From 65134d67d1976306177bd691fb1239c5e97bd1b2 Mon Sep 17 00:00:00 2001 From: snowykami Date: Fri, 6 Sep 2024 16:53:20 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20docs=20from=20@=20snowykami/mb?= =?UTF-8?q?cp@35537c5b1548ec72c19078e4cb54d7b071b1b104=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 404.html | 4 ++-- api/index.html | 6 +++--- api/mp_math/angle.html | 6 +++--- api/mp_math/const.html | 6 +++--- api/mp_math/equation.html | 6 +++--- api/mp_math/function.html | 6 +++--- api/mp_math/index.html | 6 +++--- api/mp_math/line.html | 6 +++--- api/mp_math/mp_math_typing.html | 6 +++--- api/mp_math/plane.html | 6 +++--- api/mp_math/point.html | 6 +++--- api/mp_math/segment.html | 6 +++--- api/mp_math/utils.html | 6 +++--- api/mp_math/vector.html | 10 +++++----- api/particle/index.html | 6 +++--- api/presets/index.html | 6 +++--- api/presets/model/index.html | 6 +++--- assets/api_mp_math_vector.md.Bmtslkkm.js | 1 + assets/api_mp_math_vector.md.Bmtslkkm.lean.js | 1 + assets/api_mp_math_vector.md.DjjcwrqW.js | 1 - assets/api_mp_math_vector.md.DjjcwrqW.lean.js | 1 - assets/{app.ooCHBEUz.js => app.BSLaYTq9.js} | 2 +- assets/chunks/@localSearchIndexen.CXLYQH14.js | 1 - assets/chunks/@localSearchIndexen.ke4OFQjO.js | 1 + assets/chunks/@localSearchIndexja.BCRaXGU0.js | 1 - assets/chunks/@localSearchIndexja.COlRHLLs.js | 1 + assets/chunks/@localSearchIndexroot.CVf1h8jm.js | 1 - assets/chunks/@localSearchIndexroot.xPvxH6jA.js | 1 + assets/chunks/@localSearchIndexzht.Buw3O8cF.js | 1 + assets/chunks/@localSearchIndexzht.o8aepsrg.js | 1 - ...rchBox.xTIJuz0Z.js => VPLocalSearchBox.IDVxz8uj.js} | 2 +- assets/chunks/{theme.DVJrRbLX.js => theme.5eFoszBF.js} | 4 ++-- assets/en_api_mp_math_vector.md.C89tx4nd.js | 1 - assets/en_api_mp_math_vector.md.C89tx4nd.lean.js | 1 - assets/en_api_mp_math_vector.md.DJV8Xiz8.js | 1 + assets/en_api_mp_math_vector.md.DJV8Xiz8.lean.js | 1 + assets/ja_api_mp_math_vector.md.Dg61_-jz.js | 1 - assets/ja_api_mp_math_vector.md.Dg61_-jz.lean.js | 1 - assets/ja_api_mp_math_vector.md.XtCcd31y.js | 1 + assets/ja_api_mp_math_vector.md.XtCcd31y.lean.js | 1 + assets/zht_api_mp_math_vector.md.BnvyNBhC.js | 1 + assets/zht_api_mp_math_vector.md.BnvyNBhC.lean.js | 1 + assets/zht_api_mp_math_vector.md.D-o57Jl7.js | 1 - assets/zht_api_mp_math_vector.md.D-o57Jl7.lean.js | 1 - demo/best-practice.html | 6 +++--- demo/index.html | 6 +++--- en/api/index.html | 6 +++--- en/api/mp_math/angle.html | 6 +++--- en/api/mp_math/const.html | 6 +++--- en/api/mp_math/equation.html | 6 +++--- en/api/mp_math/function.html | 6 +++--- en/api/mp_math/index.html | 6 +++--- en/api/mp_math/line.html | 6 +++--- en/api/mp_math/mp_math_typing.html | 6 +++--- en/api/mp_math/plane.html | 6 +++--- en/api/mp_math/point.html | 6 +++--- en/api/mp_math/segment.html | 6 +++--- en/api/mp_math/utils.html | 6 +++--- en/api/mp_math/vector.html | 10 +++++----- en/api/particle/index.html | 6 +++--- en/api/presets/index.html | 6 +++--- en/api/presets/model/index.html | 6 +++--- en/demo/best-practice.html | 6 +++--- en/guide/index.html | 6 +++--- en/index.html | 6 +++--- en/refer/index.html | 6 +++--- guide/index.html | 6 +++--- hashmap.json | 2 +- index.html | 6 +++--- ja/api/index.html | 6 +++--- ja/api/mp_math/angle.html | 6 +++--- ja/api/mp_math/const.html | 6 +++--- ja/api/mp_math/equation.html | 6 +++--- ja/api/mp_math/function.html | 6 +++--- ja/api/mp_math/index.html | 6 +++--- ja/api/mp_math/line.html | 6 +++--- ja/api/mp_math/mp_math_typing.html | 6 +++--- ja/api/mp_math/plane.html | 6 +++--- ja/api/mp_math/point.html | 6 +++--- ja/api/mp_math/segment.html | 6 +++--- ja/api/mp_math/utils.html | 6 +++--- ja/api/mp_math/vector.html | 10 +++++----- ja/api/particle/index.html | 6 +++--- ja/api/presets/index.html | 6 +++--- ja/api/presets/model/index.html | 6 +++--- ja/demo/best-practice.html | 6 +++--- ja/guide/index.html | 6 +++--- ja/index.html | 6 +++--- ja/refer/index.html | 6 +++--- refer/7-differential-euqtion/index.html | 6 +++--- refer/function/curry.html | 6 +++--- refer/function/function.html | 6 +++--- refer/index.html | 6 +++--- zht/api/index.html | 6 +++--- zht/api/mp_math/angle.html | 6 +++--- zht/api/mp_math/const.html | 6 +++--- zht/api/mp_math/equation.html | 6 +++--- zht/api/mp_math/function.html | 6 +++--- zht/api/mp_math/index.html | 6 +++--- zht/api/mp_math/line.html | 6 +++--- zht/api/mp_math/mp_math_typing.html | 6 +++--- zht/api/mp_math/plane.html | 6 +++--- zht/api/mp_math/point.html | 6 +++--- zht/api/mp_math/segment.html | 6 +++--- zht/api/mp_math/utils.html | 6 +++--- zht/api/mp_math/vector.html | 10 +++++----- zht/api/particle/index.html | 6 +++--- zht/api/presets/index.html | 6 +++--- zht/api/presets/model/index.html | 6 +++--- zht/demo/best-practice.html | 6 +++--- zht/guide/index.html | 6 +++--- zht/index.html | 6 +++--- zht/refer/index.html | 6 +++--- 113 files changed, 279 insertions(+), 279 deletions(-) create mode 100644 assets/api_mp_math_vector.md.Bmtslkkm.js create mode 100644 assets/api_mp_math_vector.md.Bmtslkkm.lean.js delete mode 100644 assets/api_mp_math_vector.md.DjjcwrqW.js delete mode 100644 assets/api_mp_math_vector.md.DjjcwrqW.lean.js rename assets/{app.ooCHBEUz.js => app.BSLaYTq9.js} (95%) delete mode 100644 assets/chunks/@localSearchIndexen.CXLYQH14.js create mode 100644 assets/chunks/@localSearchIndexen.ke4OFQjO.js delete mode 100644 assets/chunks/@localSearchIndexja.BCRaXGU0.js create mode 100644 assets/chunks/@localSearchIndexja.COlRHLLs.js delete mode 100644 assets/chunks/@localSearchIndexroot.CVf1h8jm.js create mode 100644 assets/chunks/@localSearchIndexroot.xPvxH6jA.js create mode 100644 assets/chunks/@localSearchIndexzht.Buw3O8cF.js delete mode 100644 assets/chunks/@localSearchIndexzht.o8aepsrg.js rename assets/chunks/{VPLocalSearchBox.xTIJuz0Z.js => VPLocalSearchBox.IDVxz8uj.js} (99%) rename assets/chunks/{theme.DVJrRbLX.js => theme.5eFoszBF.js} (99%) delete mode 100644 assets/en_api_mp_math_vector.md.C89tx4nd.js delete mode 100644 assets/en_api_mp_math_vector.md.C89tx4nd.lean.js create mode 100644 assets/en_api_mp_math_vector.md.DJV8Xiz8.js create mode 100644 assets/en_api_mp_math_vector.md.DJV8Xiz8.lean.js delete mode 100644 assets/ja_api_mp_math_vector.md.Dg61_-jz.js delete mode 100644 assets/ja_api_mp_math_vector.md.Dg61_-jz.lean.js create mode 100644 assets/ja_api_mp_math_vector.md.XtCcd31y.js create mode 100644 assets/ja_api_mp_math_vector.md.XtCcd31y.lean.js create mode 100644 assets/zht_api_mp_math_vector.md.BnvyNBhC.js create mode 100644 assets/zht_api_mp_math_vector.md.BnvyNBhC.lean.js delete mode 100644 assets/zht_api_mp_math_vector.md.D-o57Jl7.js delete mode 100644 assets/zht_api_mp_math_vector.md.D-o57Jl7.lean.js diff --git a/404.html b/404.html index 8897036..f74c953 100644 --- a/404.html +++ b/404.html @@ -8,7 +8,7 @@ - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index 2798acb..29814d2 100644 --- a/api/index.html +++ b/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
MBCP 文档

