Fix initialization problem for Mercator on native

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/MercatorAlgebra.kt

@@ -0,0 +1,97 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.geometry
+
+import space.kscience.kmath.operations.Algebra
+import kotlin.math.*
+
+/**
+ * Geodetic coordinated
+ */
+public class GeodeticCoordinates private constructor(public val latitude: Double, public val longitude: Double) {
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as GeodeticCoordinates
+
+        if (latitude != other.latitude) return false
+        if (longitude != other.longitude) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int {
+        var result = latitude.hashCode()
+        result = 31 * result + longitude.hashCode()
+        return result
+    }
+
+    override fun toString(): String {
+        return "GeodeticCoordinates(latitude=$latitude, longitude=$longitude)"
+    }
+
+
+    public companion object {
+        public fun ofRadians(latitude: Double, longitude: Double): GeodeticCoordinates {
+            require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
+            return GeodeticCoordinates(latitude, longitude.rem(PI / 2))
+        }
+
+        public fun ofDegrees(latitude: Double, longitude: Double): GeodeticCoordinates {
+            require(latitude in (-90.0)..(90.0)) { "Latitude $latitude is not in -90..90" }
+            return GeodeticCoordinates(latitude * PI / 180, (longitude.rem(180) * PI / 180))
+        }
+    }
+}
+
+public data class MercatorCoordinates(val x: Double, val y: Double)
+
+/**
+ * @param baseLongitude the longitude offset in radians
+ * @param radius the average radius of the Earth
+ * @param correctedRadius optional radius correction to account for ellipsoid model
+ */
+public open class MercatorAlgebra(
+    public val baseLongitude: Double = 0.0,
+    protected val radius: Double = DEFAULT_EARTH_RADIUS,
+    private val correctedRadius: ((GeodeticCoordinates) -> Double)? = null,
+) : Algebra<TileWebMercatorCoordinates> {
+
+    public fun MercatorCoordinates.toGeodetic(): GeodeticCoordinates {
+        val res = GeodeticCoordinates.ofRadians(
+            atan(sinh(y / radius)),
+            baseLongitude + x / radius,
+        )
+        return if (correctedRadius != null) {
+            val r = correctedRadius.invoke(res)
+            GeodeticCoordinates.ofRadians(
+                atan(sinh(y / r)),
+                baseLongitude + x / r,
+            )
+        } else {
+            res
+        }
+    }
+
+    /**
+     * https://en.wikipedia.org/wiki/Web_Mercator_projection#Formulas
+     */
+    public fun GeodeticCoordinates.toMercator(): MercatorCoordinates {
+        require(abs(latitude) <= MAXIMUM_LATITUDE) { "Latitude exceeds the maximum latitude for mercator coordinates" }
+        val r = correctedRadius?.invoke(this) ?: radius
+        return MercatorCoordinates(
+            x = r * (longitude - baseLongitude),
+            y = r * ln(tan(PI / 4 + latitude / 2))
+        )
+    }
+
+    public companion object : MercatorAlgebra(0.0, 6378137.0) {
+        public const val MAXIMUM_LATITUDE: Double = 85.05113
+        public val DEFAULT_EARTH_RADIUS: Double = radius
+    }
+}

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/WebMercatorAlgebra.kt

@@ -0,0 +1,60 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.geometry
+
+import space.kscience.kmath.operations.Algebra
+import kotlin.math.*
+
+public data class TileWebMercatorCoordinates(val zoom: Double, val x: Double, val y: Double)
+
+public object WebMercatorAlgebra : Algebra<TileWebMercatorCoordinates> {
+
+    private fun scaleFactor(zoom: Double) = 256.0 / 2 / PI * 2.0.pow(zoom)
+
+    public fun TileWebMercatorCoordinates.toGeodetic(): GeodeticCoordinates {
+        val scaleFactor = scaleFactor(zoom)
+        val longitude = x / scaleFactor - PI
+        val latitude = (atan(exp(PI - y / scaleFactor)) - PI / 4) * 2
+        return GeodeticCoordinates.ofRadians(latitude, longitude)
+    }
+
+    /**
+     * https://en.wikipedia.org/wiki/Web_Mercator_projection#Formulas
+     */
+    public fun GeodeticCoordinates.toMercator(zoom: Double): TileWebMercatorCoordinates {
+        require(abs(latitude) <= MercatorAlgebra.MAXIMUM_LATITUDE) { "Latitude exceeds the maximum latitude for mercator coordinates" }
+
+        val scaleFactor = scaleFactor(zoom)
+        return TileWebMercatorCoordinates(
+            zoom = zoom,
+            x = scaleFactor * (longitude + PI),
+            y = scaleFactor * (PI - ln(tan(PI / 4 + latitude / 2)))
+        )
+    }
+
+    /**
+     * Compute and offset of [target] coordinate relative to [base] coordinate. If [zoom] is null, then optimal zoom
+     * will be computed to put the resulting x and y coordinates between -127.0 and 128.0
+     */
+    public fun computeOffset(
+        base: GeodeticCoordinates,
+        target: GeodeticCoordinates,
+        zoom: Double? = null,
+    ): TileWebMercatorCoordinates {
+        val xOffsetUnscaled = target.longitude - base.longitude
+        val yOffsetUnscaled = ln(
+            tan(PI / 4 + target.latitude / 2) / tan(PI / 4 + base.latitude / 2)
+        )
+
+        val computedZoom = zoom ?: floor(log2(PI / max(abs(xOffsetUnscaled), abs(yOffsetUnscaled))))
+        val scaleFactor = scaleFactor(computedZoom)
+        return TileWebMercatorCoordinates(
+            computedZoom,
+            x = scaleFactor * xOffsetUnscaled,
+            y = scaleFactor * yOffsetUnscaled
+        )
+    }
+}

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/MercatorTest.kt

@@ -0,0 +1,58 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.geometry
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertTrue
+
+class MercatorTest {
+
+    @Test
+    fun boundaries() {
+        assertEquals(GeodeticCoordinates.ofDegrees(45.0, 20.0), GeodeticCoordinates.ofDegrees(45.0, 200.0))
+    }
+
+    @Test
+    fun mercatorConversion() = with(MercatorAlgebra) {
+        val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
+        val m = mskCoordinates.toMercator()
+        val r = m.toGeodetic()
+
+        assertEquals(mskCoordinates.longitude, r.longitude, 1e-4)
+        assertEquals(mskCoordinates.latitude, r.latitude, 1e-4)
+    }
+
+    @Test
+    fun webMercatorConversion() = with(WebMercatorAlgebra) {
+        val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
+        val m = mskCoordinates.toMercator(2.0)
+        val r = m.toGeodetic()
+
+        assertEquals(mskCoordinates.longitude, r.longitude, 1e-4)
+        assertEquals(mskCoordinates.latitude, r.latitude, 1e-4)
+    }
+
+    @Test
+    fun webMercatorOffset() {
+        val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
+        val spbCoordinates = GeodeticCoordinates.ofDegrees(59.9311, 30.3609)
+
+        val offset = WebMercatorAlgebra.computeOffset(mskCoordinates, spbCoordinates)
+
+        assertTrue { offset.x in -127.0..128.0 }
+        assertTrue { offset.y in -127.0..128.0 }
+        assertTrue { offset.zoom > 0.0 }
+    }
+
+    @Test
+    fun webMercatorAbsolute() {
+        val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
+        val wmc = with(WebMercatorAlgebra) { mskCoordinates.toMercator(13.0) }
+        assertEquals(wmc.x, 1267712.0, 50.0)
+        assertEquals(wmc.y, 655616.0, 50.0)
+    }
+}