mbcp/docs/en/api/mp_math/vector.md

title
mbcp.mp_math.vector

class Vector3

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

3维向量

Arguments:

• x: x轴分量

• y: y轴分量

• z: z轴分量

Source code

def __init__(self, x: float, y: float, z: float):
    """
        3维向量
        Args:
            x: x轴分量
            y: y轴分量
            z: z轴分量
        """
    self.x = x
    self.y = y
    self.z = z

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

判断两个向量是否近似相等。

Arguments:

• other:

• epsilon:

Return:

• 是否近似相等

Source code

def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
    """
        判断两个向量是否近似相等。
        Args:
            other:
            epsilon:

        Returns:
            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

计算两个向量之间的夹角。

Arguments:

• other: 另一个向量

Return:

• 夹角

Source code

def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
    """
        计算两个向量之间的夹角。
        Args:
            other: 另一个向量
        Returns:
            夹角
        """
    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method 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。

Arguments:

• other:

Return:

• 行列式的结果

Source code

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:
        Returns:
            行列式的结果
        """
    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

判断两个向量是否近似平行。

Arguments:

• other: 另一个向量

• epsilon: 允许的误差

Return:

• 是否近似平行

Source code

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: 另一个向量
            epsilon: 允许的误差
        Returns:
            是否近似平行
        """
    return self.cross(other).length < epsilon

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

判断两个向量是否平行。

Arguments:

• other: 另一个向量

Return:

• 是否平行

Source code

def is_parallel(self, other: 'Vector3') -> bool:
    """
        判断两个向量是否平行。
        Args:
            other: 另一个向量
        Returns:
            是否平行
        """
    return self.cross(other).approx(zero_vector3)

method normalize(self)

将向量归一化。

自体归一化，不返回值。

Source code

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

Source code

@property
def np_array(self) -> 'np.ndarray':
    """
        返回numpy数组
        Returns:
        """
    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float

向量的模。

Return:

• 模

Source code

@property
def length(self) -> float:
    """
        向量的模。
        Returns:
            模
        """
    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3

获取该向量的单位向量。

Return:

• 单位向量

Source code

@property
def unit(self) -> 'Vector3':
    """
        获取该向量的单位向量。
        Returns:
            单位向量
        """
    return self / self.length

method __abs__(self)

Source code

def __abs__(self):
    return self.length

@overload

method self + other: Vector3 => Vector3

Source code

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

@overload

method self + other: Point3 => Point3

Source code

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

method self + other

V + P -> P

V + V -> V

Arguments:

• other:

Source code

def __add__(self, other):
    """
        V + P -> P

        V + V -> V
        Args:
            other:
        Returns:

        """
    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)

判断两个向量是否相等。

Arguments:

• other:

Return:

• 是否相等

Source code

def __eq__(self, other):
    """
        判断两个向量是否相等。
        Args:
            other:
        Returns:
            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

P + V -> P

别去点那边实现了。 :param other: :return:

Source code

def __radd__(self, other: 'Point3') -> 'Point3':
    """
        P + V -> P

        别去点那边实现了。
        :param other:
        :return:
        """
    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3

Source code

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

@overload

method self - other: Point3 => Point3

Source code

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

method self - other

V - P -> P

V - V -> V

Arguments:

• other:

Source code

def __sub__(self, other):
    """
        V - P -> P

        V - V -> V
        Args:
            other:
        Returns:
        """
    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

P - V -> P

Arguments:

• other:

Source code

def __rsub__(self, other: 'Point3'):
    """
        P - V -> P
        Args:
            other:
        Returns:

        """
    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

Source code

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

@overload

method self * other: RealNumber => Vector3

Source code

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

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

数组运算 非点乘。点乘使用@，叉乘使用cross。

Arguments:

• other:

Source code

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:

        Returns:
        """
    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

Source code

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

method self @ other: Vector3 => RealNumber

点乘。

Arguments:

• other:

Source code

def __matmul__(self, other: 'Vector3') -> 'RealNumber':
    """
        点乘。
        Args:
            other:
        Returns:
        """
    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3

Source code

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

method - self

Source code

def __neg__(self):
    return Vector3(-self.x, -self.y, -self.z)

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