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模块 mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html index b54109e..718c146 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True) - + \ No newline at end of file diff --git a/api/mp_math/const.html b/api/mp_math/const.html index 0ec878d..c935d10 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 说明: 常量 π

  • 默认值: math.pi

var E ​

  • 说明: 自然对数的底 exp(1)

  • 默认值: math.e

var GOLDEN_RATIO ​

  • 说明: 黄金分割比

  • 默认值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 说明: 欧拉常数

  • 默认值: 0.5772156649015329

var EPSILON ​

  • 说明: 精度误差

  • 默认值: 0.0001

var APPROX ​

  • 说明: 约等于判定误差

  • 默认值: 0.001

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html index 1b4aa82..dc81e33 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/api/mp_math/function.html b/api/mp_math/function.html index 705d46d..596e7da 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html index d95ba2b..8c670ab 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html index 05faf10..c59e573 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
- + \ No newline at end of file diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html index 36abb28..f30888b 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 说明: 实数

  • 类型: TypeAlias

  • 默认值: int | float

var Number ​

  • 说明: 数

  • 类型: TypeAlias

  • 默认值: RealNumber | complex

var SingleVar ​

  • 说明: 单变量

  • 默认值: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 说明: 数组变量

  • 默认值: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 说明: 变量

  • 类型: TypeAlias

  • 默认值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 说明: 一元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 说明: 一元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 说明: 一元函数

  • 类型: TypeAlias

  • 默认值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 说明: 二元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 说明: 二元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 说明: 二元函数

  • 类型: TypeAlias

  • 默认值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 说明: 三元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 说明: 三元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 说明: 三元函数

  • 类型: TypeAlias

  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 说明: 多元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 说明: 多元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 说明: 多元函数

  • 类型: TypeAlias

  • 默认值: MultiSingleVarsFunc | MultiArraysFunc

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html index a92671d..570b862 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method self & other: Line3 => Point3 ​

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index ca70d89..ded9cec 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
- + \ No newline at end of file diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html index a54fbfc..d9a1703 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2) - + \ No newline at end of file diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html index cf3b73c..9f423e1 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html index ec9761e..72b6f6e 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

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

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

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

说明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property
@@ -79,7 +79,7 @@
     return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源代码 或 在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 ​

说明: 取负。

返回: Vector3: 负向量

源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

- + \ No newline at end of file diff --git a/api/particle/index.html b/api/particle/index.html index 4198f16..42c6ccc 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.particle ​

本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html index 41c28a4..a9ec96d 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.presets ​

本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html index abe8d26..0ea47e7 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)] - + \ No newline at end of file diff --git a/assets/api_mp_math_vector.md.Bmtslkkm.js b/assets/api_mp_math_vector.md.Bmtslkkm.js new file mode 100644 index 0000000..ae1eb1d --- /dev/null +++ b/assets/api_mp_math_vector.md.Bmtslkkm.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t('

模块 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) ​

说明: 3维向量

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

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

说明: 判断两个向量是否近似相等。

参数:

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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 ​

说明: 计算两个向量之间的夹角。

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参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

说明: 向量积 叉乘：v1 x v2 -> v3

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参数:

返回: Vector3: 叉乘结果

源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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 ​

说明: 判断两个向量是否近似平行。

参数:

返回: bool: 是否近似平行

源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

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

说明: 判断两个向量是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

说明: 将向量归一化。

自体归一化，不返回值。

源代码 或 在GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

说明: 计算自向量在另一个向量上的投影向量。

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0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

说明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源代码 或 在GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源代码 或 在GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

