Unity贝塞尔曲线与Catmull-Rom曲线工具类

之前经常需要在 Unity 里画贝塞尔曲线与 Catmull-Rom 曲线,当时特意封装了一个工具类,以方便使用。
二阶贝塞尔曲线
二阶贝塞尔曲线由起点、终点,再加一个控制点构成。曲线上任意一点的坐标与当前进度的关系如公式:
代码
public class BezierCurveTool
{
/// <summary>
/// 获取一条贝塞尔曲线(二阶)by azimiao.com
/// </summary>
/// <param name="startPoint">开始点</param>
/// <param name="endPoint">结束点</param>
/// <param name="middlePoint">中间控制点</param>
/// <param name="nultiple">曲线采样次数</param>
public static void GetWayPoints(Vector3 startPoint, Vector3 endPoint, Vector3 middlePoint, ref List<Vector3> result,int nultiple = 10)
{
if (result == null) result = new List<Vector3>();
result.Clear();
float dis1 = Vector3.Distance(startPoint, middlePoint);
float dis2 = Vector3.Distance(middlePoint, endPoint);
Vector3 directStart2Middle = Vector3.Normalize(middlePoint - startPoint);
Vector3 directMiddle2End = Vector3.Normalize(endPoint - middlePoint);
for (int i = 0; i < nultiple; i++)
{//azimiao.com
float tempPercent = (float)i / nultiple;
Vector3 point1 = startPoint + directStart2Middle * dis1 * tempPercent;
Vector3 point2 = middlePoint + directMiddle2End * dis2 * tempPercent;
Vector3 linePoint = point1 + Vector3.Normalize(point2 - point1) * dis2 * tempPercent;
result.Add(linePoint);
}
result.Add(endPoint);
}
}
Catmull-Rom 曲线
Catmull-Rom曲线即经过所有给定点的曲线(不含起始点与结束点),为了让其经过起始点与结束点,可以在列表前后各多加一个点作为起点与终点。
代码
public class CatmulCurveTool
{
//代码结构来自于:https://blog.csdn.net/qq_33520289/article/details/106234291
//根据提供的路径获取平滑路径
public static void GetWayPoints(Vector3[] points, int amountRadio, ref List<Vector3> wayPoints)
{
if (points == null || points.Length <= 1) { Debug.Log("points is empty!"); return; }
if (wayPoints == null) wayPoints = new List<Vector3>();
wayPoints.Clear();
Vector3[] vector3s = PathControlPointGenerator(points);
Vector3 prevPt = Interp(vector3s, 0);
int SmoothAmount = (points.Length - 1) * amountRadio;
for (int i = 1; i <= SmoothAmount; i++)
{
float pm = (float)i / SmoothAmount;
Vector3 currPt = Interp(vector3s, pm);
wayPoints.Add(currPt);
prevPt = currPt;
}
}
//Gizmos平滑的绘制提供的路径
public static void DrawPathHelper(Vector3[] path, Color color)
{
Vector3[] vector3s = PathControlPointGenerator(path);
Vector3 prevPt = Interp(vector3s, 0);
Gizmos.color = color;
int SmoothAmount = path.Length * 20;
for (int i = 1; i <= SmoothAmount; i++)
{
float pm = (float)i / SmoothAmount;
Vector3 currPt = Interp(vector3s, pm);
Gizmos.DrawLine(currPt, prevPt);
prevPt = currPt;
}
}
//计算路径的长度
public static float PathLength(Vector3[] path)
{
float pathLength = 0;
Vector3[] vector3s = PathControlPointGenerator(path);
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);
pathLength += Vector3.Distance(prevPt, currPt);
prevPt = currPt;
}
return pathLength;
}
//生成曲线控制点,path.length>=2(为路径添加首尾点,便于绘制Cutmull-Rom曲线)
private static Vector3[] PathControlPointGenerator(Vector3[] path)
{
Vector3[] suppliedPath;
Vector3[] vector3s;
suppliedPath = path;
int offset = 2;
vector3s = new Vector3[suppliedPath.Length + offset];
Array.Copy(suppliedPath, 0, vector3s, 1, suppliedPath.Length);
//计算第一个控制点和最后一个控制点位置
vector3s[0] = vector3s[1] + (vector3s[1] - vector3s[2]);
vector3s[vector3s.Length - 1] = vector3s[vector3s.Length - 2] + (vector3s[vector3s.Length - 2] - vector3s[vector3s.Length - 3]);
//首位点重合时,形成闭合的Catmull-Rom曲线
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);
}
//Catmull-Rom曲线 参考:https://blog.csdn.net/u012154588/article/details/98977717
private 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
);
}
}
其他
封装的两个工具类用了好久了,在路径动画、插值运动等需求中非常好用。在实际使用时,结合 DoTween 的执行队列等工具,可以创造出非常特别的动画效果。
DoTween 的使用请参考文章:使用DoTween在Unity中制作队列(Sequence)动画