step one

internal/engine/state.go

@@ -0,0 +1,50 @@
+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)
+}