说明: V + P -> P

V + V -> V

参数:

返回: Vector3 | Point3: 新的向量或点

源代码 或 在GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

说明: 判断两个向量是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

说明: P + V -> P

别去点那边实现了。

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

说明: V - P -> P

V - V -> V

参数:

返回: Vector3 | Point3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

说明: P - V -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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

说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

参数:

返回: Vector3: 数组运算结果

源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

说明: 点乘。

参数:

返回: float: 点乘结果

源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

说明: 取负。

返回: Vector3: 负向量

源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),l={name:"api/mp_math/vector.md"},h=a('

模块 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) ​

说明: 3维向量

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

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

说明: 判断两个向量是否近似相等。

参数:

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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 ​

说明: 计算两个向量之间的夹角。

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参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

说明: 向量积 叉乘：v1 x v2 -> v3

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参数:

返回: Vector3: 叉乘结果

源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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 ​

说明: 判断两个向量是否近似平行。

参数:

返回: bool: 是否近似平行

源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

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

说明: 判断两个向量是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

说明: 将向量归一化。

自体归一化，不返回值。

源代码 或 在GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

说明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源代码 或 在GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源代码 或 在GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

说明: V + P -> P

V + V -> V

参数:

返回: Vector3 | Point3: 新的向量或点

源代码 或 在GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

说明: 判断两个向量是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

说明: P + V -> P

别去点那边实现了。

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

说明: V - P -> P

V - V -> V

参数:

返回: Vector3 | Point3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

说明: P - V -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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

说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

参数:

返回: Vector3: 数组运算结果

源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

说明: 点乘。

参数:

返回: float: 点乘结果

源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

说明: 取负。

返回: Vector3: 负向量

源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"Module mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["Module mbcp.mp_math.const"]},"25":{"title":"var E","titles":["Module mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["Module mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["Module mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["Module mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["Module mbcp.mp_math.const"]},"30":{"title":"Module mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["Module mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["Module mbcp.mp_math.equation"]},"35":{"title":"Module mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["Module mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["Module mbcp.mp_math.function"]},"38":{"title":"Module mbcp.mp_math","titles":[]},"39":{"title":"Module mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["Module mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["Module mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["Module mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["Module mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["Module mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["Module mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["Module mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.line","class Line3"]},"58":{"title":"Module mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["Module mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["Module mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["Module mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"76":{"title":"Module mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"96":{"title":"Module mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["Module mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"105":{"title":"Module mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["Module mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["Module mbcp.mp_math.segment","class Segment3"]},"108":{"title":"Module mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["Module mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["Module mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["Module mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["Module mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["Module mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => 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AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"Module mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["Module mbcp.mp_math.const"]},"25":{"title":"var E","titles":["Module mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["Module mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["Module mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["Module mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["Module mbcp.mp_math.const"]},"30":{"title":"Module mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["Module mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["Module mbcp.mp_math.equation"]},"35":{"title":"Module mbcp.mp_math","titles":[]},"36":{"title":"Module mbcp.mp_math.function","titles":[]},"37":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["Module mbcp.mp_math.function"]},"38":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["Module mbcp.mp_math.function"]},"39":{"title":"Module mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["Module mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["Module mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["Module mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["Module mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["Module mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["Module mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["Module mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.line","class Line3"]},"58":{"title":"Module mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["Module mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["Module mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["Module mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"76":{"title":"Module mbcp.mp_math.point","titles":[]},"77":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"78":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"79":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"80":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"81":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"82":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"83":{"title":"method self == other","titles":["Module mbcp.mp_math.point","class Point3"]},"84":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"85":{"title":"Module mbcp.mp_math.plane","titles":[]},"86":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"87":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"96":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"97":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"98":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"99":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"100":{"title":"method self & other: Line3 => Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"101":{"title":"method self & other: Plane3 => Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"102":{"title":"method self & other","titles":["Module mbcp.mp_math.plane","class Plane3"]},"103":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"104":{"title":"method self & other: Line3 => Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"105":{"title":"Module mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["Module mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["Module mbcp.mp_math.segment","class Segment3"]},"108":{"title":"Module mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["Module mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["Module mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["Module mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["Module mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["Module mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => 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Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> 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mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var 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mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var 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Module 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) ​

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
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

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

Description: 判断两个向量是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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 ​

Description: 计算两个向量之间的夹角。

',16),h={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"向量夹角计算公式:",-1),p={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a('',1),T=[k],Q=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a('

