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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 求N元函数一阶偏导函数。这玩意不太稳定， < / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > [!warning]< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升< / span > < / span >
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< span class = "line" > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func: 函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > epsilon: 偏移量< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 偏导函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Raises:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ValueError: 无效变量类型< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > if< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > isinstance< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (var, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > int< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ):< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > partial_derivative_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> Var:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > @litedoc-hide< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *args:< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > list< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus[var] < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > +=< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > list< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus[var] < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -=< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_plus) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > -< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args_list_minus)) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > /< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 2< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > partial_derivative_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > elif< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > isinstance< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (var, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > tuple< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ):< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > high_order_partial_derivative_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> Var:< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " @litedoc-hide" " " < / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > for< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > v < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > in< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > var:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > get_partial_derivative_func(result_func, v, epsilon)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > result_func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > high_order_partial_derivative_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > else< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > raise< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > ValueError< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > ' Invalid var type' < / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > )< / span > < / span > < / code > < / pre > < / div > < / details > < h3 id = "func-curry-args-var-onevarfunc" tabindex = "-1" > < em > < strong > func< / strong > < / em > < code > curry(*args: Var) -> OneVarFunc< / code > < a class = "header-anchor" href = "#func-curry-args-var-onevarfunc" aria-label = "Permalink to "***func*** `curry(*args: Var) -> OneVarFunc`"" > < / a > < / h3 > < p > < strong > 说明< / strong > : 对多参数函数进行柯里化。< / p > < div class = "tip custom-block github-alert" > < p class = "custom-block-title" > TIP< / p > < p > 有关函数柯里化，可参考< a href = "https://zhuanlan.zhihu.com/p/355859667" target = "_blank" rel = "noreferrer" > 函数式编程--柯理化（ ） < / a > < / p > < / div > < p > < strong > 参数< / strong > :< / p > < blockquote > < ul > < li > func: 函数< / li > < li > *args: 参数< / li > < / ul > < / blockquote > < p > < strong > 返回< / strong > : 柯里化后的函数< / p > < details > < summary > < b > 源代码< / b > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > curry< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (func: MultiVarsFunc, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args: Var) -> OneVarFunc:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 对多参数函数进行柯里化。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > [!tip]< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > > 有关函数柯里化，可参考[函数式编程--柯理化（ ） < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > func: 函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *args: 参数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 柯里化后的函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#6F42C1;--shiki-dark:#B392F0;" > curried_func< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args2: Var) -> Var:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " @litedoc-hide" " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > func(< / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > args2)< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > curried_func< / span > < / span > < / code > < / pre > < / div > < / details > < h3 id = "class-curveequation" tabindex = "-1" > < strong > class< / strong > < code > CurveEquation< / code > < a class = "header-anchor" href = "#class-curveequation" aria-label = "Permalink to "**class** `CurveEquation`"" > < / a > < / h3 > < h3 id = "method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" tabindex = "-1" > < em > < strong > method< / strong > < / em > < code > __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)< / code > < a class = "header-anchor" href = "#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" aria-label = "Permalink to "***method*** `__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)`"" > < / a > < / h3 > < p > < strong > 说明< / strong > : 曲线方程。< / p > < p > < strong > 参数< / strong > :< / p > < blockquote > < ul > < li > x_func: x函数< / li > < li > y_func: y函数< / li > < li > z_func: z函数< / li > < / ul > < / blockquote > < details > < summary > < b > 源代码< / b > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > __init__< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):< / span > < / span >
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< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 曲线方程。< / span > < / span >
2024-08-28 20:35:22 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > x_func: x函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > y_func: y函数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > z_func: z函数< / span > < / span >
