应该是 TeXLive/MacTeX 版本太低或与 ctex 不匹配。
应该是 TeXLive/MacTeX 版本太低或与 ctex 不匹配。
一个随机的点可以由三个步骤生成：
然后画出点 (x, y+r) 即可。不同的随机分布可以生成不同的图形。
比如类似图 A 的
\documentclass[tikz,border=5pt]{standalone}
\ExplSyntaxOn
\cs_new_protected:Npn \fpstepfromto#1#2#3
{% from, to, nums
\fp_step_inline:nnnn {#1} { (#2-(#1))/(#3-1)*0.99 } {#2}
}
\pgfmathdeclarefunction{nrand}{0}
{% \tex_normaldeviate:D 生成均值为 0，标准差为 65536 的随机整数
\tl_set:Nx \pgfmathresult { \fp_eval:n { \tex_normaldeviate:D/65536 } }
}
\ExplSyntaxOff
\begin{document}
\begin{tikzpicture}
\draw[-stealth](0,0)--(3.5,0)node[below]{$x$};
\draw[-stealth](0,0)--(0,3.5)node[right]{$y$};
\pgfmathdeclarefunction{xx}{1}{\pgfmathparse{#1+nrand*#1/50}}
\pgfmathdeclarefunction{yy}{1}{\pgfmathparse{#1*4/5}} % y=4/5 x
\pgfmathdeclarefunction{res}{1}{\pgfmathparse{nrand/10}}
\fpstepfromto{0.5}{3}{10}{
\pgfmathparse{xx(#1)}\let\xx\pgfmathresult
\fill[black] (\xx,{yy(\xx)+res(\xx)}) circle(1pt);
}
\end{tikzpicture}
\end{document}\mateatletter 和 \makeatother，以及 LaTeX3 中空格会被忽略，但是 TikZ 中某些键需要用到空格。代码的问题就是这个造成的。.meta:nn 定义新的键，自行在我发的文件中查看实现方式。用 \node 的 rotate 键。
\documentclass{beamer}
\usepackage{tikz}
\usebackgroundtemplate{\begin{tikzpicture}
\draw[use as bounding box] (0,0) rectangle (\paperwidth,\paperheight);
\node[inner sep=0pt,outer sep=0pt,rotate=3*\value{page}] at(.25\paperwidth,.75\paperheight)
{\pgfimage[width=0.5\paperwidth]{example-image}};
\end{tikzpicture}}
\logo{\includegraphics[width=2cm, angle=\arabic{page}, origin=c]{example-image}}
\begin{document}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\frame{\arabic{page}}
\end{document}%%% autoclass.cls
\ProvidesClass{autoclass}
\DeclareKeys{% = \DeclareKeys[autoclass]
lang .choice: ,
lang/en .code:n = \def\autoclass@class{book} ,
lang/cn .code:n = \def\autoclass@class{ctexbook} ,
lang .initial:n = en ,
unknown .code:n = \autoclass@unknown ,
}
\ExplSyntaxOn
\clist_new:N \autoclass@unknownoptions
\cs_new_protected:Npn \autoclass@unknown
{
\bool_if:NTF \l__keys_no_value_bool
{ % eg. 12pt, twoside
\clist_put_right:Nx \autoclass@unknownoptions
{ \l_keys_key_str }
}
{ % eg. zihao=4, fontset=windows
\clist_put_right:Nx \autoclass@unknownoptions
{ \l_keys_key_str = { \exp_not:o \l_keys_value_tl } }
}
}
\ExplSyntaxOff
\ProcessKeyOptions % = \ProcessKeyOptions[autoclass]
\PassOptionsToClass\autoclass@unknownoptions\autoclass@class
%% 如果不需要过滤上面定义的 lang 等键，可以直接使用
%% \PassOptionsToClass\@raw@classoptionslist\autoclass@class
\LoadClass{\autoclass@class}%%% main.tex
\documentclass[lang=cn,fontset=fandol,12pt]{autoclass}
\begin{document}
Hello.
