Bezier Interpolator

bezier_interpolator.cs

using System.Collections.Generic;
using UnityEngine;
using Vuforia;

[ExecuteInEditMode]
public class CurveTrackGenerator : MonoBehaviour
{
	[SerializeField] private Color _color;
	[SerializeField, Range(1f, 10f)] private float _momentum = 3;

	private Vector3[] _points;

	private enum CurveType
	{
		BEZIER,
		BEZIER_EXPERIMENTAL,
		SMOOTH,
		STRAIGHT
	}

	[SerializeField] private CurveType _curveType;
	
	private Vector3 GetInterpolatedPoint(Vector3[] vectors, float percentage)
	{
		while (vectors.Length > 2)
		{
			var newVectors = new Vector3[vectors.Length-1];
			for (var i = 0; i < newVectors.Length; i++)
			{
				newVectors[i] = GetInterpolatedPoint(new[] {vectors[i], vectors[i + 1]}, percentage);
			}
			vectors = newVectors;
		}
		var a = vectors[0];
		var b = vectors[1];
		return a + (b - a) * percentage;
	}

	public Vector3[] GetPath(int steps)
	{
		List<Vector3> points = new List<Vector3>();
		if (_curveType == CurveType.SMOOTH)
		{
			for( var k=1; k<transform.childCount-1; k++)
			{
				var startChild = transform.GetChild(k-1);
				var middleChild = transform.GetChild(k);
				var endChild = transform.GetChild(k+1);
				if (k == 1)
				{
					var vectors = new Vector3[3];
					vectors[0] = startChild.position;
					vectors[1] = middleChild.position;
					vectors[2] = (endChild.position + middleChild.position) * 0.5f;
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float)steps));
					}
				}
				else
				{
					var vectors = new Vector3[3];
					vectors[0] = (middleChild.position + startChild.position) * 0.5f;
					vectors[1] = middleChild.position;
					if (k == transform.childCount - 2)
					{
						vectors[2] = endChild.position;
					}
					else
					{
						vectors[2] = (endChild.position + middleChild.position) * 0.5f;
					}
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float)steps));
					}
					if (k == transform.childCount - 2)
					{
						points.Add(endChild.position);
					}
				}
			}
		}
		else if (_curveType == CurveType.BEZIER_EXPERIMENTAL)
		{
			var momentum = 10 / _momentum;
			for( var k=1; k<transform.childCount-1; k++)
			{
				var p1 = transform.GetChild(k-1);
				var p2 = transform.GetChild(k);
				var p3 = transform.GetChild(k+1);
				
				var d12 = Vector3.Distance(p1.position, p2.position);
				var d23 = Vector3.Distance(p2.position, p3.position);
				
				var cp = p2.position - Vector3.Normalize(p3.position - p1.position)*d12/momentum;
				if (k == 1)
				{
					var vectors = new Vector3[3];
					vectors[0] = p1.position;
					vectors[1] = cp;
					vectors[2] = p2.position;
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float) steps));
					}
				}
				else
				{
					var p0 = transform.GetChild(k - 2);
					var d01 = Vector3.Distance(p0.position, p1.position);

					var cp1 = p1.position + Vector3.Normalize(p2.position - p0.position)*d12/momentum;
					
					var vectors = new Vector3[4];
					vectors[0] = p1.position;
					vectors[1] = cp1;
					vectors[2] = cp;
					vectors[3] = p2.position;
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float) steps));
					}
					if (k == transform.childCount - 2)
					{
						var cp2 = p2.position + Vector3.Normalize(p3.position - p1.position)*d23/momentum;
						vectors = new Vector3[3];
						vectors[0] = p2.position;
						vectors[1] = cp2;
						vectors[2] = p3.position;
						for (var j = 0; j < steps; j++)
						{
							points.Add(GetInterpolatedPoint(vectors, j / (float) steps));
						}
						points.Add(p3.position);
					}
				}
			}
		}
		else if (_curveType == CurveType.BEZIER)
		{
			if (transform.childCount > 0 && transform.GetChild(0).childCount == 0)
			{
				var end = (int) (Mathf.Floor((transform.childCount-1) / 2f) * 2 - 1);
				for( var k=0; k<end; k+=2)
				{
					var startChild = transform.GetChild(k);
					var middleChild = transform.GetChild(k+1);
					var endChild = transform.GetChild(k+2);
					var vectors = new Vector3[3];
					vectors[0] = startChild.position;
					vectors[1] = middleChild.position;
					vectors[2] = endChild.position;
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float)steps));
					}
					if (k == end-1)
					{
						points.Add(endChild.position);
					}
				}
			}
			else
			{
				for (var k = 0; k < transform.childCount; k++)
				{
					var child = transform.GetChild(k);
					Vector3[] vectors = new Vector3[child.childCount];
					if (k > 0)
					{
						vectors = new Vector3[child.childCount + 1];
						var lastchild = transform.GetChild(k - 1);
						vectors[0] = lastchild.GetChild(lastchild.childCount - 1).position;
						for (var i = 0; i < child.childCount; i++)
						{
							vectors[i + 1] = child.GetChild(i).position;
						}
					}
					else
					{
						for (var i = 0; i < child.childCount; i++)
						{
							vectors[i] = child.GetChild(i).position;
						}
					}
					for (var j = 0; j < steps; j++)
					{
						points.Add(GetInterpolatedPoint(vectors, j / (float) steps));
					}
					if (k == transform.childCount - 1)
					{
						points.Add(vectors[vectors.Length - 1]);
					}
				}
			}
		}
		else
		{
			for( var k=0; k<transform.childCount; k++)
			{
				var child = transform.GetChild(k);
				points.Add(child.position);
			}
		}
		return points.ToArray();
	}
	
	
#if UNITY_EDITOR
	void Update ()
	{
		Vector3[] bezier = GetPath(10);
		for (var i = 0; i < bezier.Length-1; i++)
		{
			Debug.DrawLine(bezier[i],bezier[i+1],_color);
		}
	}
#endif
}