mirror of
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691 lines
11 KiB
Markdown
691 lines
11 KiB
Markdown
---
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title: mbcp.mp_math.vector
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---
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### **class** `Vector3`
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### *method* `__init__(self, x: float, y: float, z: float)`
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3维向量
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**Arguments**:
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- x: x轴分量
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- y: y轴分量
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- z: z轴分量
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __init__(self, x: float, y: float, z: float):
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"""
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3维向量
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Args:
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x: x轴分量
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y: y轴分量
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z: z轴分量
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"""
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self.x = x
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self.y = y
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self.z = z
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```
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</details>
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### *method* `approx(self, other: Vector3, epsilon: float = APPROX) -> bool`
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判断两个向量是否近似相等。
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**Arguments**:
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- other:
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- epsilon:
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**Return**:
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- 是否近似相等
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
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"""
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判断两个向量是否近似相等。
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Args:
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other:
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epsilon:
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Returns:
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是否近似相等
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"""
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return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
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```
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</details>
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### *method* `cal_angle(self, other: Vector3) -> AnyAngle`
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计算两个向量之间的夹角。
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**Arguments**:
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- other: 另一个向量
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**Return**:
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- 夹角
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
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"""
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计算两个向量之间的夹角。
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Args:
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other: 另一个向量
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Returns:
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夹角
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"""
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return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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```
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</details>
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### *method* `cross(self, other: Vector3) -> Vector3`
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向量积 叉乘：v1 cross v2 -> v3
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叉乘为0，则两向量平行。
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其余结果的模为平行四边形的面积。
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**Arguments**:
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- other:
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**Return**:
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- 行列式的结果
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def cross(self, other: 'Vector3') -> 'Vector3':
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"""
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向量积 叉乘：v1 cross v2 -> v3
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叉乘为0，则两向量平行。
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其余结果的模为平行四边形的面积。
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返回如下行列式的结果：
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``i j k``
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``x1 y1 z1``
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``x2 y2 z2``
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Args:
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other:
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Returns:
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行列式的结果
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"""
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return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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```
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</details>
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### *method* `is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool`
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判断两个向量是否近似平行。
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**Arguments**:
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- other: 另一个向量
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- epsilon: 允许的误差
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**Return**:
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- 是否近似平行
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
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"""
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判断两个向量是否近似平行。
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Args:
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other: 另一个向量
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epsilon: 允许的误差
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Returns:
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是否近似平行
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"""
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return self.cross(other).length < epsilon
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```
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</details>
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### *method* `is_parallel(self, other: Vector3) -> bool`
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判断两个向量是否平行。
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**Arguments**:
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- other: 另一个向量
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**Return**:
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- 是否平行
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def is_parallel(self, other: 'Vector3') -> bool:
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"""
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判断两个向量是否平行。
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Args:
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other: 另一个向量
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Returns:
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是否平行
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"""
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return self.cross(other).approx(zero_vector3)
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```
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</details>
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### *method* `normalize(self)`
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将向量归一化。
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自体归一化，不返回值。
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def normalize(self):
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"""
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将向量归一化。
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自体归一化，不返回值。
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"""
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length = self.length
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self.x /= length
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self.y /= length
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self.z /= length
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```
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</details>
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### `@property`
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### *method* `np_array(self) -> np.ndarray`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@property
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def np_array(self) -> 'np.ndarray':
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"""
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返回numpy数组
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Returns:
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"""
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return np.array([self.x, self.y, self.z])
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```
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</details>
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### `@property`
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### *method* `length(self) -> float`
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向量的模。
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**Return**:
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- 模
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@property
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def length(self) -> float:
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"""
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向量的模。
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Returns:
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模
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"""
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return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
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```
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</details>
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### `@property`
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### *method* `unit(self) -> Vector3`
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获取该向量的单位向量。
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**Return**:
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- 单位向量
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@property
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def unit(self) -> 'Vector3':
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"""
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获取该向量的单位向量。
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Returns:
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单位向量
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"""
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return self / self.length
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```
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</details>
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### *method* `__abs__(self)`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __abs__(self):
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return self.length
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```
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</details>
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### `@overload`
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### *method* `self + other: Vector3 => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __add__(self, other: 'Vector3') -> 'Vector3':
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...
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```
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</details>
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### `@overload`
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### *method* `self + other: Point3 => Point3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __add__(self, other: 'Point3') -> 'Point3':
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...
