【Unity】运行时创建曲线（贝塞尔的运用）

[Unity]运行时创建线（贝塞尔的运用）

1. 实现的目标

在运行状态下创建一条可以使用贝塞尔方法实时编辑的网格曲线。

2. 原理介绍

2.1 曲线的创建

unity建立网格曲线可以参考Unity程序化网格体的实现方法。主要分为顶点，三角面，UV和法线。笔者有类似的文章unity 线绳管道纯代码创建方法_，详细的讲解了网格线的创建方法，这次的不同点在于法线的确立方法上。

2.2贝塞尔曲线点的确立

笔者有文章Unity 贝塞尔曲线的创建_描述了贝塞尔的创建方法。

3. 实现过程

3.1曲线的创建方法

线的组成原理
曲线由横截面圆和中心轴线组成。横截面的法线方向为前后两点向量差，如下图绿色线为中心轴线，A点为横截面所在点，横截面的法线方法为向量 $\vec{AD}$ 既向量 $\vec{CB}$ 的单位向量；终点和起点的法线方向为自身和前点或者后一点的向量。

代码源码

3.1.1 横截圆的创建

           #region 横切圆创建
           /// <summary>
           /// 得到管线横切圆
           /// </summary>
           /// <param name="Count">段数</param>
           /// <param name="R">半径</param>
           /// <returns></returns>
           Vector3[] CircularSection(int Count, float R)
           {
               Vector3[] vector3s = new Vector3[Count];
               float angle = 360 / Count;
               Vector3 vector3 = new Vector3(R, 0, 0);
               for (int i = 0; i < Count; i++)
               {
                   //根据角度得到圆的分布点
                   vector3s[i] = vector3.ToAngle(angle * i, Vector3.zero, Vector3.forward);
               }
               return vector3s;
           }
           #endregion

vector3旋转扩展方法

        /// <summary>
        /// 角度旋转
        /// </summary>
        /// <param name="vector3"></param>
        /// <param name="angle">旋转角度</param>
        /// <param name="center">旋转中心点</param>
        /// <param name="direction">旋转轴</param>
        /// <returns></returns>
        public static Vector3 ToAngle(this Vector3 vector3, float angle, Vector3 center, Vector3 direction)
        {
            Vector3 pos = center;
            Quaternion quaternion = Quaternion.AngleAxis(angle, direction);
            Matrix4x4 matrix = new Matrix4x4();
            matrix.SetTRS(pos, quaternion, Vector3.one);
            vector3 = matrix.MultiplyPoint3x4(vector3);
            return vector3;
        }

3.1.2 中心线的确立

           class LinePoint
             {
                 Vector3 location;
                 Vector3 direction;
     
                 public Vector3 Location { get => location; set => location = value; }
                 public Vector3 Direction { get => direction; set => direction = value; }
             }
             /// <summary>
             /// 中心线的确立
             /// </summary>
             /// <param name="createPoint">曲线点</param>
             /// <returns></returns>
             List<LinePoint> SetLinePoint(Vector3[] createPoint)
             {
                 List<LinePoint> pipePoints = new List<LinePoint>();
                 int length = createPoint.Length;
                 for (int i = 0; i < length; i++)
                 {
                     if (i == 0)
                     {
                         Vector3 tangent = (createPoint[i + 1] - createPoint[i]).normalized;//法线
                         AddPipePoints(createPoint[i], tangent, ref pipePoints);
                     }
                     else if (i == length - 1)
                     {
                         Vector3 tangent = (createPoint[i] - createPoint[i - 1]).normalized;//法线
                         AddPipePoints(createPoint[i], tangent, ref pipePoints);
                     }
                     else
                     {
                         Vector3 tangent = (createPoint[i+1] - createPoint[i - 1]).normalized;//法线
                         AddPipePoints(createPoint[i], tangent, ref pipePoints);
                     }
                 }
                 return pipePoints;
             }
     /// <summary>
             /// 增加中心轴线点
             /// </summary>
             /// <param name="location">位置</param>
             /// <param name="direction">法线</param>
             void AddPipePoints(Vector3 location, Vector3 direction,  ref List<LinePoint> pipePoints)
             {
                 LinePoint pipePoint = new LinePoint();
                 pipePoint.Location = location;
                 pipePoint.Direction = direction;
                 pipePoints.Add(pipePoint);
             }