\ifdefined\CTeX \CTeX 中文 \fi
\end{document}在导言区加上这个：
\ExplSyntaxOn\makeatletter
\providecommand\Hy@footnote@currentHref{}
\prop_new:N\g__codedoc_fnmark_prop
\cs_new_protected:Npn \__codedoc_fn_store:
{
\prop_gput:Nxx\g__codedoc_fnmark_prop
{fn\int_use:N\c@footnote}{{\Hy@footnote@currentHref}{\int_use:N\c@footnote}}
}
\cs_new_protected:Npn \__codedoc_fn_restore:n #1
{
\prop_get:NnN \g__codedoc_fnmark_prop {fn#1}\l__codedoc_tmpa_tl
\tl_gset:Nx\Hy@footnote@currentHref
{\exp_last_unbraced:NV\use_i:nn \l__codedoc_tmpa_tl }
\setcounter{footnote}{\exp_last_unbraced:NV\use_ii:nn \l__codedoc_tmpa_tl}
}
\cs_generate_variant:Nn \hook_gput_next_code:nn {ne}
\cs_new_protected:Npn \__codedoc_fn_footnote:nn #1 #2
{
\footnotemark
\__codedoc_fn_store:
\hook_gput_next_code:ne {env/#1/after}
{\exp_not:N\__codedoc_fn_restore:n{\int_use:N\c@footnote}{\exp_not:n{\footnotetext{#2}}}}}
\AddToHook{env/function/begin}{\def\footnote{\__codedoc_fn_footnote:nn{function}}}
\AddToHook{env/variable/begin}{\def\footnote{\__codedoc_fn_footnote:nn{variable}}}
\makeatother\ExplSyntaxOff\documentclass{article}
\usepackage[a4paper]{geometry}
\begin{document}
\makeatletter
\ExplSyntaxOn
\cs_new:Npn \ifaivpaper@TF
{
\bool_lazy_and:nnTF
{ \dim_compare_p:nNn { 297mm } = { \paperheight } } % 不能是 29.7cm
{ \dim_compare_p:nNn { 210mm } = { \paperwidth } }
}
\ExplSyntaxOff
\ifaivpaper@TF{a4paper}{not a4paper}
\makeatother
\end{document}假定使用了 geometry 和 fancyhdr 这两个宏包。
问题 1：脚注属于 total body（见 geometry.pdf 图 1、2）的一部分，footmisc 使用 bottom 的情况下，可使用 \usepackage[footskip=..]{geometry}（或 \geometry{footskip=..}）修改脚注和页脚的间距。
2：页脚横线和页脚文字的间距可用 \pagestyle{fancy}...\renewcommand\footruleskip{..} 修改。
如果以上解决办法无效，需提供完整代码。
另外，每个提问都要提供完整可编译的代码。
\documentclass{article}
\ExpandArgs{c}\NewDocumentCommand{cmd_1_a}{m O{}}{123 #1 #2}
\def\?#1 {\csname#1\endcsname}
\begin{document}
\?cmd_1_a {4}[6]
\end{document}命令名完成后加上一个空格。还有不加空格的方法（使用 \peek_analysis_map_inline:n，不可展）。
\begingroup
\ctexset{section/afterskip=5cm}
\tableofcontents
\endgroup应该用 \computegrad 的结果提取对应分量，你这个的模长不一样。
\documentclass[svgnames]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\makeatletter
\newcommand\computegrad[4][0.00025]{% [delta], function, x, y
\begingroup\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\def\@tempdelta{#1}%
\pgfmathparse{#2(#3,#4)}\let\@tempz\pgfmathresult
\pgfmathparse{#2(#3+\@tempdelta,#4)}\let\@temppxa\pgfmathresult
\pgfmathparse{#2(#3-\@tempdelta,#4)}\let\@temppxb\pgfmathresult
\edef\@temppx{\fpeval{(\@temppxa-\@temppxb)/(2*\@tempdelta)}}%
\pgfmathparse{#2(#3,#4+\@tempdelta)}\let\@temppya\pgfmathresult
\pgfmathparse{#2(#3,#4-\@tempdelta)}\let\@temppyb\pgfmathresult
\edef\@temppy{\fpeval{(\@temppya-\@temppyb)/(2*\@tempdelta)}}%
\edef\@tempu{\fpeval{(\@temppx,\@temppy,-1)/sqrt(\@temppx^2+\@temppy^2+1)}}%
\edef\?{\endgroup\def\noexpand\pgfmathresult{\@tempu}%
\def\noexpand\pgfmathresulta{\fpeval{1*(#3,#4,\@tempz)-\@tempu}}}%
\?}
\def\gradcomponent#1#2#3{%
\edef\pgfmathresult{\fpeval{#2+\expanded{\noexpand\gradcomponent@#1}{#3}}}}
\def\gradcomponent@(#1,#2,#3)#4{\ifcase
\if#4x 1 \else\if#4y 2 \else\if#4z 3 \else 4 \fi\fi\fi
