ベジェ曲線にそってオブジェクトを動かす

参考：Bezier Curve
Unityは標準ではベジェ曲線を扱うクラスはない。そこで、デベロッパーネットワークの投稿にあったベジェ曲線のクラスを使ってみた。

１．ベジェ曲線のクラス
P0〜P3は制御点、関数GetPointAtTime( float t )で、曲線上の座標を取得できる。

using UnityEngine;
using System.Collections;

[System.Serializable]
public class Bezier : System.Object
{
    public Vector3 p0;
    public Vector3 p1;
    public Vector3 p2;
    public Vector3 p3;

    public float ti = 0f;

    private Vector3 b0 = Vector3.zero;
    private Vector3 b1 = Vector3.zero;
    private Vector3 b2 = Vector3.zero;
    private Vector3 b3 = Vector3.zero;

    private float Ax;
    private float Ay;
    private float Az;

    private float Bx;
    private float By;
    private float Bz;

    private float Cx;
    private float Cy;
    private float Cz;

    // Init function v0 = 1st point, v1 = handle of the 1st point , v2 = handle of the 2nd point, v3 = 2nd point
    // handle1 = v0 + v1
    // handle2 = v3 + v2
    public Bezier( Vector3 v0, Vector3 v1, Vector3 v2, Vector3 v3 )
    {
        this.p0 = v0;
        this.p1 = v1;
        this.p2 = v2;
        this.p3 = v3;
    }
    // 0.0 >= t <= 1.0
    public Vector3 GetPointAtTime( float t )
    {
        this.CheckConstant();
        float t2 = t * t;
        float t3 = t * t * t;
        float x = this.Ax * t3 + this.Bx * t2 + this.Cx * t + p0.x;
        float y = this.Ay * t3 + this.By * t2 + this.Cy * t + p0.y;
        float z = this.Az * t3 + this.Bz * t2 + this.Cz * t + p0.z;
        return new Vector3( x, y, z );
    }

    private void SetConstant()
    {
        this.Cx = 3f * ( ( this.p0.x + this.p1.x ) - this.p0.x );
        this.Bx = 3f * ( ( this.p3.x + this.p2.x ) - ( this.p0.x + this.p1.x ) ) - this.Cx;
        this.Ax = this.p3.x - this.p0.x - this.Cx - this.Bx;
        this.Cy = 3f * ( ( this.p0.y + this.p1.y ) - this.p0.y );
        this.By = 3f * ( ( this.p3.y + this.p2.y ) - ( this.p0.y + this.p1.y ) ) - this.Cy;
        this.Ay = this.p3.y - this.p0.y - this.Cy - this.By;

        this.Cz = 3f * ( ( this.p0.z + this.p1.z ) - this.p0.z );
        this.Bz = 3f * ( ( this.p3.z + this.p2.z ) - ( this.p0.z + this.p1.z ) ) - this.Cz;
        this.Az = this.p3.z - this.p0.z - this.Cz - this.Bz;
    }

    // Check if p0, p1, p2 or p3 have change
    private void CheckConstant()
    {
        if( this.p0 != this.b0 || this.p1 != this.b1 || this.p2 != this.b2 || this.p3 != this.b3 )
        {
            this.SetConstant();
            this.b0 = this.p0;
            this.b1 = this.p1;
            this.b2 = this.p2;
            this.b3 = this.p3;
        }
    }
}

２．サンプルプログラム。このスクリプトを移動させたいゲームオブジェクトに貼り付ける。

using UnityEngine;
using System.Collections;

public class MyBezier : MonoBehaviour
{
    public Bezier myBezier;
    private float t = 0f;

    void Start()
    {
        myBezier = new Bezier( new Vector3( -1f, 1f, -1f ), Random.insideUnitSphere * 2f, Random.insideUnitSphere * 2f, new Vector3( 3f, 1f, 3f ) );
    }

    void Update()
    {
        Vector3 vec = myBezier.GetPointAtTime( t );
        transform.position = vec;

        t += 0.001f;
        if( t > 1f )
            t = 0f;
    }
}

なお、ベジェ曲線がどのように作られているかは、中学生でもわかるベジェ曲線 - Rui's Blogが、とてもわかりやすい。