用Python编写以下程序:三个二维数组分别代表三个二维坐标系坐标,求这三个坐标所在圆的半径
时间: 2023-12-03 17:46:13 浏览: 212
假设三个二维坐标系坐标依次存储在三个二维数组 x, y, z 中,可以按照如下步骤求解三个坐标所在圆的半径:
1. 分别计算三个坐标系中任意两个点之间的距离,即:
d_x1x2 = ((x[1][0] - x[0][0])**2 + (x[1][1] - x[0][1])**2)**0.5
d_x1x3 = ((x[2][0] - x[0][0])**2 + (x[2][1] - x[0][1])**2)**0.5
d_x2x3 = ((x[2][0] - x[1][0])**2 + (x[2][1] - x[1][1])**2)**0.5
d_y1y2 = ((y[1][0] - y[0][0])**2 + (y[1][1] - y[0][1])**2)**0.5
d_y1y3 = ((y[2][0] - y[0][0])**2 + (y[2][1] - y[0][1])**2)**0.5
d_y2y3 = ((y[2][0] - y[1][0])**2 + (y[2][1] - y[1][1])**2)**0.5
d_z1z2 = ((z[1][0] - z[0][0])**2 + (z[1][1] - z[0][1])**2)**0.5
d_z1z3 = ((z[2][0] - z[0][0])**2 + (z[2][1] - z[0][1])**2)**0.5
d_z2z3 = ((z[2][0] - z[1][0])**2 + (z[2][1] - z[1][1])**2)**0.5
2. 利用海伦公式计算三个坐标系中的三角形面积,即:
s_x = (d_x1x2 + d_x1x3 + d_x2x3) / 2
area_x = (s_x * (s_x - d_x1x2) * (s_x - d_x1x3) * (s_x - d_x2x3))**0.5
s_y = (d_y1y2 + d_y1y3 + d_y2y3) / 2
area_y = (s_y * (s_y - d_y1y2) * (s_y - d_y1y3) * (s_y - d_y2y3))**0.5
s_z = (d_z1z2 + d_z1z3 + d_z2z3) / 2
area_z = (s_z * (s_z - d_z1z2) * (s_z - d_z1z3) * (s_z - d_z2z3))**0.5
3. 根据三个二维坐标系中的三角形面积和海伦公式中的半径公式计算每个坐标所在圆的半径,即:
radius_x = (d_x1x2 * d_x1x3 * d_x2x3 / (4 * area_x))**0.5
radius_y = (d_y1y2 * d_y1y3 * d_y2y3 / (4 * area_y))**0.5
radius_z = (d_z1z2 * d_z1z3 * d_z2z3 / (4 * area_z))**0.5
完整代码如下:
```python
# 三个二维坐标系坐标
x = [[0, 0], [1, 0], [0, 1]]
y = [[0, 0], [1, 0], [1, 1]]
z = [[0, 0], [0, 1], [-1, 0]]
# 计算三个坐标系中任意两个点之间的距离
d_x1x2 = ((x[1][0] - x[0][0])**2 + (x[1][1] - x[0][1])**2)**0.5
d_x1x3 = ((x[2][0] - x[0][0])**2 + (x[2][1] - x[0][1])**2)**0.5
d_x2x3 = ((x[2][0] - x[1][0])**2 + (x[2][1] - x[1][1])**2)**0.5
d_y1y2 = ((y[1][0] - y[0][0])**2 + (y[1][1] - y[0][1])**2)**0.5
d_y1y3 = ((y[2][0] - y[0][0])**2 + (y[2][1] - y[0][1])**2)**0.5
d_y2y3 = ((y[2][0] - y[1][0])**2 + (y[2][1] - y[1][1])**2)**0.5
d_z1z2 = ((z[1][0] - z[0][0])**2 + (z[1][1] - z[0][1])**2)**0.5
d_z1z3 = ((z[2][0] - z[0][0])**2 + (z[2][1] - z[0][1])**2)**0.5
d_z2z3 = ((z[2][0] - z[1][0])**2 + (z[2][1] - z[1][1])**2)**0.5
# 计算三个坐标系中的三角形面积
s_x = (d_x1x2 + d_x1x3 + d_x2x3) / 2
area_x = (s_x * (s_x - d_x1x2) * (s_x - d_x1x3) * (s_x - d_x2x3))**0.5
s_y = (d_y1y2 + d_y1y3 + d_y2y3) / 2
area_y = (s_y * (s_y - d_y1y2) * (s_y - d_y1y3) * (s_y - d_y2y3))**0.5
s_z = (d_z1z2 + d_z1z3 + d_z2z3) / 2
area_z = (s_z * (s_z - d_z1z2) * (s_z - d_z1z3) * (s_z - d_z2z3))**0.5
# 计算每个坐标所在圆的半径
radius_x = (d_x1x2 * d_x1x3 * d_x2x3 / (4 * area_x))**0.5
radius_y = (d_y1y2 * d_y1y3 * d_y2y3 / (4 * area_y))**0.5
radius_z = (d_z1z2 * d_z1z3 * d_z2z3 / (4 * area_z))**0.5
# 输出结果
print("x 坐标系所在圆的半径为:", radius_x)
print("y 坐标系所在圆的半径为:", radius_y)
print("z 坐标系所在圆的半径为:", radius_z)
```
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