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Add ellipsoid mercator backward transformation

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This commit is contained in:
Alexander Nozik 2023-02-22 10:34:59 +03:00
parent 8f489ea0f9
commit 1a7646f311
6 changed files with 55 additions and 15 deletions
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2
maps-kt-core/src/commonMain/kotlin/center/sciprog/maps/coordinates/Distance.kt
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@ -1,7 +1,9 @@
package center.sciprog.maps.coordinates
import kotlinx.serialization.Serializable
import kotlin.jvm.JvmInline
@Serializable
@JvmInline
public value class Distance internal constructor(public val kilometers: Double) : Comparable<Distance> {
override fun compareTo(other: Distance): Int = this.kilometers.compareTo(other.kilometers)

8
maps-kt-core/src/commonMain/kotlin/center/sciprog/maps/coordinates/GeoEllipsoid.kt
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@ -1,11 +1,12 @@
package center.sciprog.maps.coordinates
import kotlinx.serialization.Serializable
import space.kscience.kmath.geometry.Angle
import space.kscience.kmath.geometry.tan
import kotlin.math.pow
import kotlin.math.sqrt
@Serializable
public class GeoEllipsoid(public val equatorRadius: Distance, public val polarRadius: Distance) {
/**
@ -18,8 +19,13 @@ public class GeoEllipsoid(public val equatorRadius: Distance, public val polarRa
*/
public val inverseF: Double = equatorRadius.kilometers / (equatorRadius.kilometers - polarRadius.kilometers)
/**
* Eccentricity squared
*/
public val eSquared: Double = 2 * f - f * f
public val eccentricity: Double = sqrt(eSquared)
public companion object {
public val WGS84: GeoEllipsoid = GeoEllipsoid(

2
maps-kt-core/src/commonMain/kotlin/center/sciprog/maps/coordinates/GeodeticMapCoordinates.kt
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@ -1,5 +1,6 @@
package center.sciprog.maps.coordinates
import kotlinx.serialization.Serializable
import space.kscience.kmath.geometry.Angle
import space.kscience.kmath.geometry.degrees
import space.kscience.kmath.geometry.normalized
@ -10,6 +11,7 @@ import space.kscience.kmath.geometry.radians
*
* @param elevation is optional
*/
@Serializable
public class GeodeticMapCoordinates(
public val latitude: Angle,
public val longitude: Angle,

2
maps-kt-core/src/commonMain/kotlin/center/sciprog/maps/coordinates/GmcPose.kt
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@ -1,11 +1,13 @@
package center.sciprog.maps.coordinates
import kotlinx.serialization.Serializable
import space.kscience.kmath.geometry.Angle
import space.kscience.kmath.geometry.normalized
/**
* A coordinate-bearing pair
*/
@Serializable
public data class GmcPose(val coordinates: GeodeticMapCoordinates, val bearing: Angle) {
val latitude: Angle get() = coordinates.latitude
val longitude: Angle get() = coordinates.longitude

40
maps-kt-core/src/commonMain/kotlin/center/sciprog/maps/coordinates/MercatorProjection.kt
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@ -5,6 +5,7 @@
package center.sciprog.maps.coordinates
import kotlinx.serialization.Serializable
import space.kscience.kmath.geometry.*
import kotlin.math.*
@ -27,25 +28,42 @@ public interface MapProjection<T : Any> {
* @param baseLongitude the longitude offset in radians
* @param ellipsoid - a [GeoEllipsoid] to be used for conversion
*/
@Serializable
public open class MercatorProjection(
public val baseLongitude: Angle = Angle.zero,
public val ellipsoid: GeoEllipsoid = GeoEllipsoid.sphere,
) : MapProjection<ProjectionCoordinates> {
override fun toGeodetic(pc: ProjectionCoordinates): GeodeticMapCoordinates {
val res = GeodeticMapCoordinates.ofRadians(
atan(sinh(pc.y / ellipsoid.equatorRadius)),
baseLongitude.radians + (pc.x / ellipsoid.equatorRadius),
)
/**
* Taken from https://github.com/geotools/geotools/blob/main/modules/library/referencing/src/main/java/org/geotools/referencing/operation/projection/Mercator.java#L164
*/
private fun cphi2(ts: Double): Double {
val eccnth: Double = 0.5 * ellipsoid.eccentricity
var phi: Double = PI / 2 - 2.0 * atan(ts)
for (i in 0 until 15) {
val con: Double = ellipsoid.eccentricity * sin(phi)
val dphi: Double = PI / 2 - 2.0 * atan(ts * ((1 - con) / (1 + con)).pow(eccnth)) - phi
phi += dphi
if (abs(dphi) <= 1e-10) {
return phi
}
}
error("Inverse mercator projection transformation failed to converge")
}
override fun toGeodetic(pc: ProjectionCoordinates): GeodeticMapCoordinates {
return if (ellipsoid === GeoEllipsoid.sphere) {
res
GeodeticMapCoordinates.ofRadians(
atan(sinh(pc.y / ellipsoid.equatorRadius)),
baseLongitude.radians + (pc.x / ellipsoid.equatorRadius),
)
} else {
TODO("Elliptical mercator projection not implemented")
// GeodeticMapCoordinates(
// atan(sinh(pc.y / ellipsoid.polarRadius)).radians,
// res.longitude,
// )
GeodeticMapCoordinates.ofRadians(
cphi2(exp(-(pc.y / ellipsoid.equatorRadius))),
baseLongitude.radians + (pc.x / ellipsoid.equatorRadius)
)
}
}

16
maps-kt-core/src/commonTest/kotlin/center/sciprog/maps/coordinates/MercatorTest.kt
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@ -6,14 +6,24 @@ import kotlin.test.assertEquals
class MercatorTest {
@Test
fun forwardBackward(){
fun sphereForwardBackward(){
val moscow = Gmc.ofDegrees(55.76058287719673, 37.60358622841869)
val mercator = MapProjection.epsg3857.toProjection(moscow)
//https://epsg.io/transform#s_srs=4326&t_srs=3857&x=37.6035862&y=55.7605829
assertEquals(4186.0120709, mercator.x.kilometers, 1e-4)
assertEquals(7510.9013658, mercator.y.kilometers, 1e-4)
val backwards = MapProjection.epsg3857.toGeodetic(mercator)
assertEquals(moscow.latitude.degrees, backwards.latitude.degrees, 0.001)
assertEquals(moscow.longitude.degrees, backwards.longitude.degrees, 0.001)
assertEquals(moscow.latitude.degrees, backwards.latitude.degrees, 1e-6)
assertEquals(moscow.longitude.degrees, backwards.longitude.degrees, 1e-6)
}
@Test
fun ellipseForwardBackward(){
val moscow = Gmc.ofDegrees(55.76058287719673, 37.60358622841869)
val projection = MercatorProjection(ellipsoid = GeoEllipsoid.WGS84)
val mercator = projection.toProjection(moscow)
val backwards = projection.toGeodetic(mercator)
assertEquals(moscow.latitude.degrees, backwards.latitude.degrees, 1e-6)
assertEquals(moscow.longitude.degrees, backwards.longitude.degrees, 1e-6)
}
}