C++ 二维平铺世界中矩形的并集

我试图在二维平铺世界中找到一组相邻单元（行、列）（可转换为矩形）的边界多边形

在for循环中处理单元，并使用相邻单元的邻域属性，我可以消除所有内部边并存储其余边。 边存储在std:：vector中

现在我需要合并有一个公共顶点和斜率相同的边。 合并边后，我需要从逆时针方向的顶点开始创建边界多边形

---

请帮助找到一种方法使之成为可能。

我认为这是一个实现这一点的简单算法

我们将此作为输入：

 |   |   |   |   |   |
-+---+---+---+---+---+-
 |   |   |   |   |   |
-+---+---+---+---+---+-
 |   |   | a |   |   |
-+---+---+---+---+---+-
 |   | b | c | d |   |
-+---+---+---+---+---+-
 |   |   | e |   |   |
-+---+---+---+---+---+-
 |   |   |   |   |   |

其中，

a

、

b

、

c

、

d

和

e

是作为成对向量（坐标）存储的输入分幅：

该算法的工作原理如下：

Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---* 
|   |  
*   *-------*    
|           | 
*---*       |  
    |       |  
    *-------* 

构建一个布尔数组，将整个瓷砖集包围起来。您必须遍历集合才能找到该矩形的边界。将表示集合平铺的数组位置设置为true，否则设置为false。
示例中的输出为（T为

true

，f为

false

）：

现在必须遍历外壳多边形的边界。从标志数组中标记为

true

的第一个元素开始，使用以下规则沿相同方向移动顶点，直到再次到达第一个顶点：

• 如果当前方向/位置前面的两个平铺为false，则顺时针旋转并将顶点添加到输出列表（多边形）： （

  *

  是添加到多边形的顶点，

  X

  是当前顶点，箭头是当前方向）

• 如果一个磁贴为假，一个为真，则朝同一方向移动（请注意，true false或false true表示您处于边框中）：

• 如果两个平铺均为真，则逆时针旋转并将顶点添加到输出列表中（请注意，真表示已到达平铺集的一部分，即“墙”）：

考虑事项： tilemap坐标与标志阵列坐标 flag数组表示放置平铺的平铺贴图的矩形区域。因此，其第一个元素（平铺）的平铺贴图坐标为

（左，上）

，其中

左

是所选平铺集的最小x坐标，

上

是所选平铺集的最小y坐标

在agorithm的第二步中，使用阵列作为向导，遍历一组瓷砖的边界（border）。请注意，您真正使用的是该数组，因此必须将坐标从标志坐标（逻辑坐标）转换为tilemap坐标（物理坐标）以存储多边形的顶点。当然这很容易

还请注意，该算法提取的步骤是边缘顶点（物理平铺坐标），而不是逻辑坐标。您必须确定“我在那个顶点”是什么意思，以及“前进”和“转弯”在旗子数组坐标方面的含义

边界条件和前瓷砖检查 我们已经定义了三条规则来沿着瓷砖组的边界前进。我们使用旗帜阵列作为指导来决定要做什么（前进、顺时针转动或逆时针转动）。请注意，当当前顶点位于数组的边框时，<>强>您可以（认为）它具有具有假值的相邻瓦片。 例如：

+---+---+---+  
| f | f | f |  |  
*---+---*---+  |  
| T | T | f |  v
*---+---+---+  
| f | T | f ]  
+---+---X---+  

去

+---+---+---+  
| f | f | f |  
*---+---*---+  <--
| T | T | f |  
*---+---+---+  
| f | T | f ]  
+---X---*---+  

可能的优化 第一步计算标志数组，因为算法将选定的分片集作为向量。如果平铺引擎支持它，则可以向平铺添加属性（

bool selected

）并直接传递平铺贴图，避免计算和顶点坐标变换

例子 给定此标志数组：

+---+---+---+  
| T | f | f |    
+---+---+---+    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

执行工作如下所示（注意，图纸是执行步骤后的状态）：

Current position: (0,1)
Polygon: {(0,1)} 

+---+---+---+ ^ 
| T | f | f | |  
X---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (0,0)
Polygon: {(0,1)} 

X---+---+---+ ^ 
| T | f | f | |  
*---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (1,0)
Polygon: {(0,1),(0,0)} 

*---X---+---+ 
| T | f | f |   
*---+---+---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,1)
Polygon: {(0,1),(0,0),(1,0)} 

*---*---+---+ 
| T | f | f | | 
*---X---+---+ |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---X  
| f | T | T |  
+---+---+---+ 

Current position: (3,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---X 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---+---X---* 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---X---+---* 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3)} 

*---*---+---+ 
| T | f | f | ^ 
*---*---+---* |   
| T | T | T | |
+---X---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2)} 

*---*---+---+ 
| T | f | f | 
*---*---+---*    
| T | T | T | <---
X---*---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,1)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---*---+---+ 
| T | f | f | ^ 
X---*---+---* |   
| T | T | T | |
*---*---+---+  
| f | T | T |  
+---*---+---* 

找到第一个

true

tile。在这种情况下，

（0,0）

。因此，我们从它的一个顶点开始（例如，左下角的顶点，向上看）。请注意，因为它是第一个真正的平铺，所以可以使用该顶点，确保它属于多边形。因此将第一个顶点添加到多边形中）：

启动trasverse。在这种情况下，前面的分幅为

假-真

，因此前进：

Current position: (0,1)
Polygon: {(0,1)} 

+---+---+---+ ^ 
| T | f | f | |  
X---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (0,0)
Polygon: {(0,1)} 

X---+---+---+ ^ 
| T | f | f | |  
*---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (1,0)
Polygon: {(0,1),(0,0)} 

