Bezier.cs

// Source: https://programmerbay.com/c-program-to-draw-bezier-curve-using-4-control-points/
namespace Flow.Utility;

public class Bezier
{
	public static Vector3 Approach( Vector3 start, Vector3 end, float startCurveSize, float endCurveSize, float t )
	{
		var controlPoint1 = start + Vector3.Up * startCurveSize;
		var controlPoint2 = end + Vector3.Up * endCurveSize;
		float x = (float)(Math.Pow( 1 - t, 3 ) * start.x + 3 * t * Math.Pow( 1 - t, 2 ) * controlPoint1.x + 3 * t * t * (1 - t) * controlPoint2.x + Math.Pow( t, 3 ) * end.x);
		float y = (float)(Math.Pow( 1 - t, 3 ) * start.y + 3 * t * Math.Pow( 1 - t, 2 ) * controlPoint1.y + 3 * t * t * (1 - t) * controlPoint2.y + Math.Pow( t, 3 ) * end.y);
		float z = (float)(Math.Pow( 1 - t, 3 ) * start.z + 3 * t * Math.Pow( 1 - t, 2 ) * controlPoint1.z + 3 * t * t * (1 - t) * controlPoint2.z + Math.Pow( t, 3 ) * end.z);

		return new Vector3( x, y, z );
	}
	public static Vector3 Approach( Vector3 start, Vector3 end, float curveSize, float t )
	{
		return Approach( start, end, curveSize, curveSize, t );
	}
}