\or (0,#2,#3)\or (#1,0,#3)\or (#1,#2,0)\else(#1,#2,#3)\fi}
%%%%%%%%%%%%%%%%%green
\newcommand\computegraf[4][0.00025]{\computegrad[#1]{#2}{#3}{#4}}
%%%%%%%%%%%%%%%%%yellow
\newcommand\computegrag[4][0.00025]{\computegrad[#1]{#2}{#3}{#4}%
\let\pgfmathresultb\pgfmathresult
\gradcomponent\pgfmathresult\pgfmathresulta{y}%
\let\pgfmathresulta\pgfmathresult \let\pgfmathresult\pgfmathresultb}
%%%%%%%%%%%%%%%%%red
\newcommand\computegrah[4][0.00025]{\computegrad[#1]{#2}{#3}{#4}%
\let\pgfmathresultb\pgfmathresult
\gradcomponent\pgfmathresult\pgfmathresulta{x}%
\let\pgfmathresulta\pgfmathresult \let\pgfmathresult\pgfmathresultb}
%%%%%%%%%%%%%%%%%blue
\newcommand\computegral[4][0.00025]{\computegrad[#1]{#2}{#3}{#4}%
\let\pgfmathresultb\pgfmathresult
\gradcomponent\pgfmathresult\pgfmathresulta{z}%
\let\pgfmathresulta\pgfmathresult \let\pgfmathresult\pgfmathresultb}
\makeatother
\begin{tikzpicture}
[declare function={f(\x,\y)=0.6*sin(deg(\x))*cos(deg(\y);}]
\begin{axis}[scale=2,axis equal,view={0}{0},axis lines=center,axis on top,zmax=4.5,zmin=-1,samples=30,xlabel={$X$},ylabel={$Y$},zlabel={$F(x,y)$}]%ticks=none,
\addplot3[surf,color=DarkBlue,opacity=0.5,domain=0:2*pi, y domain=0:3,faceted color=black] {f(x,y)};
%%define P
\addplot3+ [mark=ball,mark size=2pt,scatter src=rand,ball color=yellow!80!black!60]
coordinates {({0.7},{0.25},{f(x,y)})};
\addplot3+ [mark=ball,mark size=2pt,scatter src=rand,ball color=yellow!80!black!60]
coordinates {({2.8},{0.5},{f(x,y)})};
%space vector
\draw[->,green,shorten <=0cm]({0.7},{0.25},{f(0.7,0.25)})\pgfextra{\computegraf{f}{0.7}{0.25}} --\pgfmathresulta;
%y vector
\draw[->,yellow,shorten <=0cm]({0.7},{0.25},{f(0.7,0.25)})\pgfextra{\computegrag{f}{0.7}{0.25}} --\pgfmathresulta;
%x vector
\draw[->,red,shorten <=0cm]({0.7},{0.25},{f(0.7,0.25)})\pgfextra{\computegrah{f}{0.7}{0.25}} --\pgfmathresulta;
%z vector
\draw[->,blue,shorten <=0cm]({0.7},{0.25},{f(0.7,0.25)})\pgfextra{\computegral{f}{0.7}{0.25}} --\pgfmathresulta;
%%%
%space vector
\draw[->,green,shorten <=0cm]({2.8},{0.5},{f(2.8,0.5)})\pgfextra{\computegraf{f}{2.8}{0.5}} --\pgfmathresulta;
%y vector
\draw[->,yellow,shorten <=0cm]({2.8},{0.5},{f(2.8,0.5)})\pgfextra{\computegrag{f}{2.8}{0.5}} --\pgfmathresulta;
%x vector
\draw[->,red,shorten <=0cm]({2.8},{0.5},{f(2.8,0.5)})\pgfextra{\computegrah{f}{2.8}{0.5}} --\pgfmathresulta;
%z vector
\draw[->,blue,shorten <=0cm]({2.8},{0.5},{f(2.8,0.5)})\pgfextra{\computegral{f}{2.8}{0.5}} --\pgfmathresulta;
\end{axis}
\end{tikzpicture}
\end{document}需要自己计算在该点的法向量，但是 pgf 的计算精度不是很高，而且比较准确的数值算法会很慢。
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc}
\usepgfplotslibrary{colormaps,fillbetween}
\makeatletter
\newcommand\computegrad[4][0.00025]{% [delta], function, x, y
\begingroup\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\def\@tempdelta{#1}%
\pgfmathparse{#2(#3,#4)}\let\@tempz\pgfmathresult
\pgfmathparse{#2(#3+\@tempdelta,#4)}\let\@temppxa\pgfmathresult
\pgfmathparse{#2(#3-\@tempdelta,#4)}\let\@temppxb\pgfmathresult
\edef\@temppx{\fpeval{(\@temppxa-\@temppxb)/(2*\@tempdelta)}}%
\pgfmathparse{#2(#3,#4+\@tempdelta)}\let\@temppya\pgfmathresult
\pgfmathparse{#2(#3,#4-\@tempdelta)}\let\@temppyb\pgfmathresult
