unity3D：游戏分解之曲线

一提到曲线，很多新手就头疼了，包括我。查了很多资料，终于有个大概的了解。想深入了解曲线原理的，推荐一个链接http://www.cnblogs.com/jay-dong/archive/2012/09/26/2704188.html

之前写了一篇博文《unity3D：游戏分解之角色移动和相机跟随》，里面用到了曲线插值，这里算是对上篇博文的一个补充

先看一下曲线的效果

在使用NGUI的过程中，发现iTween.cs里面有两个很有用的方法，一个是输入指定路点数组，一个就是曲线的插值算法。今天我们主要就用到这两个方法来实现曲线效果。

public static Vector3[] PathControlPointGenerator(Vector3[] path)
    {
        Vector3[] suppliedPath;
        Vector3[] vector3s;

        //create and store path points:
        suppliedPath = path;

        //populate calculate path;
        int offset = 2;
        vector3s = new Vector3[suppliedPath.Length + offset];
        Array.Copy(suppliedPath, 0, vector3s, 1, suppliedPath.Length);

        //populate start and end control points:
        //vector3s[0] = vector3s[1] - vector3s[2];
        vector3s[0] = vector3s[1] + (vector3s[1] - vector3s[2]);
        vector3s[vector3s.Length - 1] = vector3s[vector3s.Length - 2] + (vector3s[vector3s.Length - 2] - vector3s[vector3s.Length - 3]);

        //is this a closed, continuous loop? yes? well then so let's make a continuous Catmull-Rom spline!
        if (vector3s[1] == vector3s[vector3s.Length - 2])
        {
            Vector3[] tmpLoopSpline = new Vector3[vector3s.Length];
            Array.Copy(vector3s, tmpLoopSpline, vector3s.Length);
            tmpLoopSpline[0] = tmpLoopSpline[tmpLoopSpline.Length - 3];
            tmpLoopSpline[tmpLoopSpline.Length - 1] = tmpLoopSpline[2];
            vector3s = new Vector3[tmpLoopSpline.Length];
            Array.Copy(tmpLoopSpline, vector3s, tmpLoopSpline.Length);
        }

        return (vector3s);
    }

    //andeeee from the Unity forum's steller Catmull-Rom class ( http://forum.unity3d.com/viewtopic.php?p=218400#218400 ):
    public static Vector3 Interp(Vector3[] pts, float t)
    {
        int numSections = pts.Length - 3;
        int currPt = Mathf.Min(Mathf.FloorToInt(t * (float)numSections), numSections - 1);
        float u = t * (float)numSections - (float)currPt;

        if(currPt == 0)
        {
            int dsd = 0;
        }

        Vector3 a = pts[currPt];
        Vector3 b = pts[currPt + 1];
        Vector3 c = pts[currPt + 2];
        Vector3 d = pts[currPt + 3];

        return .5f * (
            (-a + 3f * b - 3f * c + d) * (u * u * u)
            + (2f * a - 5f * b + 4f * c - d) * (u * u)
            + (-a + c) * u
            + 2f * b
        );
    }

直接上完整代码，把这个脚本放到相机上，然后在场景中拖几个物件作为路点，就可以实现上面的效果

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

namespace Fish.Study.Curve
{
    /// <summary>
    /// 曲线测试
    /// </summary>
    public class CurveTest : MonoBehaviour
    {
        //路点
        public GameObject[] GameObjectList;
        //各路点的坐标
        public List<Vector3> TransDataList = new List<Vector3>();

        void Start()
        {
        }

        //Gizmos
        void OnDrawGizmos()
        {
            //1个点是不能画出曲线的，2个点实际上是直线
            if (GameObjectList.Length <= 1) return;

            TransDataList.Clear();
            for (int i = 0; i < GameObjectList.Length; ++i)
            {
                TransDataList.Add(GameObjectList[i].transform.position);
            }

            if (TransDataList != null && TransDataList.Count > 1)
            {
                DrawPathHelper(TransDataList.ToArray(), Color.red);
            }
        }

        public Vector3[] GetCurveData()
        {
            if (TransDataList != null && TransDataList.Count > 1)
            {
                var v3 = (TransDataList.ToArray());
                Vector3[] vector3s = PathControlPointGenerator(v3);
                return vector3s;
            }

            return null;
        }

        //NGUI iTween.cs中的方法,输入路径点
        public static Vector3[] PathControlPointGenerator(Vector3[] path)
        {
            Vector3[] suppliedPath;
            Vector3[] vector3s;

            //create and store path points:
            suppliedPath = path;

            //populate calculate path;
            int offset = 2;
            vector3s = new Vector3[suppliedPath.Length + offset];
            Array.Copy(suppliedPath, 0, vector3s, 1, suppliedPath.Length);

            //populate start and end control points:
            vector3s[0] = vector3s[1] + (vector3s[1] - vector3s[2]);
            vector3s[vector3s.Length - 1] = vector3s[vector3s.Length - 2] + (vector3s[vector3s.Length - 2] - vector3s[vector3s.Length - 3]);

            //is this a closed, continuous loop? yes? well then so let's make a continuous Catmull-Rom spline!
            if (vector3s[1] == vector3s[vector3s.Length - 2])
            {
                Vector3[] tmpLoopSpline = new Vector3[vector3s.Length];
                Array.Copy(vector3s, tmpLoopSpline, vector3s.Length);
                tmpLoopSpline[0] = tmpLoopSpline[tmpLoopSpline.Length - 3];
                tmpLoopSpline[tmpLoopSpline.Length - 1] = tmpLoopSpline[2];
                vector3s = new Vector3[tmpLoopSpline.Length];
                Array.Copy(tmpLoopSpline, vector3s, tmpLoopSpline.Length);
            }

            return (vector3s);
        }

        //曲线插值函数
        public static Vector3 Interp(Vector3[] pts, float t)
        {
            int numSections = pts.Length - 3;
            int currPt = Mathf.Min(Mathf.FloorToInt(t * (float)numSections), numSections - 1);
            float u = t * (float)numSections - (float)currPt;

            Vector3 a = pts[currPt];
            Vector3 b = pts[currPt + 1];
            Vector3 c = pts[currPt + 2];
            Vector3 d = pts[currPt + 3];

            return .5f * (
                (-a + 3f * b - 3f * c + d) * (u * u * u)
                + (2f * a - 5f * b + 4f * c - d) * (u * u)
                + (-a + c) * u
                + 2f * b
            );
        }

        //画曲线
        private void DrawPathHelper(Vector3[] path, Color color)
        {
            Vector3[] vector3s = PathControlPointGenerator(path);

            //Line Draw:
            Vector3 prevPt = Interp(vector3s, 0);
            int SmoothAmount = path.Length * 20;
            for (int i = 1; i <= SmoothAmount; i++)
            {
                float pm = (float)i / SmoothAmount;
                Vector3 currPt = Interp(vector3s, pm);

                Gizmos.color = color;
                Gizmos.DrawSphere(currPt, 0.2f);
                prevPt = currPt;
            }
        }
    }
}