*---X---+---+ 
| T | f | f |   
*---+---+---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,1)
Polygon: {(0,1),(0,0),(1,0)} 

*---*---+---+ 
| T | f | f | | 
*---X---+---+ |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---X  
| f | T | T |  
+---+---+---+ 

Current position: (3,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---X 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---+---X---* 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---X---+---* 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3)} 

*---*---+---+ 
| T | f | f | ^ 
*---*---+---* |   
| T | T | T | |
+---X---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2)} 

*---*---+---+ 
| T | f | f | 
*---*---+---*    
| T | T | T | <---
X---*---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,1)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---*---+---+ 
| T | f | f | ^ 
X---*---+---* |   
| T | T | T | |
*---*---+---+  
| f | T | T |  
+---*---+---* 

前面的瓷砖是

false

（我们在一个边框中），因此顺时针旋转并添加顶点：

Current position: (0,1)
Polygon: {(0,1)} 

+---+---+---+ ^ 
| T | f | f | |  
X---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (0,0)
Polygon: {(0,1)} 

X---+---+---+ ^ 
| T | f | f | |  
*---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (1,0)
Polygon: {(0,1),(0,0)} 

*---X---+---+ 
| T | f | f |   
*---+---+---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,1)
Polygon: {(0,1),(0,0),(1,0)} 

*---*---+---+ 
| T | f | f | | 
*---X---+---+ |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---X  
| f | T | T |  
+---+---+---+ 

Current position: (3,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---X 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---+---X---* 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---X---+---* 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3)} 

*---*---+---+ 
| T | f | f | ^ 
*---*---+---* |   
| T | T | T | |
+---X---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2)} 

*---*---+---+ 
| T | f | f | 
*---*---+---*    
| T | T | T | <---
X---*---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,1)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---*---+---+ 
| T | f | f | ^ 
X---*---+---* |   
| T | T | T | |
*---*---+---+  
| f | T | T |  
+---*---+---* 

现在，前面的分幅是

false

（一个在数组之外，另一个是

false

）顺时针旋转并添加顶点：

Current position: (0,1)
Polygon: {(0,1)} 

+---+---+---+ ^ 
| T | f | f | |  
X---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (0,0)
Polygon: {(0,1)} 

X---+---+---+ ^ 
| T | f | f | |  
*---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (1,0)
Polygon: {(0,1),(0,0)} 

*---X---+---+ 
| T | f | f |   
*---+---+---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,1)
Polygon: {(0,1),(0,0),(1,0)} 

*---*---+---+ 
| T | f | f | | 
*---X---+---+ |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---X  
| f | T | T |  
+---+---+---+ 

Current position: (3,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---X 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---+---X---* 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---X---+---* 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3)} 

*---*---+---+ 
| T | f | f | ^ 
*---*---+---* |   
| T | T | T | |
+---X---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2)} 

*---*---+---+ 
| T | f | f | 
*---*---+---*    
| T | T | T | <---
X---*---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,1)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---*---+---+ 
| T | f | f | ^ 
X---*---+---* |   
| T | T | T | |
*---*---+---+  
| f | T | T |  
+---*---+---* 

两个前瓷砖为

true

：逆时针旋转并添加顶点：

Current position: (0,1)
Polygon: {(0,1)} 

+---+---+---+ ^ 
| T | f | f | |  
X---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (0,0)
Polygon: {(0,1)} 

X---+---+---+ ^ 
| T | f | f | |  
*---+---+---+ |    
| T | T | T |
+---+---+---+  
| f | T | T |  
+---+---+---+  

Current position: (1,0)
Polygon: {(0,1),(0,0)} 

*---X---+---+ 
| T | f | f |   
*---+---+---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,1)
Polygon: {(0,1),(0,0),(1,0)} 

*---*---+---+ 
| T | f | f | | 
*---X---+---+ |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
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两个

false

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一个

true

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false

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两个

false

（阵列外）前分幅：顺时针旋转并添加顶点：

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false-false

（一个

false

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true

前瓷砖：逆时针旋转并添加顶点：

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| T | f | f |   
*---*---X---+     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1)} 

*---*---+---+ 
| T | f | f |   
*---*---+---X     
| T | T | T | --->
+---+---+---+  
| f | T | T |  
+---+---+---+ 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---X  
| f | T | T |  
+---+---+---+ 

Current position: (3,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1)} 

*---*---+---+ 
| T | f | f | | 
*---*---+---* |   
| T | T | T | v
+---+---+---+  
| f | T | T |  
+---+---+---X 

Current position: (2,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---+---X---* 

Current position: (1,3)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3)} 

*---*---+---+ 
| T | f | f |  
*---*---+---*    
| T | T | T | <---
+---+---+---+  
| f | T | T |  
+---X---+---* 

Current position: (1,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3)} 

*---*---+---+ 
| T | f | f | ^ 
*---*---+---* |   
| T | T | T | |
+---X---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,2)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2)} 

*---*---+---+ 
| T | f | f | 
*---*---+---*    
| T | T | T | <---
X---*---+---+  
| f | T | T |  
+---*---+---* 

Current position: (0,1)
Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---*---+---+ 
| T | f | f | ^ 
X---*---+---* |   
| T | T | T | |
*---*---+---+  
| f | T | T |  
+---*---+---* 

当前顶点是多边形的第一个顶点：执行已完成。结果如下：

Polygon: {(0,1),(0,0),(1,0),(1,1),(3,1),(3,3),(1,3),(1,2),(0,2)} 

*---* 
|   |  
*   *-------*    
|           | 
*---*       |  
    |       |  
    *-------* 

---

因为瓷砖，这是一个特殊的c