# 坡度的工作原理

 使用度和使用百分比的坡度值比较

## 坡度算法

` slope_radians = ATAN ( √ ([dz/dx]2 + [dz/dy]2) )`

` slope_degrees = ATAN ( √ ([dz/dx]2 + [dz/dy]2) ) * 57.29578`

` slope_degrees = ATAN (rise_run) * 57.29578`
• 其中：

` rise_run = √ ([dz/dx]2 + [dz/dy]2]`

 表面分析扫描窗口

`  [dz/dx] = ((c + 2f + i) - (a + 2d + g) / (8 * x_cellsize)`

`  [dz/dy] = ((g + 2h + i) - (a + 2b + c)) / (8 * y_cellsize)`

## 坡度计算示例

 坡度输入示例

```  [dz/dx] = ((c + 2f + i) - (a + 2d + g) / (8 * x_cellsize)
= ((50 + 60 + 10) - (50 + 60 + 8)) / (8 * 5)
= (120 - 118) / 40
= 0.05```

```  [dz/dy] = ((g + 2h + i) - (a + 2b + c)) / (8 * y_cellsize)
= ((8 + 20 + 10) - (50 + 90 + 50)) / (8 * 5)
= (38 - 190 ) / 40
= -3.8```

```  rise_run = √ ([dz/dx]2 + [dz/dy]2)
= √ ((0.05)2 + (-3.8)2)
= √ (0.0025 + 14.44)
= 3.80032```
```  slope_degrees = ATAN (rise_run) * 57.29578
= ATAN (3.80032) * 57.29578
= 1.31349 * 57.29578
= 75.25762```

 坡度输出示例

## 参考书目

Burrough, P. A., and McDonell, R. A., 1998. Principles of Geographical Information Systems (Oxford University Press, New York), 190 pp.

5/10/2014