package engine

import "math"

// pymod returns a % b with Python semantics: the result has the sign of b,
// so for b > 0 the result is always in [0, b).
func pymod(a, b float64) float64 {
	r := math.Mod(a, b)
	if r < 0 {
		r += b
	}
	return r
}

// stateAdd is the RK4 integrator's update operation y + k*dy, with longitude
// kept wrapped to [0, 360).
//
// Time is not stored in State — it is tracked separately by the integrator
// and passed to Model.
func stateAdd(y State, k float64, dy State) State {
	return State{
		Lat:      y.Lat + k*dy.Lat,
		Lng:      pymod(y.Lng+k*dy.Lng, 360),
		Altitude: y.Altitude + k*dy.Altitude,
	}
}

// stateLerp computes the linear interpolation of two states by parameter l
// in [0, 1]. Longitude uses lngLerp so that wrap-around is handled.
func stateLerp(a, b State, l float64) State {
	return State{
		Lat:      (1-l)*a.Lat + l*b.Lat,
		Lng:      lngLerp(a.Lng, b.Lng, l),
		Altitude: (1-l)*a.Altitude + l*b.Altitude,
	}
}

// lngLerp interpolates between two longitudes in [0, 360), choosing the
// shorter great-circle arc.
func lngLerp(a, b, l float64) float64 {
	l2 := 1 - l
	if a > b {
		a, b = b, a
		l, l2 = l2, l
	}
	if b-a < 180 {
		return l2*a + l*b
	}
	return pymod(l2*(a+360)+l*b, 360)
}