using Godot;

/// <summary>
/// The island-falloff shaping functions (terrain-water task 11) — pure numeric
/// functions of their inputs (D-035; a named future C++ candidate, kept standalone).
///
///   SMOOTH CREST — the mountain spine's ridge axis is the line x = centre, and
///   `1 - |x - cx|` peaks there with a slope discontinuity. Measured on the shipped
///   terrain, that crease is the single largest slope step anywhere on the map once
///   the by-design Trench walls are excluded (top 4 of 5999 columns). SmoothAbs
///   rounds the crest without moving its height.
///
///   COAST SHELF — the height curve is identity at and below sea level, so it never
///   touched the SUBMARINE slope. Measured: land rises from the shoreline at
///   0.038 m/px while the seabed drops at 0.258 m/px — the shoreline is a shelf on
///   the land side and a ramp on the sea side. CoastShelf compresses shallow depth
///   so the shallows extend much further out, leaving deep water and the Trench
///   essentially untouched.
///
/// Every one of these is monotone in the sign of (sea - height): none of them can
/// turn water into land or land into water on its own. The coast shelf therefore
/// leaves the biome and water classification bit-identical, which is why it is
/// separable from elongation in the batch.
/// </summary>
public static class IslandFalloff
{
	// ---- centre-line crest ------------------------------------------------
	// Rounding radius in normalized spine-width units (1.0 = MapSize/2 * IslandAxisX
	// ~ 4710 px at 8K with the default axis). 0.03 ~ 141 px: it cuts the crest's
	// 1-px kink by 99.3% (-7.64e-04 -> -5.41e-06 raw) while filling at most 3.9 m,
	// decaying under 0.5 m by ~1100 px from the axis.
	public const float CREST_EPSILON = 0.03f;

	/// <summary>
	/// A C¹ stand-in for |d|: exactly 0 with zero slope at d = 0, and converging to
	/// |d| within e²/(2|d|) away from it. Replaces the V-shaped crest of the spine
	/// with a rounded one WITHOUT lowering it — SmoothAbs(0) is 0, so the peak keeps
	/// its full height.
	/// </summary>
	public static float SmoothAbs(float d, float epsilon)
	{
		float a = Mathf.Abs(d);
		return a * a / Mathf.Sqrt(a * a + epsilon * epsilon);
	}

	// ---- coast shelf ------------------------------------------------------
	// depth' = depth * (1 - STRENGTH * exp(-depth / SCALE_M)).
	// At the shoreline the seabed starts at (1 - STRENGTH) of its former gradient and
	// recovers smoothly, so the shallows widen and the deep ocean keeps its shape.
	// C^inf everywhere, and strictly positive for positive depth — it cannot move the
	// waterline by even one pixel.
	public const float SHELF_STRENGTH = 0.775f;   // 0 = off, ->1 = a flat lagoon
	public const float SHELF_SCALE_M = 100f;      // metres of depth over which it relaxes

	/// <summary>Remaps a positive depth in metres. Returns the new depth in metres.</summary>
	public static float CoastShelf(float depthMetres)
	{
		if (depthMetres <= 0f) return depthMetres;
		return depthMetres * (1f - SHELF_STRENGTH * Mathf.Exp(-depthMetres / SHELF_SCALE_M));
	}
}