 0f, p2: Float = 0f,
p3: Float = 0f, p3: Float = 0f,
) : WeatherStateBox(x, pM2, pM1, p0, p1, p2, p3) { ) : WeatherStateBox(x, pM2, pM1, p0, p1, p2, p3) {
override fun valueAt(x: Float) = polynomial.value(x + 1.0).plus(2.0).fmod(4.0).minus(2.0).toFloat()
override fun updatePolynomials() { override fun valueAt(x: Float): Float {
var pM2 = pM2 var pM2 = pM2
var pM1 = pM1 var pM1 = pM1
var p0 = p0 var p0 = p0
@@ -148,50 +172,55 @@ class WeatherDirBox(
var p2 = p2 var p2 = p2
var p3 = p3 var p3 = p3
if (x < -2f) {
if (pM1 - pM2 > 2f) { if (pM1 - pM2 > 2f) {
pM2 -= 4f pM2 -= 4f
pM1 -= 4f pM1 -= 4f
p0 -= 4f p0 -= 4f
p1 -= 4f p1 -= 4f
p2 -= 4f p2 -= 4f
p3 -= 4f p3 -= 4f
} }
else if (pM1 - pM2 < -2f) { else if (pM1 - pM2 < -2f) {
pM2 += 4f pM2 += 4f
pM1 += 4f pM1 += 4f
p0 += 4f p0 += 4f
p1 += 4f p1 += 4f
p2 += 4f p2 += 4f
p3 += 4f p3 += 4f
}
} }
if (pM1 - pM2 > 2f) { if (x < -1f) {
pM1 -= 4f if (pM1 - pM2 > 2f) {
p0 -= 4f pM1 -= 4f
p1 -= 4f p0 -= 4f
p2 -= 4f p1 -= 4f
p3 -= 4f p2 -= 4f
} p3 -= 4f
else if (pM1 - pM2 < -2f) { }
pM1 += 4f else if (pM1 - pM2 < -2f) {
p0 += 4f pM1 += 4f
p1 += 4f p0 += 4f
p2 += 4f p1 += 4f
p3 += 4f p2 += 4f
p3 += 4f
}
} }
if (p0 - pM1 > 2f) { if (x < 0f) {
p0 -= 4f if (p0 - pM1 > 2f) {
p1 -= 4f p0 -= 4f
p2 -= 4f p1 -= 4f
p3 -= 4f p2 -= 4f
} p3 -= 4f
else if (p0 - pM1 < -2f) { }
p0 += 4f else if (p0 - pM1 < -2f) {
p1 += 4f p0 += 4f
p2 += 4f p1 += 4f
p3 += 4f p2 += 4f
p3 += 4f
}
} }
if (p1 - p0 > 2f) { if (p1 - p0 > 2f) {
@@ -221,9 +250,25 @@ class WeatherDirBox(
p3 += 4f p3 += 4f
} }
polynomial = interpolator.interpolate( return when (x.floorToInt()) {
doubleArrayOf(-2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0), -2 -> interpolate2(x + 2, pM2,pM1, p0, p1)
doubleArrayOf(pM2.toDouble(), pM1.toDouble(), p0.toDouble(), p1.toDouble(), p2.toDouble(), p3.toDouble(), p3.toDouble()) -1 -> interpolate2(x + 1, pM1, p0, p1, p2)
) 0 -> interpolate2(x - 0, p0, p1, p2, p3)
1 -> interpolate2(x - 1, p1, p2, p3, p3)
2 -> interpolate2(x - 2, p2, p3, p3, p3)
3 -> interpolate2(x - 3, p3, p3, p3, p3)
else -> throw IllegalArgumentException()
}.plus(2f).fmod(4f).minus(2f)
}
private fun interpolate2(u: Float, p0: Float, p1: Float, p2: Float, p3: Float): Float {
val T = 0.5
val c1 = p1.toDouble()
val c2 = -1.0 * T * p0 + T * p2
val c3 = 2 * T * p0 + (T - 3) * p1 + (3 - 2 * T) * p2 + -T * p3
val c4 = -T * p0 + (2 - T) * p1 + (T - 2) * p2 + T * p3
return (((c4 * u + c3) * u + c2) * u + c1).toFloat()
} }
} }