mirror of https://github.com/tidwall/tile38.git
120 lines
3.1 KiB
Go
120 lines
3.1 KiB
Go
package collection
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import "math"
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func geodeticDistAlgo(center [2]float64) (
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algo func(min, max [2]float64, data interface{}, item bool) (dist float64),
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) {
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const earthRadius = 6371e3
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return func(min, max [2]float64, data interface{}, item bool) (dist float64) {
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return earthRadius * pointRectDistGeodeticDeg(
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center[1], center[0],
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min[1], min[0],
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max[1], max[0],
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)
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}
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}
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func pointRectDistGeodeticDeg(pLat, pLng, minLat, minLng, maxLat, maxLng float64) float64 {
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result := pointRectDistGeodeticRad(
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pLat*math.Pi/180, pLng*math.Pi/180,
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minLat*math.Pi/180, minLng*math.Pi/180,
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maxLat*math.Pi/180, maxLng*math.Pi/180,
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)
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return result
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}
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func pointRectDistGeodeticRad(φq, λq, φl, λl, φh, λh float64) float64 {
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// Algorithm from:
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// Schubert, E., Zimek, A., & Kriegel, H.-P. (2013).
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// Geodetic Distance Queries on R-Trees for Indexing Geographic Data.
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// Lecture Notes in Computer Science, 146–164.
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// doi:10.1007/978-3-642-40235-7_9
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const (
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twoΠ = 2 * math.Pi
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halfΠ = math.Pi / 2
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)
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// distance on the unit sphere computed using Haversine formula
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distRad := func(φa, λa, φb, λb float64) float64 {
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if φa == φb && λa == λb {
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return 0
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}
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Δφ := φa - φb
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Δλ := λa - λb
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sinΔφ := math.Sin(Δφ / 2)
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sinΔλ := math.Sin(Δλ / 2)
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cosφa := math.Cos(φa)
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cosφb := math.Cos(φb)
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return 2 * math.Asin(math.Sqrt(sinΔφ*sinΔφ+sinΔλ*sinΔλ*cosφa*cosφb))
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}
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// Simple case, point or invalid rect
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if φl >= φh && λl >= λh {
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return distRad(φl, λl, φq, λq)
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}
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if λl <= λq && λq <= λh {
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// q is between the bounding meridians of r
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// hence, q is north, south or within r
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if φl <= φq && φq <= φh { // Inside
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return 0
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}
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if φq < φl { // South
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return φl - φq
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}
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return φq - φh // North
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}
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// determine if q is closer to the east or west edge of r to select edge for
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// tests below
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Δλe := λl - λq
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Δλw := λq - λh
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if Δλe < 0 {
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Δλe += twoΠ
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}
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if Δλw < 0 {
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Δλw += twoΠ
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}
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var Δλ float64 // distance to closest edge
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var λedge float64 // longitude of closest edge
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if Δλe <= Δλw {
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Δλ = Δλe
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λedge = λl
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} else {
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Δλ = Δλw
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λedge = λh
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}
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sinΔλ, cosΔλ := math.Sincos(Δλ)
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tanφq := math.Tan(φq)
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if Δλ >= halfΠ {
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// If Δλ > 90 degrees (1/2 pi in radians) we're in one of the corners
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// (NW/SW or NE/SE depending on the edge selected). Compare against the
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// center line to decide which case we fall into
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φmid := (φh + φl) / 2
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if tanφq >= math.Tan(φmid)*cosΔλ {
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return distRad(φq, λq, φh, λedge) // North corner
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}
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return distRad(φq, λq, φl, λedge) // South corner
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}
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if tanφq >= math.Tan(φh)*cosΔλ {
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return distRad(φq, λq, φh, λedge) // North corner
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}
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if tanφq <= math.Tan(φl)*cosΔλ {
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return distRad(φq, λq, φl, λedge) // South corner
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}
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// We're to the East or West of the rect, compute distance using cross-track
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// Note that this is a simplification of the cross track distance formula
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// valid since the track in question is a meridian.
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return math.Asin(math.Cos(φq) * sinΔλ)
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}
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