2024-08-28 12:03:02 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > x_func< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > y_func< / span > < / span >
2024-08-29 18:52:57 +08:00
< span class = "line" > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > =< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > z_func< / span > < / span > < / code > < / pre > < / div > < / details > < h3 id = "method-call-self-t-var-point3-tuple-point3" tabindex = "-1" > < em > < strong > method< / strong > < / em > < code > __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]< / code > < a class = "header-anchor" href = "#method-call-self-t-var-point3-tuple-point3" aria-label = "Permalink to "***method*** `__call__(self, *t: Var) -> Point3 | tuple[Point3, ...]`"" > < / a > < / h3 > < p > < strong > 说明< / strong > : 计算曲线上的点。< / p > < p > < strong > 参数< / strong > :< / p > < blockquote > < ul > < li > *t:< / li > < li > 参数:< / li > < / ul > < / blockquote > < details > < summary > < b > 源代码< / b > < / summary > < div class = "language-python vp-adaptive-theme" > < button title = "Copy Code" class = "copy" > < / button > < span class = "lang" > python< / span > < pre class = "shiki shiki-themes github-light github-dark vp-code" tabindex = "0" > < code > < span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > def< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > __call__< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (self, < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > *< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > t: Var) -> Point3 < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > |< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > tuple[Point3, < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > ...< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]:< / span > < / span >
2024-08-28 20:35:22 +08:00
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 计算曲线上的点。< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Args:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > *t:< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > 参数< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > Returns:< / span > < / span >
< span class = "line" > < / span >
< span class = "line" > < span style = "--shiki-light:#032F62;--shiki-dark:#9ECBFF;" > " " " < / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > if< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > len< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (t) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > ==< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 1< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > Point3(< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func(t[< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > 0< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ]))< / span > < / span >
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > else< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > :< / span > < / span >
2024-08-29 13:25:00 +08:00
< span class = "line" > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > return< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > tuple< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > ([Point3(x, y, z) < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > for< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > x, y, z < / span > < span style = "--shiki-light:#D73A49;--shiki-dark:#F97583;" > in< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > zip< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > (< / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .x_func(t), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .y_func(t), < / span > < span style = "--shiki-light:#005CC5;--shiki-dark:#79B8FF;" > self< / span > < span style = "--shiki-light:#24292E;--shiki-dark:#E1E4E8;" > .z_func(t))])< / span > < / span > < / code > < / pre > < / div > < / details > < / div > < / div > < / main > < footer class = "VPDocFooter" data-v-aa782c77 data-v-f33b051d > <!-- [ --> <!-- ] --> <!-- --> < nav class = "prev-next" aria-labelledby = "doc-footer-aria-label" data-v-f33b051d > < span class = "visually-hidden" id = "doc-footer-aria-label" data-v-f33b051d > Pager< / span > < div class = "pager" data-v-f33b051d > < a class = "VPLink link pager-link prev" href = "/api/mp_math/const.html" data-v-f33b051d > <!-- [ --> < span class = "desc" data-v-f33b051d > Previous page< / span > < span class = "title" data-v-f33b051d > mbcp.mp_math.const< / span > <!-- ] --> < / a > < / div > < div class = "pager" data-v-f33b051d > < a class = "VPLink link pager-link next" href = "/api/mp_math/line.html" data-v-f33b051d > <!-- [ --> < span class = "desc" data-v-f33b051d > Next page< / span > < span class = "title" data-v-f33b051d > mbcp.mp_math.line< / span > <!-- ] --> < / a > < / div > < / nav > < / footer > <!-- [ --> <!-- ] --> < / div > < / div > < / div > <!-- [ --> <!-- ] --> < / div > < / div > <!-- --> <!-- [ --> <!-- ] --> < / div > < / div >
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< script > w i n d o w . _ _ V P _ H A S H _ M A P _ _ = J S O N . p a r s e ( " { \ " a p i - e x . m d \ " : \ " D O s K a L 8 H \ " , \ " a p i _ i n d e x . m d \ " : \ " B v a z T q T B \ " , \ " a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " e A y 7 w 1 H N \ " , \ " a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D 9 z s 7 _ _ H \ " , \ " a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " D 6 Q h N v H e \ " , \ " a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " 4 P 0 h k 6 g b \ " , \ " a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D s J Q D c h M \ " , \ " a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " C O r E _ f d 3 \ " , \ " a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " C m o V v P i w \ " , \ " a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " C l J D 8 5 m P \ " , \ " a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " 7 j B t S 4 F 1 \ " , \ " a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B M w t m 7 T J \ " , \ " a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " C R O C I D X X \ " , \ " a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " B R C S x C 3 e \ " , \ " a p i _ p r e s e t s _ i n d e x . m d \ " : \ " D l 6 S s 9 1 J \ " , \ " a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " D U Z x 1 3 A W \ " , \ " e n _ a p i _ i n d e x . m d \ " : \ " B g u - L D 1 B \ " , \ " e n _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B u h p K H n t \ " , \ " e n _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " D _ F l p j 8 t \ " , \ " e n _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " C d q Z I J E O \ " , \ " e n _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D r j D U Y B Y \ " , \ " e n _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " B E v x d W Y Q \ " , \ " e n _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " C y X X F d S 4 \ " , \ " e n _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " D U u 9 P 3 n M \ " , \ " e n _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " D M i g 0 F I 1 \ " , \ " e n _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " C c a o k A F 8 \ " , \ " e n _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " D Z o h q w 2 b \ " , \ " e n _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " S d _ I Z s g E \ " , \ " e n _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " C m C 1 Q X 5 o \ " , \ " e n _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " C Z 5 h l _ 7 D \ " , \ " e n _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " C s 8 v O N 2 C \ " , \ " g u i d e _ i n d e x . m d \ " : \ " B E 2 y l o i k \ " , \ " i n d e x . m d \ " : \ " B E 1 q C h T t \ " , \ " j a _ a p i _ i n d e x . m d \ " : \ " 4 B n f l F I m \ " , \ " j a _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " D L 9 J 6 R E 2 \ " , \ " j a _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " C y a I J k F x \ " , \ " j a _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " B 2 l D - V S I \ " , \ " j a _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " C S A M H Y s B \ " , \ " j a _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " f j - _ s 5 U g \ " , \ " j a _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " B l 5 k y h p I \ " , \ " j a _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " y L e k g C v K \ " , \ " j a _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " C p H H r S k 8 \ " , \ " j a _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " C B 1 _ z - r n \ " , \ " j a _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " B r f E E f l - \ " , \ " j a _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " p 5 4 T K A C E \ " , \ " j a _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " E 2 Y n H 7 E N \ " , \ " j a _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " A T G c H t 9 d \ " , \ " j a _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " D 8 y Z m O 5 R \ " , \ " m d - e x . m d \ " : \ " B X 0 W q O q v \ " , \ " z h t _ a p i _ i n d e x . m d \ " : \ " D q 4 X P U K Z \ " , \ " z h t _ a p i _ m p _ m a t h _ a n g l e . m d \ " : \ " B 4 T 6 L 2 5 M \ " , \ " z h t _ a p i _ m p _ m a t h _ c o n s t . m d \ " : \ " B 8 u Q O I r _ \ " , \ " z h t _ a p i _ m p _ m a t h _ e q u a t i o n . m d \ " : \ " H 6 Y 4 8 0 q 1 \ " , \ " z h t _ a p i _ m p _ m a t h _ i n d e x . m d \ " : \ " D 0 9 y 2 u b g \ " , \ " z h t _ a p i _ m p _ m a t h _ l i n e . m d \ " : \ " D Y C 1 X 0 o D \ " , \ " z h t _ a p i _ m p _ m a t h _ m p _ m a t h _ t y p i n g . m d \ " : \ " D L x 0 I i b M \ " , \ " z h t _ a p i _ m p _ m a t h _ p l a n e . m d \ " : \ " B 6 G W R R F 6 \ " , \ " z h t _ a p i _ m p _ m a t h _ p o i n t . m d \ " : \ " B m 1 I E w l I \ " , \ " z h t _ a p i _ m p _ m a t h _ s e g m e n t . m d \ " : \ " B o p 8 t 2 I E \ " , \ " z h t _ a p i _ m p _ m a t h _ u t i l s . m d \ " : \ " C E R v 8 c - M \ " , \ " z h t _ a p i _ m p _ m a t h _ v e c t o r . m d \ " : \ " B T W x l p B 1 \ " , \ " z h t _ a p i _ p a r t i c l e _ i n d e x . m d \ " : \ " k A m 9 V A E w \ " , \ " z h t _ a p i _ p r e s e t s _ i n d e x . m d \ " : \ " B m o u a E a T \ " , \ " z h t _ a p i _ p r e s e t s _ m o d e l _ i n d e x . m d \ " : \ " S Q 5 P P d a L \ " } " ) ; w i n d o w . _ _ V P _ S I T E _ D A T A _ _ = J S O N . p a r s e ( " { \ " l a n g \ " : \ " e n - U S \ " , \ " d i r \ " : \ " l t r \ " , \ " t i t l e \ " : \ " M B C P d o c s \ " , \ " d e s c r i p t i o n \ " : \ " M B C P l i b r a r y d o c s \ " , \ " b a s e \ " : \ " / \ " , \ " h e a d \ " : [ ] , \ " r o u t e r \ " : { \ " p r e f e t c h L i n k s \ " : t r u e } , \ " a p p e a r a n c e \ " : t r u e , \ " t h e m e C o n f i g \ " : { \ " s o c i a l L i n k s \ " : [ { \ " i c o n \ " : \ " g i t h u b \ " , \ " l i n k \ " : \ " h t t p s : / / g i t h u b . c o m / s n o w y k a m i / m b c p \ " } ] , \ " s i d e b a r \ " : { \ " / a p i / \ " : [ { \ " t e x t \ " : \ " a p i \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p \ " , \ " l i n k \ " : \ " / a p i / i n d e x . m d \ " } , { \ " t e x t \ " : \ " m p _ m a t h \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p . m p _ m a t h \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / i n d e x . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . a n g l e \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / a n g l e . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . c o n s t \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / c o n s t . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . e q u a t i o n \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / e q u a t i o n . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . l i n e \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / l i n e . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . m p _ m a t h _ t y p i n g \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / m p _ m a t h _ t y p i n g . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . p l a n e \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / p l a n e . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . p o i n t \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / p o i n t . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . s e g m e n t \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / s e g m e n t . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . u t i l s \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / u t i l s . m d \ " } , { \ " t e x t \ " : \ " m b c p . m p _ m a t h . v e c t o r \ " , \ " l i n k \ " : \ " / a p i / m p _ m a t h / v e c t o r . m d \ " } ] } , { \ " t e x t \ " : \ " p a r t i c l e \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p . p a r t i c l e \ " , \ " l i n k \ " : \ " / a p i / p a r t i c l e / i n d e x . m d \ " } ] } , { \ " t e x t \ " : \ " p r e s e t s \ " , \ " i t e m s \ " : [ { \ " t e x t \ " : \ " m b c p . p r e s e t s \ " , \ " l i n k \ " : \ " / a p i / p r e s e t s / i n d e x . m d \ " } , { \ " t e x t \ " : \ " m o d e l
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