package numerics

import "math"

// PointInPolygon reports whether (lat, lng) lies inside the closed polygon
// whose vertices are given as parallel latitude/longitude slices (degrees).
//
// The test is ray casting in plate-carrée space. Every longitude is
// normalised to within 180° of the first vertex before testing, so a polygon
// spanning the antimeridian is handled correctly as long as it spans no more
// than 180° in longitude. polyLat and polyLng must have equal length >= 3.
func PointInPolygon(lat, lng float64, polyLat, polyLng []float64) bool {
	n := len(polyLat)
	if n < 3 || len(polyLng) != n {
		return false
	}
	ref := polyLng[0]
	qx := NormalizeLng(lng, ref)

	inside := false
	for i, j := 0, n-1; i < n; j, i = i, i+1 {
		yi, yj := polyLat[i], polyLat[j]
		xi := NormalizeLng(polyLng[i], ref)
		xj := NormalizeLng(polyLng[j], ref)

		if (yi > lat) != (yj > lat) {
			xIntersect := (xj-xi)*(lat-yi)/(yj-yi) + xi
			if qx < xIntersect {
				inside = !inside
			}
		}
	}
	return inside
}

// NormalizeLng rewrites v so that it lies within 180° of ref. For example,
// NormalizeLng(350, 10) returns -10. Used to make longitude comparisons
// continuous across the antimeridian.
func NormalizeLng(v, ref float64) float64 {
	return ref + math.Mod(v-ref+540, 360) - 180
}