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

Description: 向量积 叉乘：v1 x v2 -> v3

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Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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 ​

Description: 判断两个向量是否近似平行。

Arguments:

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

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

Description: 判断两个向量是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

Description: 将向量归一化。

自体归一化，不返回值。

Source code or View on GitHub
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method 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
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

Source code or View on GitHub
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

Description: V + P -> P

V + V -> V

Arguments:

Return: Vector3 | Point3: 新的向量或点

Source code or View on GitHub
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

Description: 判断两个向量是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

Description: P + V -> P

别去点那边实现了。

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

Description: V - P -> P

V - V -> V

Arguments:

Return: Vector3 | Point3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

Description: P - V -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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

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

Arguments:

Return: Vector3: 数组运算结果

Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

Description: 点乘。

Arguments:

Return: float: 点乘结果

Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

Description: 取负。

Return: Vector3: 负向量

Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':\n    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)

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Module 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) ​

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
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

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

Description: 判断两个向量是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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 ​

Description: 计算两个向量之间的夹角。

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Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

Description: 向量积 叉乘：v1 x v2 -> v3

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Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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 ​

Description: 判断两个向量是否近似平行。

Arguments:

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

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

Description: 判断两个向量是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

Description: 将向量归一化。

自体归一化，不返回值。

Source code or View on GitHub
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

Description: 计算自向量在另一个向量上的投影向量。

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0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method 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
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

Source code or View on GitHub
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

Description: V + P -> P

V + V -> V

Arguments:

Return: Vector3 | Point3: 新的向量或点

Source code or View on GitHub
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

Description: 判断两个向量是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

Description: P + V -> P

别去点那边实现了。

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

Description: V - P -> P

V - V -> V

Arguments:

Return: Vector3 | Point3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

Description: P - V -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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

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

Arguments:

Return: Vector3: 数组运算结果

Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

Description: 点乘。

Arguments:

Return: float: 点乘结果

Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

Description: 取负。

Return: Vector3: 负向量

Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':\n    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)

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z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),l={name:"ja/api/mp_math/vector.md"},h=a('

モジュール 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

引数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    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。

引数:

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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。

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引数:

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    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 x v2 -> v3

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引数:

戻り値: Vector3: 叉乘结果

ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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。

引数:

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:\n    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。

ソースコード または GitHubで表示
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property\ndef length(self) -> float:\n    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。

戻り値: Vector3: 单位向量

ソースコード または GitHubで表示
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

ソースコード または GitHubで表示
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

引数:

戻り値: Vector3 | Point3: 新的向量或点

ソースコード または GitHubで表示
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

引数:

戻り値: bool: 是否相等

ソースコード または GitHubで表示
python
def __eq__(self, other):\n    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。

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

引数:

戻り値: Vector3 | Point3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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。

引数:

戻り値: Vector3: 数组运算结果

ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

引数:

戻り値: float: 点乘结果

ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

説明: 取负。

戻り値: Vector3: 负向量

ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

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モジュール 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

引数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    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。

引数:

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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。

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引数:

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    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 x v2 -> v3

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引数:

戻り値: Vector3: 叉乘结果

ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    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。

引数:

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    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。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:\n    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。

ソースコード または GitHubで表示
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

説明: 计算自向量在另一个向量上的投影向量。

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引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property\ndef length(self) -> float:\n    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。

戻り値: Vector3: 单位向量

ソースコード または GitHubで表示
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

ソースコード または GitHubで表示
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

引数:

戻り値: Vector3 | Point3: 新的向量或点

ソースコード または GitHubで表示
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

引数:

戻り値: bool: 是否相等

ソースコード または GitHubで表示
python
def __eq__(self, other):\n    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。

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

引数:

戻り値: Vector3 | Point3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

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。

引数:

戻り値: Vector3: 数组运算结果

ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

引数:

戻り値: float: 点乘结果

ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':\n    return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':\n    return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

説明: 取负。

戻り値: Vector3: 负向量

ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

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o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t('

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:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    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:\n    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。

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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':\n    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 x v2 -> v3

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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':\n    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:\n    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:\n    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):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

説明: 计算自向量在另一个向量上的投影向量。

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變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    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\ndef length(self) -> float:\n    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\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method 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):\n    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':\n    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\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

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

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):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        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'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        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\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        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':\n    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':\n    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':\n    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':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

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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:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    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:\n    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。

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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':\n    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 x v2 -> v3

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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':\n    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:\n    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:\n    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):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

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

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    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\ndef length(self) -> float:\n    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\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method 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):\n    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':\n    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\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

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

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):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        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'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        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\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        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':\n    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':\n    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':\n    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':\n    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

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MBCP 文档

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/index.html b/en/api/index.html index 28d0da7..272c7c2 100644 --- a/en/api/index.html +++ b/en/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Module mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html index 6522a9a..781cd7a 100644 --- a/en/api/mp_math/angle.html +++ b/en/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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- + \ No newline at end of file diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html index 7889768..8be7ee6 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Module mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • Description: 常量 π

  • Default: math.pi

var E ​

  • Description: 自然对数的底 exp(1)

  • Default: math.e

var GOLDEN_RATIO ​

  • Description: 黄金分割比

  • Default: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • Description: 欧拉常数

  • Default: 0.5772156649015329

var EPSILON ​

  • Description: 精度误差

  • Default: 0.0001

var APPROX ​

  • Description: 约等于判定误差

  • Default: 0.001

Documentation built with VitePress | API references generated by litedoc

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- + \ No newline at end of file diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html index 1bd247f..a94b104 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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- + \ No newline at end of file diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html index 3f14c95..931f2a7 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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- + \ No newline at end of file diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html index 79d6220..b1518b3 100644 --- a/en/api/mp_math/index.html +++ b/en/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Module mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html index 660ed0d..566cd3d 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

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- + \ No newline at end of file diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html index 8165235..9b8ddb7 100644 --- a/en/api/mp_math/mp_math_typing.html +++ b/en/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Module mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • Description: 实数

  • Type: TypeAlias

  • Default: int | float

var Number ​

  • Description: 数

  • Type: TypeAlias

  • Default: RealNumber | complex

var SingleVar ​

  • Description: 单变量

  • Default: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • Description: 数组变量

  • Default: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • Description: 变量

  • Type: TypeAlias

  • Default: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • Description: 一元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • Description: 一元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • Description: 一元函数

  • Type: TypeAlias

  • Default: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • Description: 二元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • Description: 二元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • Description: 二元函数

  • Type: TypeAlias

  • Default: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • Description: 三元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • Description: 三元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • Description: 三元函数

  • Type: TypeAlias

  • Default: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • Description: 多元单变量函数

  • Type: TypeAlias

  • Default: Callable[..., SingleVar]

var MultiArraysFunc ​

  • Description: 多元数组函数

  • Type: TypeAlias

  • Default: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • Description: 多元函数

  • Type: TypeAlias

  • Default: MultiSingleVarsFunc | MultiArraysFunc

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html index bccd2a3..9db5190 100644 --- a/en/api/mp_math/plane.html +++ b/en/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool ​

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method self & other: Line3 => Point3 ​

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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- + \ No newline at end of file diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html index 3e853dc..9ebb2b2 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

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- + \ No newline at end of file diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html index 75de8e3..57f91e2 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

Documentation built with VitePress | API references generated by litedoc

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- + \ No newline at end of file diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html index 4672a2f..265f578 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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- + \ No newline at end of file diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html index 6281105..5cd75e3 100644 --- a/en/api/mp_math/vector.html +++ b/en/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

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

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

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

Description: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property
@@ -79,7 +79,7 @@
     return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

Description: 取负。

Return: Vector3: 负向量

Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
     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)

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/particle/index.html b/en/api/particle/index.html index c243c3c..2667563 100644 --- a/en/api/particle/index.html +++ b/en/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/index.html b/en/api/presets/index.html index 9aad9c7..6bf607a 100644 --- a/en/api/presets/index.html +++ b/en/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html index 5270a2c..927b520 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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- + \ No newline at end of file diff --git a/en/demo/best-practice.html b/en/demo/best-practice.html index 88c03a4..7f95cf4 100644 --- a/en/demo/best-practice.html +++ b/en/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/guide/index.html b/en/guide/index.html index 61c25b7..e1bd0f7 100644 --- a/en/guide/index.html +++ b/en/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
MBCP docs

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开始不了一点 ​

∫12x111

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- + \ No newline at end of file diff --git a/en/index.html b/en/index.html index 00ae943..2ac1a0d 100644 --- a/en/index.html +++ b/en/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
MBCP docs

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MBCP

More basic change particle

A Library for Python to create Minecraft particle effects and geometric figures

Get Started
API Reference
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Easy to use

Through a simple interface, most of the geometric operations and particle production requirements have been achieved

📦

Integrated

Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra

🧊

Rich presets

Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects

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- + \ No newline at end of file diff --git a/en/refer/index.html b/en/refer/index.html index 83d8533..900a7a9 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Reference ​

help us to improve the documentation

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- + \ No newline at end of file diff --git a/guide/index.html b/guide/index.html index d07ac7c..a14b4e5 100644 --- a/guide/index.html +++ b/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
MBCP 文档

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快速开始 ​

TIP

建议：把你项目所使用的Python换成PyPy，这样可以提高性能(兼容性优先)

安装 ​

shell
pip install mbcp

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- + \ No newline at end of file diff --git a/hashmap.json b/hashmap.json index 540ad9c..a435f5e 100644 --- a/hashmap.json +++ b/hashmap.json @@ -1 +1 @@ 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diff --git a/index.html b/index.html index e4d0003..d31ccf8 100644 --- a/index.html +++ b/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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MBCP

更多基础变换粒子

用于几何运算和Minecraft粒子制作的库

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高可用性

通过简单的接口，实现了大部分几何运算和粒子制作的需求

📦

高集成度

对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单

🧊

内置预设

提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作

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モジュール mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

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- + \ No newline at end of file diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html index d9ac6cd..00bc318 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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モジュール mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 説明: 常量 π

  • デフォルト: math.pi

var E ​

  • 説明: 自然对数的底 exp(1)

  • デフォルト: math.e

var GOLDEN_RATIO ​

  • 説明: 黄金分割比

  • デフォルト: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 説明: 欧拉常数

  • デフォルト: 0.5772156649015329

var EPSILON ​

  • 説明: 精度误差

  • デフォルト: 0.0001

var APPROX ​

  • 説明: 约等于判定误差

  • デフォルト: 0.001

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- + \ No newline at end of file diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html index 5743443..f7ff8ca 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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- + \ No newline at end of file diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html index 16698ca..c6c4fec 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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- + \ No newline at end of file diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html index d18f489..ea15bef 100644 --- a/ja/api/mp_math/index.html +++ b/ja/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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モジュール mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

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- + \ No newline at end of file diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html index fa22273..176a80a 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html index e3a765c..b49a50f 100644 --- a/ja/api/mp_math/mp_math_typing.html +++ b/ja/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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モジュール mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 説明: 实数

  • タイプ: TypeAlias

  • デフォルト: int | float

var Number ​

  • 説明: 数

  • タイプ: TypeAlias

  • デフォルト: RealNumber | complex

var SingleVar ​

  • 説明: 单变量

  • デフォルト: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 説明: 数组变量

  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 説明: 变量

  • タイプ: TypeAlias

  • デフォルト: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 説明: 一元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 説明: 一元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 説明: 一元函数

  • タイプ: TypeAlias

  • デフォルト: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 説明: 二元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 説明: 二元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 説明: 二元函数

  • タイプ: TypeAlias

  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 説明: 三元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 説明: 三元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 説明: 三元函数

  • タイプ: TypeAlias

  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 説明: 多元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 説明: 多元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 説明: 多元函数

  • タイプ: TypeAlias

  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc

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- + \ No newline at end of file diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html index c2992e3..eb93964 100644 --- a/ja/api/mp_math/plane.html +++ b/ja/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool ​

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method self & other: Line3 => Point3 ​

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html index d6ee23b..809a0af 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html index f024754..a847af1 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html index 3d8d263..e260ba5 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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- + \ No newline at end of file diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html index 4754f3d..7e88e55 100644 --- a/ja/api/mp_math/vector.html +++ b/ja/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

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

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

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

説明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property
@@ -79,7 +79,7 @@
     return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
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。

戻り値: Vector3: 负向量

ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

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- + \ No newline at end of file diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html index 534b783..40cd1e7 100644 --- a/ja/api/particle/index.html +++ b/ja/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html index 94e7c6d..aed80e6 100644 --- a/ja/api/presets/index.html +++ b/ja/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html index 12cb837..e2ebb14 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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开始不了一点 ​

∫12x111

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MBCP

More basic change particle

ジオメトリ演算とパーティクル作成のためのライブラリ

はじめる
API リファレンス
ベストプラクティス
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高可用性

