Question

我想实现我可以细分给定距离的贝塞尔曲线。现在，如果Bezier为直线，则可以使用，但是如果我更改Controll-Point（B＆C）以使Bezier弯曲，则计算出的点之间的间隙就不再像给定的距离！

我浏览了整个网络，但没有遇到类似的问题。

float t = Distance between subdividedParts / bezier length;

//A,B,C,D = ControllPoints of Bezier

GetPoint(A,B,C,D,t);

//GetPoint equation:
public static Vector3 GetPoint (Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t) {
         t = Mathf.Clamp01(t);
         float OneMinusT = 1f - t;
         return
             OneMinusT * OneMinusT * OneMinusT * p0 +
             3f * OneMinusT * OneMinusT * t * p1 +
             3f * OneMinusT * t * t * p2 +
             t * t * t * p3;
     }

Answer 1

我现在设法获得了一种非常准确的方式来分割贝塞尔曲线并获得位置=>，但是它的性能消耗随着精度的提高而增加。因此，可以通过以下代码对此进行改进：

UsageStatsManager

为了获得更高的性能，我现在这样做：

Vector3 []数组输出的代码

 //if accuracy is 0.001 = good performance | if 0.000001 laggy performance
    public Vector3[] GetPoints (float gap,float accuracy){
     SimpsonVec sv = SV_Setup(0);
     Vector3 last_spawn = Bezier.GetPoint(sv.A,sv.B,sv.C,sv.D,0);

     List<Vector3> allPoints = new List<Vector3>();
     allPoints.Add(last_spawn);

     for(float t = accuracy;t <= 1.0f; t +=accuracy){
         Vector3 trial = Bezier.GetPoint(sv.A,sv.B,sv.C,sv.D,t);
         if(Vector3.Distance(trial,last_spawn) >= gap){
             last_spawn = trial;
             allPoints.Add(trial);
         }
     }
     return allPoints.ToArray();
 }

结构：

public Vector3[] GetAllPoints(float gap,float acc){

    SimpsonVector = SV_SETUP_ALL();
    BezierPoints bp = new BezierPoints();
    bp.bp_vector3 = new List<Vector3>();
    bp.bp_lastSpawn = new List<Vector3>();

    for(int i = 0; i<points.Length / 3;i++){

        Vector3 ls = new Vector3();
        if(i == 0){
            ls = Bezier.GetPoint(SimpsonVector[0].A,SimpsonVector[0].B,SimpsonVector[0].C,SimpsonVector[0].D,0);
        }if (i > 0){
            ls = bp.bp_lastSpawn[i-1];
        }
        BezierPoints bp_temp = GetSegmentPoints(gap,acc,i,ls);
        bp.bp_lastSpawn.Add(bp_temp.bp_lastSpawn[0]);
        bp.bp_vector3.AddRange(bp_temp.bp_vector3);
        SimpsonVector_TEMP = SimpsonVector;
    }


    return bp.bp_vector3.ToArray();
}

BezierPoints GetSegmentPoints (float gap,float acc,int index, Vector3 ls)
{
    SimpsonVec sv = SimpsonVector[index];
    Vector3 last_spawn = ls;

    BezierPoints bp = new BezierPoints();
    bp.bp_vector3 = new List<Vector3>();
    bp.bp_lastSpawn = new List<Vector3>();

    float step = 0.1f;
    float t = step;
    float lastT = new float();

    while (t >= 0 && t <= 1f)
    {
        while (t < 1f && Vector3.Distance(Bezier.GetPoint(sv.A,sv.B,sv.C,sv.D,t), last_spawn) < gap){
            t += step;}
        step /= acc;
        while (t > lastT && Vector3.Distance(Bezier.GetPoint(sv.A,sv.B,sv.C,sv.D,t), last_spawn) > gap){
            t -= step;}
        step /= acc;
        if (t > 1f || t < lastT){
            break;}
        if(step < 0.000001f){
            last_spawn = Bezier.GetPoint(sv.A,sv.B,sv.C,sv.D,t);
            bp.bp_vector3.Add(last_spawn + transform.position);
            lastT = t;
            step = 0.1f;
        }
    }
    bp.bp_lastSpawn.Add(last_spawn);
    return bp;
}

帮助器方法：

public struct SimpsonVec{
    [SerializeField] public Vector3 A;
    [SerializeField] public Vector3 B;
    [SerializeField] public Vector3 C;
    [SerializeField] public Vector3 D;
}

public struct  BezierPoints
{
    [SerializeField] public List<Vector3> bp_vector3;
    [SerializeField] public List<Vector3> bp_lastSpawn; 
}

Answer 2

无论如何，您都已经需要绘制曲线，因此请保留曲线的查找表并预先计算每个条目的距离，或者通过选择t值，计算距离并以二进制方式搜索获胜的方式，然后然后在上/下移动t值的一半时（如果不使用），然后重复进行直到达到所需的精度为止。而且由于二进制搜索非常有效，因此尝试的次数可以忽略不计。

有关原理，请参见https://pomax.github.io/bezierinfo/#tracing，有关计算曲线长度的信息，请参见https://pomax.github.io/bezierinfo/#arclength（其中https://pomax.github.io/bezierinfo/#splitting是获取值的显而易见的部分，您需要确定某条曲线的长度）点t）和“ https://pomax.github.io/bezierinfo的全部以获取更多信息”。

细分贝塞尔曲线

2 个答案: