stoy tratando de emular la aceleración y la desaceleración en Unity.

He escrito en el código para generar una pista en Unity y colocar un objeto en una ubicación específica de la pista en función del tiempo. El resultado se parece un poco a esto.

El problema que tengo actualmente es que cada sección de la spline tiene una longitud diferente y el cubo se mueve a través de cada sección a una velocidad diferente, pero uniforme. Esto hace que haya saltos repentinos en el cambio de la velocidad del cubo al hacer la transición entre secciones.

Para intentar solucionar este problema, intenté usarRobert Penner ecuaciones de relajación sobre elGetTime(Vector3 p0, Vector3 p1, float alpha) método. Sin embargo, si bien esto ayudó un poco, no fue suficiente. Todavía había saltos de velocidad entre las transiciones.

¿Alguien tiene alguna idea sobre cómo podría reducir dinámicamente la posición del cubo para que parezca que se acelera y desacelera, sin grandes saltos de velocidad entre los segmentos de la pista?

He escrito un script que muestra una implementación simple de mi código. Se puede adjuntar a cualquier objeto del juego. Para que sea fácil ver lo que sucede cuando se ejecuta el código, adjúntelo a algo como un cubo o una esfera.

using System.Collections.Generic;
using UnityEngine;
#if UNITY_EDITOR
using UnityEditor;
#endif

public class InterpolationExample : MonoBehaviour {
    [Header("Time")]
    [SerializeField]
    private float currentTime;
    private float lastTime = 0;
    [SerializeField]
    private float timeModifier = 1;
    [SerializeField]
    private bool running = true;
    private bool runningBuffer = true;

    [Header("Track Settings")]
    [SerializeField]
    [Range(0, 1)]
    private float catmullRomAlpha = 0.5f;
    [SerializeField]
    private List<SimpleWayPoint> wayPoints = new List<SimpleWayPoint>
    {
        new SimpleWayPoint() {pos = new Vector3(-4.07f, 0, 6.5f), time = 0},
        new SimpleWayPoint() {pos = new Vector3(-2.13f, 3.18f, 6.39f), time = 1},
        new SimpleWayPoint() {pos = new Vector3(-1.14f, 0, 4.55f), time = 6},
        new SimpleWayPoint() {pos = new Vector3(0.07f, -1.45f, 6.5f), time = 7},
        new SimpleWayPoint() {pos = new Vector3(1.55f, 0, 3.86f), time = 7.2f},
        new SimpleWayPoint() {pos = new Vector3(4.94f, 2.03f, 6.5f), time = 10}
    };

    [Header("Debug")]
    [Header("WayPoints")]
    [SerializeField]
    private bool debugWayPoints = true;
    [SerializeField]
    private WayPointDebugType debugWayPointType = WayPointDebugType.SOLID;
    [SerializeField]
    private float debugWayPointSize = 0.2f;
    [SerializeField]
    private Color debugWayPointColour = Color.green;
    [Header("Track")]
    [SerializeField]
    private bool debugTrack = true;
    [SerializeField]
    [Range(0, 1)]
    private float debugTrackResolution = 0.04f;
    [SerializeField]
    private Color debugTrackColour = Color.red;

    [System.Serializable]
    private class SimpleWayPoint
    {
        public Vector3 pos;
        public float time;
    }

    [System.Serializable]
    private enum WayPointDebugType
    {
        SOLID,
        WIRE
    }

    private void Start()
    {
        wayPoints.Sort((x, y) => x.time.CompareTo(y.time));
        wayPoints.Insert(0, wayPoints[0]);
        wayPoints.Add(wayPoints[wayPoints.Count - 1]);
    }

    private void LateUpdate()
    {
        //This means that if currentTime is paused, then resumed, there is not a big jump in time
        if(runningBuffer != running)
        {
            runningBuffer = running;
            lastTime = Time.time;
        }

        if(running)
        {
            currentTime += (Time.time - lastTime) * timeModifier;
            lastTime = Time.time;
            if(currentTime > wayPoints[wayPoints.Count - 1].time)
            {
                currentTime = 0;
            }
        }
        transform.position = GetPosition(currentTime);
    }

    #region Catmull-Rom Math
    public Vector3 GetPosition(float time)
    {
        //Check if before first waypoint
        if(time <= wayPoints[0].time)
        {
            return wayPoints[0].pos;
        }
        //Check if after last waypoint
        else if(time >= wayPoints[wayPoints.Count - 1].time)
        {
            return wayPoints[wayPoints.Count - 1].pos;
        }

