为什么这个四叉树查询经常什么都不返回？

问题描述

任何“W”指半宽，任何“H”指半高。任何“X”和“Y”都是指与坐标轴对齐的矩形的中心。

我正在尝试编写一些用于物理模拟和游戏设计的通用四叉树代码。起初，它返回完全被搜索区域包围的四叉树内容中的所有点。在添加了一堆 print() 语句来阐明过程后，我设法解决了这个问题，但现在我有了一个我似乎无法弄清楚的新问题。出于某种原因，当我在矩形区域内查询“Placeables”的四叉树时，我要么得到完全正确的结果，但通常情况下我根本没有得到任何返回。 Placeables 定义如下：

abstract class Placeable{ //things that can be stored in quadtree
  PVector pos;
  abstract void show();}

四叉树代码的重要部分：

class Quadtree{ //Data structure for storing objects in 2D
  Quadtree nw,ne,sw,se; //children
  Quadtree parent;
  ArrayList<Placeable> contents;//contents of THIS branch only,child object contents not included
  float x,y,w,h;//center point,half-width and half-height
  boolean divided;  //false if leaf node
  static final int capacity = 6; //controls maximum capacity all quadtree nodes for case-by-case tuning 
...

...
boolean intersects(float rX,float rY,float rW,float rH){//Do I intersect with the rectangle defined by rX,rY,rW,rH?
    return !(rX-rW >= x+w || rX+rW <= x-w 
          || rY-rH >= y+h || rY+rH <= y-h);}
      
  //return all Placeables inside a rectangular region
  ArrayList<Placeable> query(float X,float Y,float W,float H){
    return query(X,Y,W,H,new ArrayList<Placeable>());}
  ArrayList<Placeable> query(float X,float H,ArrayList<Placeable> found){
    print("Querying:",contents.size(),"/",Integer.toString(capacity),"\t");
    
    if (!intersects(X,H)){ //if no intersection,return arraylist unmodified
      print("Does Not Intersect\n");
      return found;
    } else {  //if intersection,check contents for Placeables within the region
      print("Does Intersect!\n");
      for (Placeable p : contents){
        if ( (p.pos.x <= X+W) && (p.pos.x >= X-W) //capitals refer to search region
          && (p.pos.y <= Y+H) && (p.pos.y >= Y-H) ){
          found.add(p);
          print("Found Point\t",p.pos.x,"\t",p.pos.y,"\n");}
      }
      if (divided){ //after checking own contents,recursively query children appending to same array
        print("Descending\n");
        print("NW ");
        nw.query(X,found);
        print("NE ");
        ne.query(X,found);
        print("SW ");
        sw.query(X,found);
        print("SE ");
        se.query(X,found);
        print("Raising\n");}
      return found;
    }
  }
.....
}

以下是在 1024x768 窗口中正确输出的示例：

Querying: 6 / 6     Does Intersect!
Descending
NW Querying: 6 / 6  Does Not Intersect
NE Querying: 6 / 6  Does Intersect!
Descending
NW Querying: 4 / 6  Does Not Intersect
NE Querying: 3 / 6  Does Not Intersect
SW Querying: 6 / 6  Does Intersect!
Found Point  665.36365   379.79324 
Descending
NW Querying: 1 / 6  Does Not Intersect
NE Querying: 0 / 6  Does Not Intersect
SW Querying: 0 / 6  Does Intersect!
SE Querying: 0 / 6  Does Intersect!
Raising
SE Querying: 5 / 6  Does Intersect!
Found Point  772.9317    375.3352 
Raising
SW Querying: 6 / 6  Does Not Intersect
SE Querying: 6 / 6  Does Intersect!
Found Point  790.5205    386.4734 
Found Point  633.3443    390.43515 
Found Point  797.5499    397.1355 
Descending
NW Querying: 6 / 6  Does Intersect!
Found Point  723.5054    450.78967 
Found Point  741.98676   389.52292 
Found Point  683.0763    488.69083 
NE Querying: 4 / 6  Does Intersect!
Found Point  775.3038    432.92847 
SW Querying: 6 / 6  Does Not Intersect
SE Querying: 4 / 6  Does Not Intersect
Raising
Raising
Found: 9 

正确的输出图像：

以下是本应返回3分的同一窗口中的错误输出示例：

Querying: 6 / 6     Does Intersect!
Descending
NW Querying: 6 / 6  Does Not Intersect
NE Querying: 6 / 6  Does Not Intersect
SW Querying: 6 / 6  Does Intersect!
Descending
NW Querying: 3 / 6  Does Not Intersect
NE Querying: 5 / 6  Does Not Intersect
SW Querying: 6 / 6  Does Not Intersect
SE Querying: 6 / 6  Does Not Intersect
Raising
SE Querying: 6 / 6  Does Not Intersect
Raising
Found: 0 

这是伴随错误输出的窗口。 （发现点变为纯绿色。）

我无法发现哪个区域产生正确输出的模式，但我的直觉说左侧的区域更经常不正确。

完整文件 here 可用，因此您可以在需要时运行它，但我很困惑，上周我已经回到了这个问题几次。请帮忙。

解决方法

哇，这是一个很难找到的问题（至少，我希望我解决了它）。

问题在于您在 rW 中对 rH 和 setup() 的定义：

rW = constrain(randomGaussian(),-1,1)*width/6;
rH = constrain(randomGaussian(),1)*height/6;

您不能为 rW 或 rH 设置负值。例如，假设我们测试以下值（假设 y 值也相交）：

rW = -100;
rX = 500
x = 256;
w = 256;

理想情况下，intersects() 将进行如下测试：

         !(400 >= 512 || 600 <= 512)
/*-->*/  !(false || false)
/*-->*/  true //(yes,they intersect)

但实际发生的是

         !(rX-rW >= x+w || rX+rW <= x-w)
/*-->*/  !(500-(-100) >= 256+256 || 500+(-100) <= 256-256)
/*-->*/  !(600 >= 512 || 400 <= 0)
/*-->*/  !(true || false)
/*-->*/  false //(no,they do not intersect)

这就像您在测试该地区的错误方面。

这是一个非常简单的修复，只需在定义 abs() 和 rW 时使用 rH：

rW = abs(constrain(randomGaussian(),1))*width/6;
rH = abs(constrain(randomGaussian(),1))*height/6;