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.
/// </summary>
public static class IslandFalloff
{
	// ---- centre-line crest ------------------------------------------------
	// Rounding radius in normalized spine-width units (1.0 = MapSize/2 * 1.15
	// ~ 4710 px at 8K). 0.03 ~ 141 px: it cuts the crest's 1-px kink by 99.3%
	// (-7.64e-04 -> -5.41e-06 raw, against a natural profile curvature of ~1.1e-07)
	// 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);
	}
}