BezierTension.cs

using UnityEngine;

[ExecuteInEditMode]
public class BezierTension : MonoBehaviour
{
#region Pretend you never saw this
    public Transform Initial;
    public Transform Mid;
    public Transform End;

    [Range(0F, 1F)]
    public float t;

    [Range(0F, 1F)]
    public float Tension;

    public Transform TestObj;

    private Vector3 StartPoint { get { return Initial.position; } }
    private Vector3 MidPoint { get { return Mid.position; } }
    private Vector3 EndPoint { get { return End.position; } }

    private void Update()
    {
        TestObj.position =
            QuadraticBezier(StartPoint, MidPoint, EndPoint, t, Tension);

        for (float tense = 0F; tense <= 1F; tense += 0.09F)
        {
            float innerTension = tense * Tension;

            const int numVertices = 50;
            for (int i = 0; i < numVertices; i++)
            {
                var vertsStart = (float)i / numVertices;
                var vertsEnd = (float)(i + 1) / numVertices;
                Debug.DrawLine(
                    QuadraticBezier(StartPoint, MidPoint, EndPoint, vertsStart, innerTension),
                    QuadraticBezier(StartPoint, MidPoint, EndPoint, vertsEnd, innerTension),
                    Color.red);

                Debug.DrawLine(
                    QuadraticBezier(StartPoint, MidPoint, EndPoint, vertsStart, 0F),
                    QuadraticBezier(StartPoint, MidPoint, EndPoint, vertsStart, innerTension),
                    Color.blue);
            }
        }
    }
#endregion

    public static Vector3 QuadraticBezier(
        Vector3 startPoint,
        Vector3 midPoint,
        Vector3 endPoint,
        float t,
        float tension)
    {
        //// Calc Bezier
        var a = Vector3.Lerp(startPoint, midPoint, t);
        var b = Vector3.Lerp(midPoint, endPoint, t);
        var normalBezierResult = Vector3.Lerp(a, b, t);

        var finalTension = (-Mathf.Pow(2 * t - 1, 2F) + 1) * (0.85F * tension);
        var tenseBezierResult = Vector3.Lerp(normalBezierResult, midPoint, finalTension);

        return tenseBezierResult;
    }
}