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。