3.1.3网格创建

        /// <summary>
        /// 立体网格创建
        /// </summary>
        /// <param name="createPoint">创建的点数据</param>
        /// <param name="circularCount">圆的段数</param>
        /// <param name="circularR">圆的半径</param>
        /// <returns></returns>
        public Mesh CreateLine3D(Vector3[] createPoint, int circularCount, float circularR)
        {
            //截面圆
            Vector3[] circul = CircularSection(circularCount, circularR);
            //中心线
            List<LinePoint> centreLine = SetLinePoint(createPoint);
            //网格点数据
            Vector3[] meshPoint = CreateMeshPoint(centreLine, circul);
            float uvX = Vector3.Distance(circul[0], circul[1]);
            //返回网格
            return CreatMesh(centreLine, meshPoint, circul.Length, uvX);
        }
/// <summary>
        /// 创建网格点数据
        /// </summary>
        /// <param name="linePoint"></param>
        /// <param name="circular"></param>
        /// <returns></returns>
        Vector3[] CreateMeshPoint(List<LinePoint> linePoint, Vector3[] circular)
        {
            int length = linePoint.Count;
            int circularCount = circular.Length;
            Vector3[] meshPoint = new Vector3[length * circularCount];
            for (int i = 0; i < length; i++)
            {
                for (int j = 0; j < circularCount; j++)
                {
                    meshPoint[(i * circularCount) + j] = circular[j].FromToMoveRotation(linePoint[i].Location, linePoint[i].Direction);
                }
            }
            return meshPoint;
        }
        /// <summary>
        /// 网格创建
        /// </summary>
        /// <param name="linePoints">线的轴心线组</param>
        /// <param name="meshPoint">网格点</param>
        /// <param name="count">段数</param>
        /// <param name="uvX">uv宽度</param>
        /// <returns></returns>
        Mesh CreatMesh(List<LinePoint> linePoints, Vector3[] meshPoint, int count, float uvX)
        {
            Mesh mesh = new Mesh();
            mesh.vertices = meshPoint;
            mesh.triangles = GetTriangles(linePoints.Count, count);
            mesh.uv = GetUV(linePoints, count, uvX);
            mesh.RecalculateNormals();
            mesh.RecalculateBounds();
            return mesh;
        }
   /// <param name="length">线段段数</param>
        /// <param name="count">横截面段数（也就是圆的段数）</param>
        /// <returns></returns>
        int[] GetTriangles(int length, int count)
        {
            int[] triangles = new int[(count * (length - 1)) * 6];
            int k = 0;
            if (count == 1)
            {
                for (int i = 0; i < length-1; i++)
                {
                    int a = i * 2;
                    triangles[k] = a;
                    triangles[k + 1] = a + 1;
                    triangles[k + 2] = a + 3;
                    triangles[k + 3] = a;
                    triangles[k + 4] = a + 3;
                    triangles[k + 5] = a + 2;
                    k += 6;
                }
            }
            else
            {
                for (int i = 0; i < length - 1; i++)
                {
                    
                    for (int j = 0; j < count; j++)
                    {
                        if (j == count - 1)
                        {
                           // Debug.Log("k=" + k);
                            triangles[k] = (i * count) + j;
                            triangles[k + 1] = (i * count) + 0;
                            triangles[k + 2] = ((i + 1) * count) + 0;
                            triangles[k + 3] = (i * count) + j;
                            triangles[k + 4] = ((i + 1) * count) + 0;
                            triangles[k + 5] = ((i + 1) * count) + j;
                        }
                        else
                        {
                            triangles[k] = (i * count) + j;
                            triangles[k + 1] = (i * count) + j + 1;
                            triangles[k + 2] = ((i + 1) * count) + j + 1;
                            triangles[k + 3] = (i * count) + j;
                            triangles[k + 4] = ((i + 1) * count) + j + 1;
                            triangles[k + 5] = ((i + 1) * count) + j;
                        }
                        k += 6;
                    }
                }
            }
            return triangles;
        }
  /// <summary>
        /// 创建uv
        /// </summary>
        /// <param name="linePoints"></param>
        /// <param name="count"></param>
        /// <param name="uvX"></param>
        /// <returns></returns>
        Vector2[] GetUV(List<LinePoint> linePoints,int count, float uvX)
        {
            int length = linePoints.Count;
            if (count == 1) { count = 2; }
            Vector2[] uvs = new Vector2[(count * length)];
            float lineDis = 0;
            int k = 0;
            for (int i = 0; i < length; i ++)
            {
                
                if (i != 0)
                {
                    lineDis += Vector3.Distance(linePoints[i].Location, linePoints[i - 1].Location);
                }
                for (int j = 0; j < count; j++)
                {
                    Vector2 vector2;
                    if (j % 2 != 0)
                    {
                        vector2 = new Vector2(uvX, lineDis);
                    }
                    else
                    {
                        vector2 = new Vector2(0, lineDis);
                    }
                    uvs[k] = vector2;
                    k += 1;
                }
            }
            return uvs;
        }

3.2贝塞尔曲线的建立方法

源码

 /// <summary>
    /// 获取绘制点
    /// </summary>
    /// <param name="controlPoints"></param>
    /// <param name="segmentsPerCurve"></param>
    /// <returns></returns>
    public List<Vector3> GetDrawingPoints(List<Vector3> controlPoints, int segmentsPerCurve)
    {
        List<Vector3> points = new List<Vector3>();
        // 下一段的起始点和上段终点是一个，所以是 i+=3
        for (int i = 0; i <= controlPoints.Count - 4; i += 3)
        {

            var p0 = controlPoints[i];
            var p1 = controlPoints[i + 1];
            var p2 = controlPoints[i + 2];
            var p3 = controlPoints[i + 3];
            float dis = Vector3.Distance(p0, p3);
            int count = Mathf.CeilToInt(segmentsPerCurve * dis);
            if (count < segmentsPerCurve)
            {
                count = segmentsPerCurve;
            }

            for (int j = 0; j <= count; j++)
            {
                var t = j / (float)count;
                points.Add(CalculateBezierPoint(t, p0, p1, p2, p3));
            }
        }
        return points;
    }
    // 三阶公式
    Vector3 CalculateBezierPoint(float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
    {
        Vector3 result;

        Vector3 p0p1 = (1 - t) * p0 + t * p1;
        Vector3 p1p2 = (1 - t) * p1 + t * p2;
        Vector3 p2p3 = (1 - t) * p2 + t * p3;

        Vector3 p0p1p2 = (1 - t) * p0p1 + t * p1p2;
        Vector3 p1p2p3 = (1 - t) * p1p2 + t * p2p3;

        result = (1 - t) * p0p1p2 + t * p1p2p3;
        return result;
    }