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📝 优化文档显示
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@@ -1,11 +1,5 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/6 下午12:54
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : __init__.py
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@Software: PyCharm
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本模块塞了一些预设的粒子生成器
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"""
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from .mp_math import *
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@@ -1,12 +1,14 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/6 下午12:57
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : __init__.py.py
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@Software: PyCharm
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本包定义了一些常用的导入，可直接从`mbcp.mp_math`导入使用
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导入的类有：
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- `AnyAngle`：任意角
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- `CurveEquation`：曲线方程
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- `Line3`：三维直线
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- `Plane3`：三维平面
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- `Point3`：三维点
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- `Segment3`：三维线段
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- `Vector3`：三维向量
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"""
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from .angle import AnyAngle
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from .const import *
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@@ -1,12 +1,6 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/26 上午6:29
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : angle.py
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@Software: PyCharm
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本模块定义了角度相关的类
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"""
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import math
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from typing import overload
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@@ -1,21 +1,19 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/25 下午9:45
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : const.py
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@Software: PyCharm
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本模块定义了一些常用的常量
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"""
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import math
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PI = math.pi
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"""常量 π"""
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E = math.e
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"""自然对数的底 exp(1)"""
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GOLDEN_RATIO = (1 + math.sqrt(5)) / 2
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"""黄金分割比"""
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GAMMA = 0.57721566490153286060651209008240243104215933593992
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"""欧拉常数"""
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EPSILON = 0.0001
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"""ε"""
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"""精度误差"""
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APPROX = 0.001
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"""约等于误差"""
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"""约等于判定误差"""
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@@ -1,17 +1,11 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/9 上午11:32
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : equation.py
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@Software: PyCharm
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本模块定义了方程相关的类和函数以及一些常用的数学函数
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"""
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from mbcp.mp_math.mp_math_typing import OneVarFunc, Var, MultiVarsFunc, Number
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from mbcp.mp_math.point import Point3
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from mbcp.mp_math.const import EPSILON
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from .mp_math_typing import OneVarFunc, Var, MultiVarsFunc, Number
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from .point import Point3
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from .const import EPSILON
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class CurveEquation:
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@@ -34,7 +28,7 @@ class CurveEquation:
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*t:
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参数
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Returns:
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目标点
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"""
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if len(t) == 1:
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return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
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@@ -73,7 +67,14 @@ def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...],
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return partial_derivative_func
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elif isinstance(var, tuple):
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def high_order_partial_derivative_func(*args: Var) -> Var:
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"""@litedoc-hide"""
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"""
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@litedoc-hide
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求高阶偏导函数
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Args:
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*args: 参数
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Returns:
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高阶偏导数值
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"""
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result_func = func
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for v in var:
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result_func = get_partial_derivative_func(result_func, v, epsilon)
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27
mbcp/mp_math/function.py
Normal file
27
mbcp/mp_math/function.py
Normal file
@@ -0,0 +1,27 @@
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"""
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AAA
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"""
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from .mp_math_typing import ThreeSingleVarsFunc
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from .point import Point3
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from .vector import Vector3
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from .const import EPSILON
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def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3:
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r"""
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计算三元函数在某点的梯度向量。
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> [!tip]
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> 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
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$\nabla f(x_0, y_0, z_0) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$
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Args:
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func: 三元函数
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p: 点
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epsilon: 偏移量
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Returns:
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梯度
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"""
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dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
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dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
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dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
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return Vector3(dx, dy, dz)
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@@ -1,12 +1,6 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/6 下午12:57
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : other.py
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@Software: PyCharm
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本模块定义了三维空间中的直线类
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"""
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import math
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from typing import TYPE_CHECKING
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@@ -1,12 +1,6 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/9 上午11:35
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : mp_math_typing.py
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@Software: PyCharm
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本模块用于内部类型提示
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"""
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from typing import Callable, Iterable, TypeAlias, TypeVar
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@@ -1,17 +1,16 @@
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# -*- coding: utf-8 -*-
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"""
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平面模块
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本模块定义了三维空间中的平面类
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"""
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import math
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from typing import TYPE_CHECKING, overload
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import numpy as np
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from .const import APPROX
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from .vector import Vector3, zero_vector3
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from .line import Line3
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from .point import Point3
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from .utils import approx, sign
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from .vector import Vector3, zero_vector3
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if TYPE_CHECKING:
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from .angle import AnyAngle
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@@ -1,3 +1,7 @@
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"""
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本模块定义了三维空间中点的类。
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"""
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from typing import TYPE_CHECKING, overload
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from .const import APPROX
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@@ -1,12 +1,6 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/7 上午12:42
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : segment.py
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@Software: PyCharm
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本模块定义了三维空间中的线段类
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"""
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from typing import TYPE_CHECKING
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@@ -1,12 +1,6 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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@Time : 2024/8/12 下午9:16
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : utils.py
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@Software: PyCharm
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本模块定义了一些常用的工具函数
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"""
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from typing import overload, TYPE_CHECKING
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@@ -1,17 +1,18 @@
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"""
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本模块定义了3维向量的类Vector3，以及一些常用的向量。
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"""
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import math
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from typing import overload, TYPE_CHECKING
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from typing import overload
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import numpy as np
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from .angle import AnyAngle
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from .const import APPROX
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from .mp_math_typing import RealNumber
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from .point import Point3
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from .angle import AnyAngle
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from .utils import approx
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# if TYPE_CHECKING:
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#
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class Vector3:
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def __init__(self, x: float, y: float, z: float):
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@@ -1,10 +1,4 @@
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# -*- coding: utf-8 -*-
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"""
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Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
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||||
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@Time : 2024/8/12 下午8:54
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@Author : snowykami
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@Email : snowykami@outlook.com
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@File : __init__.py.py
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@Software: PyCharm
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||||
本模块定义了粒子生成相关的工具
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"""
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