# Jumping on cubic Hermite spline

Hello!

I have a problem with implementing of cubic Hermite spline. I need to move my gameobject towards by spline. I found Hermite spline definition on Wiki Cubic Hermite spline - Wikipedia and implemented it in the scripts below. When my gameobject moves through the control point it jumps a little. I suggest that the problem is the difference between derivatives before and after that point.

``````using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class Spline {

public Vector3[] points, derivatives;
private int fragmentIndex = 0;
private float t = 0f;

public void ConfigSpline(Vector3 derivativeAt0){
derivatives = new Vector3[points.Length];

float sum = 0;
derivatives[0] = derivativeAt0;
for (int i = 1; i < derivatives.Length - 1; i++) {
/*[i] = (points[i+1] - points[i-1])/
((points[i-1]-points[i+1]).magnitude);*/
derivatives [i] = (points [i + 1] - points [i]) / (2 * (points [i + 1] - points [i]).magnitude) +
(points [i] - points [i - 1]) / (2 * (points [i] - points [i - 1]).magnitude);
sum += (points [i - 1] - points [i]).magnitude;
}
derivatives[derivatives.Length - 1] = (points[derivatives.Length - 1] - points[0])/
(sum + (points[derivatives.Length - 1] - points[derivatives.Length - 2]).magnitude);
}

public Vector3 GetPoint(float dt){

t += dt;
if (t > 1f) {
t -= 1.0f;
fragmentIndex++;
if (fragmentIndex == points.Length)
//TODO
;
}
return (2 * Mathf.Pow (t, 3) - 3 * Mathf.Pow (t, 2) + 1) * points [fragmentIndex] +
(Mathf.Pow (t, 3) - 2 * Mathf.Pow (t, 2) + t) * (points [fragmentIndex + 1] - points [fragmentIndex]).magnitude * derivatives [fragmentIndex] +
(-2 * Mathf.Pow (t, 3) + 3 * Mathf.Pow (t, 2)) * points [fragmentIndex + 1] +
(Mathf.Pow (t, 3) - Mathf.Pow (t, 2)) * (points [fragmentIndex + 1] - points [fragmentIndex]).magnitude * derivatives [fragmentIndex + 1];
}

public void Reset () {

fragmentIndex = 0;
t = 0f;
}
}
``````

This spline is used in that method:

``````private void MoveTowardsByPath () {
originTrajectory.transform.position = spline.GetPoint (Time.deltaTime);
originTrajectory.transform.rotation = Quaternion.LookRotation (moveDirection);
transform.rotation = originTrajectory.transform.rotation;
transform.position = originTrajectory.transform.position;
moveDirection = transform.position - lastPosition;
lastPosition = transform.position;
}
``````

Not sure but it might be happening because you have different tangents on the second spline compared to the first spline. You need to make sure this condition is true:

“Cubic Hermite Splines can be smoothly concatenated by ensuring that the tangents of neighboring splines are equivalent.”

It might be worth trying this code: UnityCubicSpline/CubicSpline.cs at master · nuhash/UnityCubicSpline · GitHub

The problem was that this kind of spline doesn’t provide continuity of second derivative, so the first derivative wasn’t smooth. I’ve solved this by using cubic spline interpolation Spline interpolation - Wikipedia instead of Hermite spline.