class Vector3
method __init__(self, x: float, y: float, z: float)
説明: 3维向量
變數説明:
- x: x轴分量
- y: y轴分量
- z: z轴分量
源碼
python
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 = zmethod 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:
- other:
- epsilon:
返回: 是否近似相等
源碼
python
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
説明: 计算两个向量之间的夹角。
變數説明:
- other: 另一个向量
返回: 夹角
源碼
python
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
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:
- other:
返回: 行列式的结果
源碼
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:
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
説明: 判断两个向量是否近似平行。
變數説明:
- other: 另一个向量
- epsilon: 允许的误差
返回: 是否近似平行
源碼
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: 另一个向量
epsilon: 允许的误差
Returns:
是否近似平行
"""
return self.cross(other).length < epsilonmethod is_parallel(self, other: Vector3) -> bool
説明: 判断两个向量是否平行。
變數説明:
- other: 另一个向量
返回: 是否平行
源碼
python
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)
説明: 将向量归一化。
自体归一化，不返回值。
源碼
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
源碼
python
@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
説明: 向量的模。
返回: 模
源碼
python
@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
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
def unit(self) -> 'Vector3':
"""
获取该向量的单位向量。
Returns:
单位向量
"""
return self / self.lengthmethod __abs__(self)
源碼
python
def __abs__(self):
return self.length@overload
method self + other: Vector3 => Vector3
源碼
python
@overload
def __add__(self, other: 'Vector3') -> 'Vector3':
...@overload
method self + other: Point3 => Point3
源碼
python
@overload
def __add__(self, other: 'Point3') -> 'Point3':
...method self + other
説明: V + P -> P
V + V -> V
變數説明:
- other:
源碼
python
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)
説明: 判断两个向量是否相等。
變數説明:
- other:
返回: 是否相等
源碼
python
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
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
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
源碼
python
@overload
def __sub__(self, other: 'Vector3') -> 'Vector3':
...@overload
method self - other: Point3 => Point3
源碼
python
@overload
def __sub__(self, other: 'Point3') -> 'Point3':
...method self - other
説明: V - P -> P
V - V -> V
變數説明:
- other:
源碼
python
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
説明: P - V -> P
變數説明:
- other:
源碼
python
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
源碼
python
@overload
def __mul__(self, other: 'Vector3') -> 'Vector3':
...@overload
method self * other: RealNumber => Vector3
源碼
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:
- other:
源碼
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:
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
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
return self.__mul__(other)method self @ other: Vector3 => RealNumber
説明: 点乘。
變數説明:
- other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
"""
点乘。
Args:
other:
Returns:
"""
return self.x * other.x + self.y * other.y + self.z * other.zmethod self / other: RealNumber => Vector3
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
return Vector3(self.x / other, self.y / other, self.z / other)method - self
源碼
python
def __neg__(self):
return Vector3(-self.x, -self.y, -self.z)var zero_vector3 = Vector3(0, 0, 0)
類型:
Vector3説明: 零向量
var x_axis = Vector3(1, 0, 0)
類型:
Vector3説明: x轴单位向量
var y_axis = Vector3(0, 1, 0)
類型:
Vector3説明: y轴单位向量
var z_axis = Vector3(0, 0, 1)
類型:
Vector3説明: z轴单位向量