        //Check time boundaries - Find the nearest WayPoint your object has passed
        float minTime = -1;
        float maxTime = -1;
        int minIndex = -1;
        for(int i = 1; i < wayPoints.Count; i++)
        {
            if(time > wayPoints[i - 1].time && time <= wayPoints[i].time)
            {
                maxTime = wayPoints[i].time;
                int index = i - 1;
                minTime = wayPoints[index].time;
                minIndex = index;
            }
        }

        float timeDiff = maxTime - minTime;
        float percentageThroughSegment = 1 - ((maxTime - time) / timeDiff);

        //Define the 4 points required to make a Catmull-Rom spline
        Vector3 p0 = wayPoints[ClampListPos(minIndex - 1)].pos;
        Vector3 p1 = wayPoints[minIndex].pos;
        Vector3 p2 = wayPoints[ClampListPos(minIndex + 1)].pos;
        Vector3 p3 = wayPoints[ClampListPos(minIndex + 2)].pos;

        return GetCatmullRomPosition(percentageThroughSegment, p0, p1, p2, p3, catmullRomAlpha);
    }

    //Prevent Index Out of Array Bounds
    private int ClampListPos(int pos)
    {
        if(pos < 0)
        {
            pos = wayPoints.Count - 1;
        }

        if(pos > wayPoints.Count)
        {
            pos = 1;
        }
        else if(pos > wayPoints.Count - 1)
        {
            pos = 0;
        }

        return pos;
    }

    //Math behind the Catmull-Rom curve. See here for a good explanation of how it works. https://stackoverflow.com/a/23980479/4601149
    private Vector3 GetCatmullRomPosition(float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float alpha)
    {
        float dt0 = GetTime(p0, p1, alpha);
        float dt1 = GetTime(p1, p2, alpha);
        float dt2 = GetTime(p2, p3, alpha);

        Vector3 t1 = ((p1 - p0) / dt0) - ((p2 - p0) / (dt0 + dt1)) + ((p2 - p1) / dt1);
        Vector3 t2 = ((p2 - p1) / dt1) - ((p3 - p1) / (dt1 + dt2)) + ((p3 - p2) / dt2);

        t1 *= dt1;
        t2 *= dt1;

        Vector3 c0 = p1;
        Vector3 c1 = t1;
        Vector3 c2 = (3 * p2) - (3 * p1) - (2 * t1) - t2;
        Vector3 c3 = (2 * p1) - (2 * p2) + t1 + t2;
        Vector3 pos = CalculatePosition(t, c0, c1, c2, c3);

        return pos;
    }

    private float GetTime(Vector3 p0, Vector3 p1, float alpha)
    {
        if(p0 == p1)
            return 1;
        return Mathf.Pow((p1 - p0).sqrMagnitude, 0.5f * alpha);
    }

    private Vector3 CalculatePosition(float t, Vector3 c0, Vector3 c1, Vector3 c2, Vector3 c3)
    {
        float t2 = t * t;
        float t3 = t2 * t;
        return c0 + c1 * t + c2 * t2 + c3 * t3;
    }

    //Utility method for drawing the track
    private void DisplayCatmullRomSpline(int pos, float resolution)
    {
        Vector3 p0 = wayPoints[ClampListPos(pos - 1)].pos;
        Vector3 p1 = wayPoints[pos].pos;
        Vector3 p2 = wayPoints[ClampListPos(pos + 1)].pos;
        Vector3 p3 = wayPoints[ClampListPos(pos + 2)].pos;

        Vector3 lastPos = p1;
        int maxLoopCount = Mathf.FloorToInt(1f / resolution);

        for(int i = 1; i <= maxLoopCount; i++)
        {
            float t = i * resolution;
            Vector3 newPos = GetCatmullRomPosition(t, p0, p1, p2, p3, catmullRomAlpha);
            Gizmos.DrawLine(lastPos, newPos);
            lastPos = newPos;
        }
    }
    #endregion

    private void OnDrawGizmos()
    {
        #if UNITY_EDITOR
        if(EditorApplication.isPlaying)
        {
            if(debugWayPoints)
            {
                Gizmos.color = debugWayPointColour;
                foreach(SimpleWayPoint s in wayPoints)
                {
                    if(debugWayPointType == WayPointDebugType.SOLID)
                    {
                        Gizmos.DrawSphere(s.pos, debugWayPointSize);
                    }
                    else if(debugWayPointType == WayPointDebugType.WIRE)
                    {
                        Gizmos.DrawWireSphere(s.pos, debugWayPointSize);
                    }
                }
            }

            if(debugTrack)
            {
                Gizmos.color = debugTrackColour;
                if(wayPoints.Count >= 2)
                {
                    for(int i = 0; i < wayPoints.Count; i++)
                    {
                        if(i == 0 || i == wayPoints.Count - 2 || i == wayPoints.Count - 1)
                        {
                            continue;
                        }

                        DisplayCatmullRomSpline(i, debugTrackResolution);
                    }
                }
            }
        }
        #endif
    }
}