// Package world defines the static shape of the belt: bodies on analytic
// (on-rails) orbits and the procedural generation that creates them.
//
// The star pulls with acceleration v^2/r (v = config OrbitSpeed), so a circular
// orbit at any radius has the same speed v. Every body on rails is therefore
// on a circle traversed at speed v; only the period (2*pi*r/v) varies.
package world

import "wh/fixed"

// Orbit is a circular orbit around the origin (the star).
type Orbit struct {
	A      fixed.F // radius, km
	Period int64   // seconds
	M0     fixed.F // phase at t=0, radians
	Inc    fixed.F // inclination to the ecliptic (XY plane), radians
	Node   fixed.F // longitude of the ascending node, radians
}

// PeriodFor returns the period in seconds of a circle of radius a at speed v.
func PeriodFor(a, v fixed.F) int64 {
	return fixed.TwoPi.Mul(a).Div(v).Int()
}

// State returns position (km) and velocity (km/s) at absolute time t seconds.
func (o Orbit) State(t int64) (pos, vel fixed.Vec) {
	frac := fixed.FromInt(t % o.Period).Div(fixed.FromInt(o.Period))
	s, c := fixed.SinCos(o.M0 + fixed.TwoPi.Mul(frac))
	k := fixed.TwoPi.Mul(o.A).Div(fixed.FromInt(o.Period)) // speed
	pos = fixed.Vec{X: o.A.Mul(c), Y: o.A.Mul(s)}
	vel = fixed.Vec{X: -k.Mul(s), Y: k.Mul(c)}
	return o.orient(pos), o.orient(vel)
}

// orient rotates a vector from the orbital plane into the ecliptic frame:
// Rz(Node) * Rx(Inc).
func (o Orbit) orient(v fixed.Vec) fixed.Vec {
	return v.RotateX(o.Inc).RotateZ(o.Node)
}