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```
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</details>
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### *method* `self + other`
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V + P -> P
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V + V -> V
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**Arguments**:
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- other:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __add__(self, other):
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"""
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V + P -> P
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V + V -> V
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Args:
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other:
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Returns:
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
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elif isinstance(other, Point3):
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return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
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else:
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raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
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```
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</details>
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### *method* `__eq__(self, other)`
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判断两个向量是否相等。
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**Arguments**:
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- other:
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**Return**:
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- 是否相等
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __eq__(self, other):
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"""
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判断两个向量是否相等。
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Args:
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other:
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Returns:
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是否相等
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"""
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return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
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```
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</details>
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### *method* `self + other: Point3 => Point3`
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P + V -> P
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别去点那边实现了。
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:param other:
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:return:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __radd__(self, other: 'Point3') -> 'Point3':
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"""
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P + V -> P
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别去点那边实现了。
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:param other:
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:return:
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"""
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return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
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```
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</details>
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### `@overload`
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### *method* `self - other: Vector3 => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __sub__(self, other: 'Vector3') -> 'Vector3':
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...
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```
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</details>
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### `@overload`
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### *method* `self - other: Point3 => Point3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __sub__(self, other: 'Point3') -> 'Point3':
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...
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```
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</details>
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### *method* `self - other`
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V - P -> P
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V - V -> V
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**Arguments**:
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- other:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __sub__(self, other):
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"""
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V - P -> P
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V - V -> V
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Args:
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other:
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Returns:
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
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elif isinstance(other, Point3):
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return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
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else:
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raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
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```
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</details>
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### *method* `self - other: Point3`
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P - V -> P
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**Arguments**:
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- other:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __rsub__(self, other: 'Point3'):
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"""
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P - V -> P
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Args:
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other:
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Returns:
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"""
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if isinstance(other, Point3):
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return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
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else:
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raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
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```
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</details>
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### `@overload`
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### *method* `self * other: Vector3 => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __mul__(self, other: 'Vector3') -> 'Vector3':
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...
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```
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</details>
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### `@overload`
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### *method* `self * other: RealNumber => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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@overload
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def __mul__(self, other: RealNumber) -> 'Vector3':
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...
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```
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</details>
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### *method* `self * other: int | float | Vector3 => Vector3`
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数组运算 非点乘。点乘使用@，叉乘使用cross。
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**Arguments**:
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- other:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
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"""
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数组运算 非点乘。点乘使用@，叉乘使用cross。
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Args:
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other:
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Returns:
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
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elif isinstance(other, (float, int)):
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return Vector3(self.x * other, self.y * other, self.z * other)
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else:
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raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
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```
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</details>
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### *method* `self * other: RealNumber => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __rmul__(self, other: 'RealNumber') -> 'Vector3':
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return self.__mul__(other)
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```
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</details>
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### *method* `self @ other: Vector3 => RealNumber`
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点乘。
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**Arguments**:
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- other:
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __matmul__(self, other: 'Vector3') -> 'RealNumber':
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"""
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点乘。
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Args:
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other:
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Returns:
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"""
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return self.x * other.x + self.y * other.y + self.z * other.z
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```
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</details>
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### *method* `self / other: RealNumber => Vector3`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __truediv__(self, other: RealNumber) -> 'Vector3':
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return Vector3(self.x / other, self.y / other, self.z / other)
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```
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</details>
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### *method* `- self`
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<details>
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<summary> <i>Source code</i> </summary>
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```python
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def __neg__(self):
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return Vector3(-self.x, -self.y, -self.z)
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```
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</details>
|
||
|
||
### ***var*** `zero_vector3 = Vector3(0, 0, 0)`
|
||
|
||
- **Type**: `Vector3`
|
||
|
||
- **Description**: 零向量
|
||
|
||
### ***var*** `x_axis = Vector3(1, 0, 0)`
|
||
|
||
- **Type**: `Vector3`
|
||
|
||
- **Description**: x轴单位向量
|
||
|
||
### ***var*** `y_axis = Vector3(0, 1, 0)`
|
||
|
||
- **Type**: `Vector3`
|
||
|
||
- **Description**: y轴单位向量
|
||
|
||
### ***var*** `z_axis = Vector3(0, 0, 1)`
|
||
|
||
- **Type**: `Vector3`
|
||
|
||
- **Description**: z轴单位向量
|
||
|