シンプルなインターフェースを通じて、ほとんどのジオメトリ演算とパーティクル作成のニーズを実現しました

📦

高集積度

numpy、scipy、およびsympyをラップして統合し、Geogebraを使用するように簡単にスクリプトを作成できます

🧊

組み込みプリセット

多くのプリセットを提供しており、一般的なジオメトリ図形やパーティクル効果など、迅速に作成できます

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微分方程 ​

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- + \ No newline at end of file diff --git a/refer/function/curry.html b/refer/function/curry.html index 1daa583..418569b 100644 --- a/refer/function/curry.html +++ b/refer/function/curry.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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- + \ No newline at end of file diff --git a/zht/api/index.html b/zht/api/index.html index 8eba367..105cb74 100644 --- a/zht/api/index.html +++ b/zht/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模組 mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

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- + \ No newline at end of file diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html index 47b61c3..4cdf0a3 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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- + \ No newline at end of file diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html index 05ec460..3322bcc 100644 --- a/zht/api/mp_math/const.html +++ b/zht/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模組 mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 説明: 常量 π

  • 默認值: math.pi

var E ​

  • 説明: 自然对数的底 exp(1)

  • 默認值: math.e

var GOLDEN_RATIO ​

  • 説明: 黄金分割比

  • 默認值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 説明: 欧拉常数

  • 默認值: 0.5772156649015329

var EPSILON ​

  • 説明: 精度误差

  • 默認值: 0.0001

var APPROX ​

  • 説明: 约等于判定误差

  • 默認值: 0.001

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- + \ No newline at end of file diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html index 7c1121a..e62593e 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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- + \ No newline at end of file diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html index 9bf83af..1cf6048 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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- + \ No newline at end of file diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html index 47475b7..47d26ea 100644 --- a/zht/api/mp_math/index.html +++ b/zht/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模組 mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

文檔由 VitePress 構建 | API引用由 litedoc 生成

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- + \ No newline at end of file diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html index 61bd6ef..426abf9 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

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- + \ No newline at end of file diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html index b3e0c87..c6360ce 100644 --- a/zht/api/mp_math/mp_math_typing.html +++ b/zht/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模組 mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 説明: 实数

  • 類型: TypeAlias

  • 默認值: int | float

var Number ​

  • 説明: 数

  • 類型: TypeAlias

  • 默認值: RealNumber | complex

var SingleVar ​

  • 説明: 单变量

  • 默認值: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 説明: 数组变量

  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 説明: 变量

  • 類型: TypeAlias

  • 默認值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 説明: 一元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 説明: 一元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 説明: 一元函数

  • 類型: TypeAlias

  • 默認值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 説明: 二元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 説明: 二元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 説明: 二元函数

  • 類型: TypeAlias

  • 默認值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 説明: 三元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 説明: 三元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 説明: 三元函数

  • 類型: TypeAlias

  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 説明: 多元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 説明: 多元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 説明: 多元函数

  • 類型: TypeAlias

  • 默認值: MultiSingleVarsFunc | MultiArraysFunc

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html index 5f6c3be..19208f0 100644 --- a/zht/api/mp_math/plane.html +++ b/zht/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool ​

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method self & other: Line3 => Point3 ​

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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- + \ No newline at end of file diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html index bf758de..535ee6d 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html index 2b5cb8d..35be59a 100644 --- a/zht/api/mp_math/segment.html +++ b/zht/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

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- + \ No newline at end of file diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html index c4c38ef..b249d88 100644 --- a/zht/api/mp_math/utils.html +++ b/zht/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html index 7d1f534..3c04eb8 100644 --- a/zht/api/mp_math/vector.html +++ b/zht/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

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

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

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

説明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@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':
     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
@@ -79,7 +79,7 @@
     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':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html index f7e979d..5a83f7c 100644 --- a/zht/api/particle/index.html +++ b/zht/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html index 7a25383..2865007 100644 --- a/zht/api/presets/index.html +++ b/zht/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html index 8a0641f..2a7a74c 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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- + \ No newline at end of file diff --git a/zht/demo/best-practice.html b/zht/demo/best-practice.html index d49c3a8..943b8a2 100644 --- a/zht/demo/best-practice.html +++ b/zht/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/guide/index.html b/zht/guide/index.html index 92959eb..c61f0d9 100644 --- a/zht/guide/index.html +++ b/zht/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Reference ​

Help us to improve the documentation

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