mbcp.mp_math.vector

Description: 本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3

def __init__(self, x: float, y: float, z: float)

Description: 3维向量

Arguments:

• x (float): x轴分量
• y (float): y轴分量
• z (float): z轴分量

Source code or View on GitHub

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

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

Description: 判断两个向量是否近似相等。

Arguments:

• other (Vector3): 另一个向量
• epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub

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])

def cal_angle(self, other: Vector3) -> AnyAngle

Description: 计算两个向量之间的夹角。

Arguments:

• other (Vector3): 另一个向量

Return: AnyAngle: 夹角

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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)

def cross(self, other: Vector3) -> Vector3

Description: 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。

Arguments:

• other (Vector3): 另一个向量

Return: Vector3: 叉乘结果

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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)

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

Description: 判断两个向量是否近似平行。

Arguments:

• other (Vector3): 另一个向量
• epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub

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

def is_parallel(self, other: Vector3) -> bool

Description: 判断两个向量是否平行。

Arguments:

• other (Vector3): 另一个向量

Return: bool: 是否平行

Source code or View on GitHub

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)

def normalize(self)

Description: 将向量归一化。

自体归一化，不返回值。

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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

def np_array(self) -> np.ndarray

Return: np.ndarray: numpy数组

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@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

def length(self) -> float

Description: 向量的模。

Return: float: 模

Source code or View on GitHub

@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

def unit(self) -> Vector3

Description: 获取该向量的单位向量。

Return: Vector3: 单位向量

Source code or View on GitHub

@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

def __abs__(self)

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def __abs__(self):
    return self.length

@overload

def self + other: Vector3 => Vector3

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@overload
def __add__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

def self + other: Point3 => Point3

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@overload
def __add__(self, other: 'Point3') -> 'Point3':
    ...

def self + other

Description: V + P -> P

V + V -> V

Arguments:

• other (Vector3 | Point3): 另一个向量或点

Return: Vector3 | Point3: 新的向量或点

Source code or View on GitHub

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)}'")

def __eq__(self, other)

Description: 判断两个向量是否相等。

Arguments:

• other (Vector3): 另一个向量

Return: bool: 是否相等

Source code or View on GitHub

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)

def self + other: Point3 => Point3

Description: P + V -> P

别去点那边实现了。

Arguments:

• other (Point3): 另一个点

Return: Point3: 新的点

Source code or View on GitHub

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

def self - other: Vector3 => Vector3

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@overload
def __sub__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

def self - other: Point3 => Point3

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@overload
def __sub__(self, other: 'Point3') -> 'Point3':
    ...

def self - other

Description: V - P -> P

V - V -> V

Arguments:

• other (Vector3 | Point3): 另一个向量或点

Return: Vector3 | Point3: 新的向量

Source code or View on GitHub

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)}"')

def self - other: Point3

Description: P - V -> P

Arguments:

• other (Point3): 另一个点

Return: Point3: 新的点

Source code or View on GitHub

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

def self * other: Vector3 => Vector3

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@overload
def __mul__(self, other: 'Vector3') -> 'Vector3':
    ...

@overload

def self * other: RealNumber => Vector3

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@overload
def __mul__(self, other: RealNumber) -> 'Vector3':
    ...

def self * other: int | float | Vector3 => Vector3

Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。

Arguments:

• other (Vector3 | float): 另一个向量或数

Return: Vector3: 数组运算结果

Source code or View on GitHub

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)}'")

def self * other: RealNumber => Vector3

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def __rmul__(self, other: 'RealNumber') -> 'Vector3':
    return self.__mul__(other)

def self @ other: Vector3 => RealNumber

Description: 点乘。

Arguments:

• other (Vector3): 另一个向量

Return: float: 点乘结果

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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

def self / other: RealNumber => Vector3

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def __truediv__(self, other: RealNumber) -> 'Vector3':
    return Vector3(self.x / other, self.y / other, self.z / other)

def - self => Vector3

Description: 取负。

Return: Vector3: 负向量

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def __neg__(self) -> 'Vector3':
    """
        取负。
        Returns:
            [`Vector3`](#class-vector3): 负向量
        """
    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3

• Description: 零向量

• Type: Vector3

• Default: Vector3(0, 0, 0)

var x_axis

• Description: x轴单位向量

• Type: Vector3

• Default: Vector3(1, 0, 0)

var y_axis

• Description: y轴单位向量

• Type: Vector3

• Default: Vector3(0, 1, 0)

var z_axis

• Description: z轴单位向量

• Type: Vector3

• Default: Vector3(0, 0, 1)