forked from kscience/kmath
Web mercator conversion
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081304f110
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@ -9,24 +9,55 @@ import space.kscience.kmath.operations.Algebra
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import kotlin.math.*
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public class GeodeticCoordinates private constructor(public val latitude: Double, public val longitude: Double) {
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init {
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require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
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require(latitude in (-PI / 2)..(PI / 2)) { "Latitude $latitude is not in (-PI/2)..(PI/2)" }
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override fun equals(other: Any?): Boolean {
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if (this === other) return true
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if (other == null || this::class != other::class) return false
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other as GeodeticCoordinates
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if (latitude != other.latitude) return false
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if (longitude != other.longitude) return false
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return true
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}
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public companion object {
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public fun ofRadians(longitude: Double, latitude: Double): GeodeticCoordinates =
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GeodeticCoordinates(latitude, longitude)
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override fun hashCode(): Int {
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var result = latitude.hashCode()
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result = 31 * result + longitude.hashCode()
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return result
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}
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public fun ofDegrees(longitude: Double, latitude: Double): GeodeticCoordinates =
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GeodeticCoordinates(latitude * PI / 180, longitude * PI / 180)
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override fun toString(): String {
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return "GeodeticCoordinates(latitude=$latitude, longitude=$longitude)"
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}
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public companion object {
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public fun ofRadians(latitude: Double, longitude: Double): GeodeticCoordinates {
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require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
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return GeodeticCoordinates(latitude, longitude.rem(PI / 2))
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}
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public fun ofDegrees(latitude: Double, longitude: Double): GeodeticCoordinates {
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require(latitude in (-90.0)..(90.0)) { "Latitude $latitude is not in -90..90" }
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return GeodeticCoordinates(latitude * PI / 180, (longitude.rem(180) * PI / 180))
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}
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}
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}
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public data class WebMercatorCoordinates(val zoom: Double, val x: Double, val y: Double)
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public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
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fun WebMercatorCoordinates.toGeodetic(): GeodeticCoordinates = TODO()
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private fun scaleFactor(zoom: Double) = 256.0 / 2 / PI * 2.0.pow(zoom)
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public fun WebMercatorCoordinates.toGeodetic(): GeodeticCoordinates {
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val scaleFactor = scaleFactor(zoom)
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val longitude = x / scaleFactor - PI
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val latitude = (atan(exp(PI - y / scaleFactor)) - PI / 4) * 2
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return GeodeticCoordinates.ofRadians(latitude, longitude)
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}
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/**
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* https://en.wikipedia.org/wiki/Web_Mercator_projection#Formulas
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@ -34,7 +65,7 @@ public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
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public fun GeodeticCoordinates.toMercator(zoom: Double): WebMercatorCoordinates {
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require(abs(latitude) <= 2 * atan(E.pow(PI)) - PI / 2) { "Latitude exceeds the maximum latitude for mercator coordinates" }
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val scaleFactor = 256.0 / 2 / PI * 2.0.pow(zoom)
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val scaleFactor = scaleFactor(zoom)
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return WebMercatorCoordinates(
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zoom = zoom,
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x = scaleFactor * (longitude + PI),
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@ -56,8 +87,8 @@ public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
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tan(PI / 4 + target.latitude / 2) / tan(PI / 4 + base.latitude / 2)
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)
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val computedZoom = zoom ?: floor( log2(PI / max(abs(xOffsetUnscaled), abs(yOffsetUnscaled))))
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val scaleFactor = 256.0 / 2 / PI * 2.0.pow(computedZoom)
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val computedZoom = zoom ?: floor(log2(PI / max(abs(xOffsetUnscaled), abs(yOffsetUnscaled))))
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val scaleFactor = scaleFactor(computedZoom)
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return WebMercatorCoordinates(
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computedZoom,
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x = scaleFactor * xOffsetUnscaled,
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@ -6,19 +6,35 @@
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package space.kscience.kmath.geometry
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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class MercatorTest {
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@Test
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fun mercatorOffset(){
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fun boundaries() {
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assertEquals(GeodeticCoordinates.ofDegrees(45.0, 20.0), GeodeticCoordinates.ofDegrees(45.0, 200.0))
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}
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@Test
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fun webMercatorConversion() = with(WebMercatorAlgebra) {
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val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
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val m = mskCoordinates.toMercator(2.0)
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val r = m.toGeodetic()
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assertEquals(mskCoordinates.longitude, r.longitude,1e-4)
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assertEquals(mskCoordinates.latitude, r.latitude,1e-4)
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}
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@Test
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fun webMercatorOffset() {
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val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
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val spbCoordinates = GeodeticCoordinates.ofDegrees(59.9311, 30.3609)
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val offset = WebMercatorAlgebra.computeOffset(mskCoordinates, spbCoordinates)
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val offset = WebMercatorAlgebra.computeOffset(mskCoordinates, spbCoordinates)
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assertTrue { offset.x in -127.0..128.0 }
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assertTrue { offset.y in -127.0..128.0 }
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assertTrue { offset.zoom > 1.0 }
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assertTrue { offset.zoom > 0.0 }
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}
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}
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