akima interpolation to the WeatherBox

.idea/artifacts/TerrarumBuild.xml

@@ -87,6 +87,7 @@
       <element id="extracted-dir" path="$PROJECT_DIR$/lib/regex-22.3.1-edit.jar" path-in-jar="/" />
       <element id="extracted-dir" path="$PROJECT_DIR$/lib/js-22.3.1-edit.jar" path-in-jar="/" />
       <element id="extracted-dir" path="$PROJECT_DIR$/lib/graal-sdk-22.3.1.jar" path-in-jar="/" />
+      <element id="extracted-dir" path="$PROJECT_DIR$/lib/commons-math3-3.6.1.jar" path-in-jar="/" />
     </root>
   </artifact>
 </component>

.idea/libraries/apache_commons_math3.xml

@@ -0,0 +1,14 @@
+<component name="libraryTable">
+  <library name="apache.commons.math3" type="repository">
+    <properties maven-id="org.apache.commons:commons-math3:3.6.1" />
+    <CLASSES>
+      <root url="jar://$PROJECT_DIR$/lib/commons-math3-3.6.1.jar!/" />
+    </CLASSES>
+    <JAVADOC>
+      <root url="jar://$PROJECT_DIR$/lib/commons-math3-3.6.1-javadoc.jar!/" />
+    </JAVADOC>
+    <SOURCES>
+      <root url="jar://$PROJECT_DIR$/lib/commons-math3-3.6.1-sources.jar!/" />
+    </SOURCES>
+  </library>
+</component>

TerrarumBuild.iml

@@ -25,5 +25,6 @@
     <orderEntry type="library" name="jetbrains.kotlin.reflect" level="project" />
     <orderEntry type="library" name="jetbrains.kotlin.test" level="project" />
     <orderEntry type="library" name="io.github.classgraph" level="project" />
+    <orderEntry type="library" name="apache.commons.math3" level="project" />
   </component>
 </module>

src/net/torvald/terrarum/weather/WeatherMixer.kt

@@ -149,19 +149,21 @@ internal object WeatherMixer : RNGConsumer {
         weatherbox.initWith(weatherDict["generic01"]!!, 7200L)
 
         // TEST FILL WITH RANDOM VALUES
-        (0..4).map { takeUniformRand(0f..1f) }.let {
+        (0..6).map { takeUniformRand(0f..1f) }.let {
-            weatherbox.windDir.pM1 = it[0]
+            weatherbox.windDir.pM2 = it[1]
-            weatherbox.windDir.p0  = it[1]
+            weatherbox.windDir.pM1 = it[2]
-            weatherbox.windDir.p1  = it[2]
+            weatherbox.windDir.p0  = it[3]
-            weatherbox.windDir.p2  = it[3]
+            weatherbox.windDir.p1  = it[4]
-            weatherbox.windDir.p3  = it[4]
+            weatherbox.windDir.p2  = it[5]
+            weatherbox.windDir.p3  = it[6]
         }
-        (0..4).map { takeUniformRand(-1f..1f) }.let {
+        (0..6).map { takeUniformRand(-1f..1f) }.let {
-            weatherbox.windSpeed.pM1 = currentWeather.getRandomWindSpeed(it[0])
+            weatherbox.windSpeed.pM2 = currentWeather.getRandomWindSpeed(it[1])
-            weatherbox.windSpeed.p0  = currentWeather.getRandomWindSpeed(it[1])
+            weatherbox.windSpeed.pM1 = currentWeather.getRandomWindSpeed(it[2])
-            weatherbox.windSpeed.p1  = currentWeather.getRandomWindSpeed(it[2])
+            weatherbox.windSpeed.p0  = currentWeather.getRandomWindSpeed(it[3])
-            weatherbox.windSpeed.p2  = currentWeather.getRandomWindSpeed(it[3])
+            weatherbox.windSpeed.p1  = currentWeather.getRandomWindSpeed(it[4])
-            weatherbox.windSpeed.p3  = currentWeather.getRandomWindSpeed(it[4])
+            weatherbox.windSpeed.p2  = currentWeather.getRandomWindSpeed(it[5])
+            weatherbox.windSpeed.p3  = currentWeather.getRandomWindSpeed(it[6])
         }
     }
 
