Web mercator conversion

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Alexander Nozik 2022-06-16 20:46:43 +03:00
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/*
* 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 class GeodeticCoordinates private constructor(public val latitude: Double, public val longitude: Double) {
init {
require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
require(latitude in (-PI / 2)..(PI / 2)) { "Latitude $latitude is not in (-PI/2)..(PI/2)" }
}
public companion object {
public fun ofRadians(longitude: Double, latitude: Double): GeodeticCoordinates =
GeodeticCoordinates(latitude, longitude)
public fun ofDegrees(longitude: Double, latitude: Double): GeodeticCoordinates =
GeodeticCoordinates(latitude * PI / 180, longitude * PI / 180)
}
}
public data class WebMercatorCoordinates(val zoom: Double, val x: Double, val y: Double)
public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
fun WebMercatorCoordinates.toGeodetic(): GeodeticCoordinates = TODO()
/**
* https://en.wikipedia.org/wiki/Web_Mercator_projection#Formulas
*/
public fun GeodeticCoordinates.toMercator(zoom: Double): WebMercatorCoordinates {
require(abs(latitude) <= 2 * atan(E.pow(PI)) - PI / 2) { "Latitude exceeds the maximum latitude for mercator coordinates" }
val scaleFactor = 256.0 / 2 / PI * 2.0.pow(zoom)
return WebMercatorCoordinates(
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,
): WebMercatorCoordinates {
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 = 256.0 / 2 / PI * 2.0.pow(computedZoom)
return WebMercatorCoordinates(
computedZoom,
x = scaleFactor * xOffsetUnscaled,
y = scaleFactor * yOffsetUnscaled
)
}
}

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/*
* 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.assertTrue
class MercatorTest {
@Test
fun mercatorOffset(){
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 > 1.0 }
}
}