\edef\@temppy{\fpeval{(\@temppya-\@temppyb)/(2*\@tempdelta)}}%
\edef\@tempu{\fpeval{(\@temppx,\@temppy,-1)/sqrt(\@temppx^2+\@temppy^2+1)}}%
\edef\?{\endgroup\def\noexpand\pgfmathresult{\@tempu}%
\def\noexpand\pgfmathresulta{\fpeval{(#3,#4,\@tempz)+\@tempu}}}%
\?}
\makeatother
\begin{document}
\begin{tikzpicture}[declare function={f(\x,\y)=0.8*sin(deg(\x))+1.2*ln(\y);}]
\begin{axis}[axis equal image,view={-45}{15},
domain=-2:5,y domain=0:5,samples=20,axis lines=center,axis on top,
xmax=6,ymax=8,zmax=4,xmin=-2,ymin=-1,zmin=-2.5,
xlabel=\tiny $X$,ylabel=\tiny $Y$,zlabel=\tiny $Z$]
\addplot3[colormap/bone,surf,z buffer=sort,] (x,y,{f(x,y)});
%%define P
\addplot3+ [mark=ball,mark size=2pt,scatter src=rand,ball color=yellow!80!black!60]
coordinates {({0.25*pi},{3},{f(x,y)})};
\draw[->,shorten <=-1cm] ({0.25*pi},{3},{f(0.25*pi,3)})
\pgfextra{\computegrad{f}{0.25*pi}{3}} -- \pgfmathresulta;
\draw[red,->,shorten <=-1cm] (0.785398, 3., 1.88402)--(1.35108, 3.4, 0.88402);
\end{axis}
\end{tikzpicture}
\end{document}看看你的电脑上是否有这个文件夹：
c:\texlive\2024\texmf-dist\xindy\modules可以保存切点和向量终点的坐标，然后利用 perpendicular 坐标系统即可画出。
\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{decorations.markings}
\makeatletter
\def\my@tangentparse#1{\in@{ at}{#1}%
\ifin@\my@tangentparse@#1\@nil\else\my@tangentparse@ last at#1\@nil\fi}
\def\my@tangentparse@#1 at#2\@nil{\pgfkeysalso{postaction=decorate,
decoration = { % 对path进行装饰（decorate）
markings, % 启用marking
mark = at position #2 % 在指定位置#1添加marking
with{ % marking的具体内容
% 定义(0, 0)为tangent point xxx，即切点
\coordinate (tangent point #1) at (0, 0);
% 定义(1, 0)为tangent unit vector xxx，即单位切向量
\coordinate (tangent unit vector #1) at (1, 0);
% 定义(0, 1)为tangent orthogonal unit vector xxx，即单位法向量
\coordinate (tangent orthogonal unit vector #1) at (0, 1);
}
},
}}
\tikzset{
tangent/.code = \my@tangentparse{#1},
use tangent/.style = { % 定义use tangent样式，参数#1是切点的序号
shift = (tangent point #1), % 以tangent point-xxx为原点
x = (tangent unit vector #1), % 以tangent unit vector-xxx为x轴单位向量
y = (tangent orthogonal unit vector #1)% 以tangent orthogonal unit vector-xxx为y轴单位向量
},
use tangent/.default = last,
}
\makeatother
\begin{document}
\begin{tikzpicture}
\draw[->] (-1,0) -- (3,0) node[anchor=south east]{$x$};
\draw[->] (0,-1) -- (0,2) node[anchor=south west]{$y$};
\draw[tangent=A at 0.65,tangent=B at 0.8] (0, 0) .. controls (1, 0) and (1, 1) .. (2, 0.5);
\fill[use tangent=A] circle(1pt) node[below=1] {$p$};
\draw[black!20,use tangent=A] (-1.5, 0) -- (1.5, 0);%切线
\draw[->, use tangent=A] (0, 0) -- (0, 1) coordinate(L) node[scale=0.4,above=2] {$vector$}; %法线
\draw[dotted,black!10, shorten <=-1cm] (L) -- (0,0 |- L); %辅助线
\draw[dotted,black!10] (L) -- (0,0 -| L); %辅助线
\draw[red,->] (tangent point A) -- (L |- tangent point A);
\draw[red,->] (tangent point A) -- (L -| tangent point A);
\draw[->, use tangent=B] (0, 0) -- (0, 1) coordinate(L);
\draw[red,->] (tangent point B) -- (L |- tangent point B);
\draw[red,->] (tangent point B) -- (L -| tangent point B);
\end{tikzpicture}
\end{document}在导言区加上 \usefonttheme{professionalfonts}。可以放在 \usepackage{mtpro2} 前一行。
问 ctex和ctexart都出现以下问题？不知道什么原因？