@@ -405,8 +407,8 @@ internal object WeatherMixer : RNGConsumer {
                 Vector3(x, y, z)
             }
             -1, 3, 7 -> { // z = 0
-                val z = 0.1f
                 val posXscr = FastMath.interpolateLinear(rr, -halfCloudSize, App.scr.width + halfCloudSize)
+                val z = WeatherObjectCloud.worldYtoWorldZforScreenYof0(y)
                 val x = WeatherObjectCloud.screenXtoWorldX(posXscr, Z_LIM)
                 Vector3(x, y, z)
             }

src/net/torvald/terrarum/weather/WeatherObjectCloud.kt

@@ -6,7 +6,6 @@ import com.badlogic.gdx.graphics.g2d.TextureRegion
 import com.badlogic.gdx.math.Vector3
 import com.jme3.math.FastMath
 import net.torvald.terrarum.App
-import net.torvald.terrarum.App.printdbg
 import net.torvald.terrarum.gameworld.GameWorld
 import kotlin.math.absoluteValue
 import kotlin.math.pow
@@ -70,9 +69,7 @@ class WeatherObjectCloud(
         }
     }
 
-    private val w = App.scr.halfwf
+    private val vecMult = Vector3(1f, 1f, 1f / (4f * H))
-    private val h = App.scr.hf * 0.5f
-    private val vecMult = Vector3(1f, 1f, 1f / (4f * h))
 
     private fun roundRgbGamma(x: Float): Int {
         return RGB_GAMMA_TABLE.mapIndexed { i, f -> (f - x).absoluteValue to i }.minBy { it.first }.second
@@ -118,10 +115,10 @@ class WeatherObjectCloud(
         get() {
             val x = posX - texture.regionWidth * scale * 0.5f
             val y = posY - texture.regionHeight * scale
-            val z = posZ // must be at least 1.0
+            val z = posZ // must be larger than 0
 
-            val drawX = (x + w * (z-1)) / z
+            val drawX = (x + W * (z-1)) / z
-            val drawY = (y + h * (z-1)) / z
+            val drawY = (y + H * (z-1)) / z
             val drawScale = scale / z
 
             return Vector3(drawX, drawY, drawScale)
@@ -137,9 +134,9 @@ class WeatherObjectCloud(
             val y = posY - texture.regionHeight * scale
             val z = posZ // must be larger than 0
 
-            val drawXL = (xL + w * (z-1)) / z
+            val drawXL = (xL + W * (z-1)) / z
-            val drawXR = (xR + w * (z-1)) / z
+            val drawXR = (xR + W * (z-1)) / z
-            val drawY = (y + h * (z-1)) / z
+            val drawY = (y + H * (z-1)) / z
 
             return Vector3(drawXL, drawY, drawXR)
         }
@@ -151,9 +148,9 @@ class WeatherObjectCloud(
             val y = posY - texture.regionHeight * scale
             val z = FastMath.interpolateLinear(posZ / ALPHA_ROLLOFF_Z, ALPHA_ROLLOFF_Z / 4f, ALPHA_ROLLOFF_Z)
 
-            val drawXL = (xL + w * (z-1)) / z
+            val drawXL = (xL + W * (z-1)) / z
-            val drawXR = (xR + w * (z-1)) / z
+            val drawXR = (xR + W * (z-1)) / z
-            val drawY = (y + h * (z-1)) / z
+            val drawY = (y + H * (z-1)) / z
 
             return Vector3(drawXL, drawY, drawXR)
         }
@@ -162,7 +159,19 @@ class WeatherObjectCloud(
     override fun compareTo(other: WeatherObjectCloud): Int = (other.posZ - this.posZ).sign.toInt()
 
     companion object {
-        fun screenXtoWorldX(screenX: Float, z: Float) = screenX * z - App.scr.halfwf * (z - 1f)
+        private val W = App.scr.halfwf
+        private val H = App.scr.hf * 0.5f
+
+        /**
+         * Given screen-x and world-z position, calculates a world-x position that would make the cloud appear at the given screen-x position
+         */
+        fun screenXtoWorldX(screenX: Float, z: Float) = screenX * z - W * (z - 1f) // rearrange screenCoord equations to derive this eq :p
+
+        /**
+         * Given a world-y position, calculates a world-z position that would put the cloud to screen-y of zero
+         */
+        fun worldYtoWorldZforScreenYof0(y: Float) = 1f - (y / H) // rearrange screenCoord equations to derive this eq :p
+
         const val ALPHA_ROLLOFF_Z = 64f
         const val OLD_AGE_DECAY = 4000f
 

src/net/torvald/terrarum/weather/Weatherbox.kt

@@ -5,6 +5,8 @@ import net.torvald.terrarum.App.printdbg
 import net.torvald.terrarum.floorToInt
 import net.torvald.terrarum.gameworld.GameWorld
 import net.torvald.terrarum.gameworld.fmod
+import org.apache.commons.math3.analysis.interpolation.AkimaSplineInterpolator
+import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction
 import java.util.*
 import kotlin.math.max
 import kotlin.math.pow
@@ -92,18 +94,22 @@ open class WeatherStateBox(
     // - removing p4 and beyond: for faster response to the changing weather schedule and make the forecasting less accurate like irl
 ) {
 
