export interface LonLatPoint {
  lon: number
  lat: number
}

export interface WebMercatorPoint {
  x: number
  y: number
}

export interface WorldTilePoint {
  x: number
  y: number
}

const MAX_LATITUDE = 85.05112878
const EARTH_RADIUS = 6378137

function clampLatitude(lat: number): number {
  return Math.max(-MAX_LATITUDE, Math.min(MAX_LATITUDE, lat))
}

export function lonLatToWebMercator(point: LonLatPoint): WebMercatorPoint {
  const latitude = clampLatitude(point.lat)
  const lonRad = point.lon * Math.PI / 180
  const latRad = latitude * Math.PI / 180

  return {
    x: EARTH_RADIUS * lonRad,
    y: EARTH_RADIUS * Math.log(Math.tan(Math.PI / 4 + latRad / 2)),
  }
}

export function webMercatorToLonLat(point: WebMercatorPoint): LonLatPoint {
  return {
    lon: point.x / EARTH_RADIUS * 180 / Math.PI,
    lat: (2 * Math.atan(Math.exp(point.y / EARTH_RADIUS)) - Math.PI / 2) * 180 / Math.PI,
  }
}

export function lonLatToWorldTile(point: LonLatPoint, zoom: number): WorldTilePoint {
  const latitude = clampLatitude(point.lat)
  const scale = Math.pow(2, zoom)
  const latRad = latitude * Math.PI / 180

  return {
    x: (point.lon + 180) / 360 * scale,
    y: (1 - Math.log(Math.tan(latRad) + 1 / Math.cos(latRad)) / Math.PI) / 2 * scale,
  }
}

export function worldTileToLonLat(point: WorldTilePoint, zoom: number): LonLatPoint {
  const scale = Math.pow(2, zoom)
  const lon = point.x / scale * 360 - 180
  const latRad = Math.atan(Math.sinh(Math.PI * (1 - 2 * point.y / scale)))

  return {
    lon,
    lat: latRad * 180 / Math.PI,
  }
}