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模組 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

説明: 3维向量

變數説明:

源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
    """
        3维向量
        Args:
            x ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量
            y (\`float\`): y轴分量
            z (\`float\`): z轴分量
        """
    self.x = x
    self.y = y
    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似相等。

變數説明:

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
    """
        判断两个向量是否近似相等。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差

        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
        """
    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

説明: 计算两个向量之间的夹角。

變數説明:

返回: AnyAngle: 夹角

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
    """
        计算两个向量之间的夹角。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
        Returns:
            [\`AnyAngle\`](./angle#class-anyangle): 夹角
        """
    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

説明: 向量积 叉乘：v1 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

變數説明:

返回: Vector3: 叉乘结果

源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
    """
        向量积 叉乘：v1 cross v2 -> v3

        叉乘为0，则两向量平行。
        其余结果的模为平行四边形的面积。

        返回如下行列式的结果：

        \`\`i  j  k\`\`

        \`\`x1 y1 z1\`\`

        \`\`x2 y2 z2\`\`

        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
        Returns:
            [\`Vector3\`](#class-vector3): 叉乘结果
        """
    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)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似平行。

變數説明:

返回: bool: 是否近似平行

源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
    """
        判断两个向量是否近似平行。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
        """
    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

説明: 判断两个向量是否平行。

變數説明:

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
    """
        判断两个向量是否平行。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
        """
    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

源碼 或 於GitHub上查看
python
def normalize(self):
    """
        将向量归一化。

        自体归一化，不返回值。
        """
    length = self.length
    self.x /= length
    self.y /= length
    self.z /= length

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property
def np_array(self) -> 'np.ndarray':
    """
        返回numpy数组
        Returns:
            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
        """
    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

返回: float: 模

源碼 或 於GitHub上查看
python
@property
def length(self) -> float:
    """
        向量的模。
        Returns:
            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
        """
    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源碼 或 於GitHub上查看
python
@property
def unit(self) -> 'Vector3':
    """
        获取该向量的单位向量。
        Returns:
            [\`Vector3\`](#class-vector3): 单位向量
        """
    return self / self.length

method __abs__(self) ​

源碼 或 於GitHub上查看
python
def __abs__(self):
    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload
def __add__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

method self + other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload
def __add__(self, other: 'Point3') -> 'Point3':
    ...

method self + other ​

説明: V + P -> P

V + V -> V

變數説明:

返回: Vector3 | Point3: 新的向量或点

源碼 或 於GitHub上查看
python
def __add__(self, other):
    """
        V + P -> P

        V + V -> V
        Args:
            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
        Returns:
            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
        """
    if isinstance(other, Vector3):
        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
    elif isinstance(other, Point3):
        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
    else:
        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(self, other) ​

説明: 判断两个向量是否相等。

變數説明:

返回: bool: 是否相等

源碼 或 於GitHub上查看
python
def __eq__(self, other):
    """
        判断两个向量是否相等。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
        Returns:
            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
        """
    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
    """
        P + V -> P

        别去点那边实现了。
        Args:
            other ([\`Point3\`](./point#class-point3)): 另一个点
        Returns:
            [\`Point3\`](./point#class-point3): 新的点
        """
    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload
def __sub__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

method self - other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload
def __sub__(self, other: 'Point3') -> 'Point3':
    ...

method self - other ​

説明: V - P -> P

V - V -> V

變數説明:

返回: Vector3 | Point3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other):
    """
        V - P -> P

        V - V -> V
        Args:
            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
        Returns:
            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
        """
    if isinstance(other, Vector3):
        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
    elif isinstance(other, Point3):
        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
    else:
        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):
    """
        P - V -> P
        Args:
            other ([\`Point3\`](./point#class-point3)): 另一个点
        Returns:
            [\`Point3\`](./point#class-point3): 新的点
        """
    if isinstance(other, Point3):
        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
    else:
        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload
def __mul__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
@overload
def __mul__(self, other: RealNumber) -> 'Vector3':
    ...

method self * other: int | float | Vector3 => Vector3 ​

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

變數説明:

返回: Vector3: 数组运算结果

源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
    """
        数组运算 非点乘。点乘使用@，叉乘使用cross。
        Args:
            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
        Returns:
            [\`Vector3\`](#class-vector): 数组运算结果
        """
    if isinstance(other, Vector3):
        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
    elif isinstance(other, (float, int)):
        return Vector3(self.x * other, self.y * other, self.z * other)
    else:
        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

變數説明:

返回: float: 点乘结果

源碼 或 於GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
    """
        点乘。
        Args:
            other ([\`Vector3\`](#class-vector3)): 另一个向量
        Returns:
            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
        """
    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

説明: 取负。

返回: Vector3: 负向量

源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
    """
        取负。
        Returns:
            [\`Vector3\`](#class-vector3): 负向量
        """
    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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