Catenary calculation functions in c#

catenary.cs

// Function to calculate y-value of catenary curve at a particular x-value.
public static float CatenaryY(Vector2 start, Vector2 end, float length, float x) {
	float h = end.X - start.X;
	float v = end.Y - start.Y;
	float a = FindA(h, v, length);
	float p = (start.X + end.X - a * MathF.Log((length + v) / (length - v))) / 2;
	float q = (start.Y + end.Y - length * (1 / MathF.Tanh(h / (2 * a)))) / 2;
	return a * MathF.Cosh((x - p) / a) + q;
}

// Helper function to find the correct value for a.
public static float FindA(float h, float v, float l) {
	// You can't calculate a, you can only pick a number and then check how well it works.
	// Do a linear scan of possible values for a first.
	// Note that the code I derived this from uses a *much* smaller step, but this step size yields
	// the fastest results for where I'm using it. YMMV.
	const float step = 50f;
	float a = 0;
	do
	{
		a += step;
	}
	while (MathF.Sqrt(MathF.Pow(l, 2) - MathF.Pow(v, 2)) < 2 * a * MathF.Sinh(h / (2 * a)));

	// Again, the code I derived this from uses a much higher target precision, but this is enough
	// for my needs.
	const float precision = 0.1f;

	float aPrev = a - step;
	float aNext = a;

	do
	{
		a = (aPrev + aNext) / 2f;
		if (Math.Sqrt(Math.Pow(l, 2) - Math.Pow(v, 2)) < 2 * a * MathF.Sinh(h / (2 * a))) {
			aPrev = a;
		} else {
			aNext = a;
		}
	} while (aNext - aPrev > precision);

	return a;
}