定义一个三维向量类,并定义相应的特殊方法实现:1)两个该类对象的加、减运算(要求支持运算符+、-);2)实现该类对象与标量的乘、除运算(要求支持运算符*、/,乘法时包括标量在前和后两种情况);3)以及向量的print方法; 向量的长度的定义;向量的点积以及叉积的定义; 定义一个类属性,表征已经实例化的对象的个数在一个模块中定义三维向量类,在另外一个文件中使用和测试创建的类; 1)在使用类的文件中,要求有入口函数,并分别对类的属性和方法进行结果测试; 2)创建1000个随机三维向量,要求x轴的范围在0~100,y的范围在-100~0;z的范围在-50~50,并用matplotlib把1000个向量的x坐标、y坐标和z坐标分别用三条2D曲线绘制出来(一个plot),然后给出Axis grid、 xlabel、legend、line线形等config。
时间: 2023-10-27 12:30:57 浏览: 93
以下是三维向量类的实现,包括上述要求的方法和属性:
```python
import math
import random
class Vector3D:
count = 0 # 类属性,用于记录实例化的对象个数
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
Vector3D.count += 1
def __str__(self):
return f"({self.x}, {self.y}, {self.z})"
def __add__(self, other):
return Vector3D(self.x + other.x, self.y + other.y, self.z + other.z)
def __sub__(self, other):
return Vector3D(self.x - other.x, self.y - other.y, self.z - other.z)
def __mul__(self, other):
if isinstance(other, (int, float)):
return Vector3D(self.x * other, self.y * other, self.z * other)
elif isinstance(other, Vector3D):
return self.dot(other)
else:
raise TypeError("unsupported operand type(s) for *: 'Vector3D' and '%s'" % type(other).__name__)
def __rmul__(self, other):
return Vector3D(self.x * other, self.y * other, self.z * other)
def __truediv__(self, other):
if isinstance(other, (int, float)):
return Vector3D(self.x / other, self.y / other, self.z / other)
else:
raise TypeError("unsupported operand type(s) for /: 'Vector3D' and '%s'" % type(other).__name__)
def length(self):
return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
def dot(self, other):
return self.x * other.x + self.y * other.y + self.z * other.z
def cross(self, other):
x = self.y * other.z - self.z * other.y
y = self.z * other.x - self.x * other.z
z = self.x * other.y - self.y * other.x
return Vector3D(x, y, z)
def print(self):
print(f"({self.x}, {self.y}, {self.z})")
```
以下是使用该类的文件的代码,包括创建1000个随机向量并进行绘图:
```python
import matplotlib.pyplot as plt
from vector import Vector3D
import random
# 测试类方法和属性
v1 = Vector3D(1, 2, 3)
v2 = Vector3D(4, 5, 6)
assert v1 + v2 == Vector3D(5, 7, 9)
assert v1 - v2 == Vector3D(-3, -3, -3)
assert v1 * 2 == Vector3D(2, 4, 6)
assert 2 * v1 == Vector3D(2, 4, 6)
assert v1 / 2 == Vector3D(0.5, 1, 1.5)
assert v1.length() == math.sqrt(14)
assert v1.dot(v2) == 32
assert v1.cross(v2) == Vector3D(-3, 6, -3)
assert Vector3D.count == 2
# 创建1000个随机向量并绘图
xs, ys, zs = [], [], []
for i in range(1000):
x = random.uniform(0, 100)
y = random.uniform(-100, 0)
z = random.uniform(-50, 50)
v = Vector3D(x, y, z)
xs.append(x)
ys.append(y)
zs.append(z)
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
ax.plot(xs, ys, zs, ".", markersize=2)
ax.set_xlabel("X Label")
ax.set_ylabel("Y Label")
ax.set_zlabel("Z Label")
ax.grid(True)
ax.legend()
plt.show()
```
运行以上代码,即可得到绘制的三维向量图形。
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