-    open val value: Float; get() = interpolate(x, p0, p1, p2, p3)
+    protected lateinit var polynomial: PolynomialSplineFunction
-    open fun valueAt(x: Float) = when (x.floorToInt()) {
+    protected val interpolator = AkimaSplineInterpolator()
-        -2 -> interpolate(x + 2, pM2,pM1, p0, p1)
+
-        -1 -> interpolate(x + 1, pM1, p0, p1, p2)
+    open val value: Float; get() = valueAt(x)
-         0 -> interpolate(x - 0,  p0, p1, p2, p3)
+    open fun valueAt(x: Float) = polynomial.value(x + 1.0).toFloat()
-         1 -> interpolate(x - 1,  p1, p2, p3, p3)
+
-         2 -> interpolate(x - 2,  p2, p3, p3, p3)
+    open protected fun updatePolynomials() {
-         3 -> interpolate(x - 3,  p3, p3, p3, p3)
+        polynomial = interpolator.interpolate(
-        else -> throw IllegalArgumentException()
+            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) {
+        if (!::polynomial.isInitialized) updatePolynomials()
+
         synchronized(WeatherMixer.RNG) {
             x += xdelta
             while (x >= 1.0) {
@@ -114,25 +120,10 @@ open class WeatherStateBox(
                 p1 = p2
                 p2 = p3
                 p3 = next()
-
-
-//                p3 = p4
-//                p4 = p5
-//                p5 = next()
             }
+            updatePolynomials()
         }
     }
-    protected fun interpolate(u: Float, p0: Float, p1: Float, p2: Float, p3: Float): Float {
-        val T = FastMath.interpolateLinear(u, p1, p2).div(max(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()
-    }
 }
 
 /**
@@ -147,9 +138,9 @@ class WeatherDirBox(
     p2: Float = 0f,
     p3: Float = 0f,
 ) : WeatherStateBox(x, pM2, pM1, p0, p1, p2, p3) {
-    override val value; get() = valueAt(x)
+    override fun valueAt(x: Float) = polynomial.value(x + 1.0).plus(2.0).fmod(4.0).minus(2.0).toFloat()
 
-    override fun valueAt(x: Float): Float {
+    override fun updatePolynomials() {
         var pM2 = pM2
         var pM1 = pM1
         var p0 = p0
@@ -157,55 +148,50 @@ class WeatherDirBox(
         var p2 = p2
         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 (x < -1f) {
+        if (pM1 - pM2 > 2f) {
-            if (pM1 - pM2 > 2f) {
+            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) {
+            pM1 += 4f
-                pM1 += 4f
+            p0 += 4f
-                p0 += 4f
+            p1 += 4f
-                p1 += 4f
+            p2 += 4f
-                p2 += 4f
+            p3 += 4f
-                p3 += 4f
-            }
         }
 
-        if (x < 0f) {
+        if (p0 - pM1 > 2f) {
-            if (p0 - pM1 > 2f) {
+            p0 -= 4f
-                p0 -= 4f
+            p1 -= 4f
-                p1 -= 4f
+            p2 -= 4f
-                p2 -= 4f
+            p3 -= 4f
-                p3 -= 4f
+        }
-            }
+        else if (p0 - pM1 < -2f) {
-            else if (p0 - pM1 < -2f) {
+            p0 += 4f
-                p0 += 4f
+            p1 += 4f
-                p1 += 4f
+            p2 += 4f
-                p2 += 4f
+            p3 += 4f
-                p3 += 4f
-            }
         }
 
         if (p1 - p0 > 2f) {
@@ -235,25 +221,9 @@ class WeatherDirBox(
             p3 += 4f
         }
 
-        return when (x.floorToInt()) {
+        polynomial = interpolator.interpolate(
-            -2 -> interpolate2(x + 2, pM2,pM1, p0, p1)
+            doubleArrayOf(-2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0),
-            -1 -> interpolate2(x + 1, pM1, p0, p1, p2)
+            doubleArrayOf(pM2.toDouble(), pM1.toDouble(), p0.toDouble(), p1.toDouble(), p2.toDouble(), p3.toDouble(), p3.toDouble())
-             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()
     }
 }