tile38/internal/collection/geodesic.go

120 lines
3.1 KiB
Go
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

package collection
import "math"
func geodeticDistAlgo(center [2]float64) (
algo func(min, max [2]float64, data interface{}, item bool) (dist float64),
) {
const earthRadius = 6371e3
return func(min, max [2]float64, data interface{}, item bool) (dist float64) {
return earthRadius * pointRectDistGeodeticDeg(
center[1], center[0],
min[1], min[0],
max[1], max[0],
)
}
}
func pointRectDistGeodeticDeg(pLat, pLng, minLat, minLng, maxLat, maxLng float64) float64 {
result := pointRectDistGeodeticRad(
pLat*math.Pi/180, pLng*math.Pi/180,
minLat*math.Pi/180, minLng*math.Pi/180,
maxLat*math.Pi/180, maxLng*math.Pi/180,
)
return result
}
func pointRectDistGeodeticRad(φq, λq, φl, λl, φh, λh float64) float64 {
// Algorithm from:
// Schubert, E., Zimek, A., & Kriegel, H.-P. (2013).
// Geodetic Distance Queries on R-Trees for Indexing Geographic Data.
// Lecture Notes in Computer Science, 146164.
// doi:10.1007/978-3-642-40235-7_9
const (
twoΠ = 2 * math.Pi
halfΠ = math.Pi / 2
)
// distance on the unit sphere computed using Haversine formula
distRad := func(φa, λa, φb, λb float64) float64 {
if φa == φb && λa == λb {
return 0
}
Δφ := φa - φb
Δλ := λa - λb
sinΔφ := math.Sin(Δφ / 2)
sinΔλ := math.Sin(Δλ / 2)
cosφa := math.Cos(φa)
cosφb := math.Cos(φb)
return 2 * math.Asin(math.Sqrt(sinΔφ*sinΔφ+sinΔλ*sinΔλ*cosφa*cosφb))
}
// Simple case, point or invalid rect
if φl >= φh && λl >= λh {
return distRad(φl, λl, φq, λq)
}
if λl <= λq && λq <= λh {
// q is between the bounding meridians of r
// hence, q is north, south or within r
if φl <= φq && φq <= φh { // Inside
return 0
}
if φq < φl { // South
return φl - φq
}
return φq - φh // North
}
// determine if q is closer to the east or west edge of r to select edge for
// tests below
Δλe := λl - λq
Δλw := λq - λh
if Δλe < 0 {
Δλe += twoΠ
}
if Δλw < 0 {
Δλw += twoΠ
}
var Δλ float64 // distance to closest edge
var λedge float64 // longitude of closest edge
if Δλe <= Δλw {
Δλ = Δλe
λedge = λl
} else {
Δλ = Δλw
λedge = λh
}
sinΔλ, cosΔλ := math.Sincos(Δλ)
tanφq := math.Tan(φq)
if Δλ >= halfΠ {
// If Δλ > 90 degrees (1/2 pi in radians) we're in one of the corners
// (NW/SW or NE/SE depending on the edge selected). Compare against the
// center line to decide which case we fall into
φmid := (φh + φl) / 2
if tanφq >= math.Tan(φmid)*cosΔλ {
return distRad(φq, λq, φh, λedge) // North corner
}
return distRad(φq, λq, φl, λedge) // South corner
}
if tanφq >= math.Tan(φh)*cosΔλ {
return distRad(φq, λq, φh, λedge) // North corner
}
if tanφq <= math.Tan(φl)*cosΔλ {
return distRad(φq, λq, φl, λedge) // South corner
}
// We're to the East or West of the rect, compute distance using cross-track
// Note that this is a simplification of the cross track distance formula
// valid since the track in question is a meridian.
return math.Asin(math.Cos(φq) * sinΔλ)
}