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package io.data2viz.geo
import io.data2viz.geo.projection.Stream
import io.data2viz.geojson.GeoJsonObject
import io.data2viz.math.EPSILON
import io.data2viz.math.EPSILON2
import io.data2viz.math.toDegrees
import io.data2viz.math.toRadians
import kotlin.math.*
// TODO : fun geoCentroid(geo) = GeoCentroid().result(geo) and generalizes to all measurements classes
/**
* Returns the spherical centroid of the specified GeoJSON object.
* This is the spherical equivalent of PathCentroid.
*/
class GeoCentroid : Stream {
private var _W0 = .0
private var _W1 = .0
private var _X0 = .0
private var _Y0 = .0
private var _Z0 = .0
private var _X1 = .0
private var _Y1 = .0
private var _Z1 = .0
private var _X2 = .0
private var _Y2 = .0
private var _Z2 = .0
private var lambda00 = Double.NaN
private var phi00 = Double.NaN // first point
private var x0 = Double.NaN
private var y0 = Double.NaN
private var z0 = Double.NaN // previous point
private var currentPoint: (Double, Double) -> Unit = ::centroidPoint
private var currentLineStart: () -> Unit = ::centroidLineStart
private var currentLineEnd: () -> Unit = ::centroidLineEnd
// TODO : invoke ?
fun result(geo: GeoJsonObject): DoubleArray {
_W0 = .0
_W1 = .0
_X0 = .0
_Y0 = .0
_Z0 = .0
_X1 = .0
_Y1 = .0
_Z1 = .0
_X2 = .0
_Y2 = .0
_Z2 = .0
stream(geo, this)
var x = _X2
var y = _Y2
var z = _Z2
var m = x * x + y * y + z * z;
// If the area-weighted centroid is undefined, fall back to length-weighted ccentroid.
if (m < EPSILON2) {
x = _X1
y = _Y1
z = _Z1
// If the feature has zero length, fall back to arithmetic mean of point vectors.
if (_W1 < EPSILON) {
x = _X0
y = _Y0
z = _Z0
}
m = x * x + y * y + z * z
// If the feature still has an undefined centroid, then return.
if (m < EPSILON2) return doubleArrayOf(Double.NaN, Double.NaN)
}
return doubleArrayOf(atan2(y, x).toDegrees(), asin(z / sqrt(m)).toDegrees())
}
override fun point(x: Double, y: Double, z: Double) = currentPoint(x, y)
override fun lineStart() = currentLineStart()
override fun lineEnd() = currentLineEnd()
override fun polygonStart() {
currentLineStart = ::centroidRingStart
currentLineEnd = ::centroidRingEnd
}
override fun polygonEnd() {
currentLineStart = ::centroidLineStart
currentLineEnd = ::centroidLineEnd
}
// Arithmetic mean of Cartesian vectors.
private fun centroidPoint(x: Double, y: Double) {
val lambda = x.toRadians()
val phi = y.toRadians()
val cosPhi = cos(phi)
centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi))
}
private fun centroidPointCartesian(x: Double, y: Double, z: Double) {
++_W0
_X0 += (x - _X0) / _W0
_Y0 += (y - _Y0) / _W0
_Z0 += (z - _Z0) / _W0
}
private fun centroidLineStart() {
currentPoint = ::centroidLinePointFirst
}
private fun centroidLinePointFirst(x: Double, y: Double) {
val lambda = x.toRadians()
val phi = y.toRadians()
val cosPhi = cos(phi)
x0 = cosPhi * cos(lambda)
y0 = cosPhi * sin(lambda)
z0 = sin(phi)
currentPoint = ::centroidLinePoint
centroidPointCartesian(x0, y0, z0)
}
private fun centroidLinePoint(x: Double, y: Double) {
val lambda = x.toRadians()
val phi = y.toRadians()
val cosPhi = cos(phi)
val a = cosPhi * cos(lambda)
val b = cosPhi * sin(lambda)
val c = sin(phi)
val w1 = y0 * c - z0 * b
val w2 = z0 * a - x0 * c
val w3 = x0 * b - y0 * a
val w = atan2(sqrt((w1 * w1) + (w2 * w2) + (w3 * w3)), x0 * a + y0 * b + z0 * c)
_W1 += w
_X1 += w * (x0 + a)
x0 = a
_Y1 += w * (y0 + b)
y0 = b
_Z1 += w * (z0 + c)
z0 = c
centroidPointCartesian(x0, y0, z0)
}
private fun centroidLineEnd() {
currentPoint = ::centroidPoint
}
// See J. E. Brock, The Inertia Tensor for a Spherical Triangle,
// J. Applied Mechanics 42, 239 (1975).
private fun centroidRingStart() {
currentPoint = ::centroidRingPointFirst
}
private fun centroidRingEnd() {
centroidRingPoint(lambda00, phi00)
currentPoint = ::centroidPoint
}
private fun centroidRingPointFirst(x: Double, y: Double) {
lambda00 = x
phi00 = y
val lambda = x.toRadians()
val phi = y.toRadians()
val cosPhi = cos(phi)
currentPoint = ::centroidRingPoint
x0 = cosPhi * cos(lambda)
y0 = cosPhi * sin(lambda)
z0 = sin(phi)
centroidPointCartesian(x0, y0, z0)
}
private fun centroidRingPoint(x: Double, y: Double) {
val lambda = x.toRadians()
val phi = y.toRadians()
val cosPhi = cos(phi)
val a = cosPhi * cos(lambda)
val b = cosPhi * sin(lambda)
val c = sin(phi)
val cx = y0 * c - z0 * b
val cy = z0 * a - x0 * c
val cz = x0 * b - y0 * a
val m = sqrt(cx * cx + cy * cy + cz * cz)
val w = asin(m) // line weight = angle
val v = if (m == .0) .0 else -w / m // area weight multiplier
_X2 += v * cx
_Y2 += v * cy
_Z2 += v * cz
_W1 += w
_X1 += w * (x0 + a)
x0 = a
_Y1 += w * (y0 + b)
y0 = b
_Z1 += w * (z0 + c)
z0 = c
centroidPointCartesian(x0, y0, z0)
}
}
