选自Riemann sum plot

\documentclass[10pt,x11names, pdf]{standalone}
\usepackage{pstricks-add}
%\usepackage{pst-func, pst-plot}
\begin{document}
\psset{algebraic=true,dimen=middle,dotstyle=o,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25,unit=3,plotpoints = 2000}
\begin{pspicture*}(-2,-2)(2,2)\psset{linecolor =SteelBlue4, linewidth = 1.2pt}\pscustom[fillstyle = solid, fillcolor =lightgray!25!LightSteelBlue2!10!]{\parametricplot{-0.99}{0}{3*t/(1 + t^3) | 3*t^2/(1 + t^3)}\parametricplot{-600}{-1.01}{3*t/(1 + t^3) | 3*t^2/(1 + t^3)}}
\pscustom[fillstyle = solid, fillcolor =LightSteelBlue2!25! ]{\parametricplot{0}{5}{3*t/(1 + t^3) | 3*t^2/(1 + t^3)}\parametricplot{5}{200}{3*t/(1 + t^3) | 3*t^2/(1 + t^3)}\closepath}%\psline[linewidth = 0.4pt, linecolor = black](-2.5; 45)(2.5 ; 45)\psline[linewidth = 0.4pt, linecolor = black](-2,1)(2,-3)
\psaxes[linecolor=gray,xAxis=true,yAxis=true,labels=none,ticks=none]{->}(0,0)(-2,-2)(2,2)
\rput(-0.1,-0.1){$O$}\rput(1.95,-0.1){$x$}\rput(-0.1,1.95){$y$}
\rput(-0.5,-0.08){$a$}\rput(-0.08,-0.5){$a$}
\end{pspicture*}
\end{document}

选自 Riemann Sum for Double Integral

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations,calc,intersections}%Mark Wibrow's code for stippling
% https://tex.stackexchange.com/a/267037/3954
\pgfkeys{/pgf/decoration/.cd,stipple density/.store in=\pgfstippledensity,stipple density=.1,stipple scaling function/.store in=\pgfstipplescalingfunction,stipple scaling function=sin(\pgfstipplex*180)*0.875+0.125,stipple radius/.store in=\pgfstippleradius,stipple radius=0.25pt
}
\pgfdeclaredecoration{stipple}{draw}{
\state{draw}[width=\pgfdecorationsegmentlength]{\pgfmathparse{\pgfdecoratedcompleteddistance/\pgfdecoratedpathlength}%\let\pgfstipplex=\pgfmathresult%\pgfmathparse{int(\pgfstippledensity*100)}%\let\pgfstipplen=\pgfmathresult\pgfmathloop\ifnum\pgfmathcounter<\pgfmathresult\relax\pgfpathcircle{%\pgfpoint{(rnd)*\pgfdecorationsegmentlength}%{(\pgfstipplescalingfunction)*(rnd^4)*\pgfdecorationsegmentamplitude+\pgfstippleradius}}% {\pgfstippleradius}%\repeatpgfmathloop
}
}\tikzset{stipple/.style={decoration={stipple, segment length=2pt, #1},decorate,fill
}}
% end of stippling code\newcommand\DrawBlock[3]{
\ifx#1b\relax\path[draw](lm\the\numexpr#2-1\relax) -- ++(0,0,#3) coordinate (blocklf)(bm\the\numexpr#2-1\relax) -- ++(0,0,#3) coordinate (blocklb)(lm#2) -- ++(0,0,#3) coordinate (blockrf)(bm#2) -- ++(0,0,#3) coordinate (blockrb);\filldraw[fill=white,draw=black](lm\the\numexpr#2-1\relax) -- (blocklf) -- (blocklb) -- (blockrb) -- (blockrf) -- (lm#2);
\else  \ifx#1f\relax\path[draw](fm\the\numexpr#2-1\relax) -- ++(0,0,#3) coordinate (blocklf)(lm\the\numexpr#2-1\relax) -- ++(0,0,#3) coordinate (blocklb)(fm#2) -- ++(0,0,#3) coordinate (blockrf)(lm#2) -- ++(0,0,#3) coordinate (blockrb);\filldraw[fill=white,draw=black](fm\the\numexpr#2-1\relax) -- (blocklf) -- (blocklb) -- (blockrb) -- (blockrf) -- (fm#2);\fi
\fi
\draw (blocklf) -- (blockrf);
}\begin{document}
\begin{tikzpicture}[y={(0:1cm)},x={(225:0.86cm)}, z={(90:1cm)}]% coordinates for the lower grid
\path(1,3,0) coordinate (bm0) -- (4,3,0) coordinate (fm0) coordinate[midway] (lm0) --(4,8,0) coordinate[pos=0.25] (fm1) coordinate[midway] (fm2) coordinate[pos=0.75] (fm3) coordinate (fm4) --(1,8,0) coordinate (bm4) coordinate[midway] (lm4)--(bm0) coordinate[pos=0.25] (bm3) coordinate[midway] (bm2) coordinate[pos=0.75] (bm1);
\draw[dashed](lm0) -- (lm4) coordinate[pos=0.25] (lm1) coordinate[midway] (lm2) coordinate[pos=0.75] (lm3);% the blocks
\DrawBlock{b}{1}{4}
\DrawBlock{b}{2}{3.7}
\DrawBlock{b}{3}{4.3}
\DrawBlock{b}{4}{5}
\DrawBlock{f}{1}{3.3}
\DrawBlock{f}{2}{3.5}
\DrawBlock{f}{3}{4}
\DrawBlock{f}{4}{4.7}\foreach \Point/\Height in {lm1/3.7,lm2/4.3,lm3/5}\draw[ultra thin,dashed,opacity=0.2] (\Point) -- ++(0,0,\Height);% the lower grid
\foreach \x in {1,2,3}\draw[dashed] (fm\x) -- (bm\x);
\draw[dashed] (fm0) -- (bm0) -- (bm4);
\draw (fm0) -- (fm4) -- (bm4);
\draw[dashed] (lm0) -- (lm4);% coordinates for the surface
\coordinate (curvefm0) at ( $ (fm0) + (0,0,4) $ );
\coordinate (curvebm0) at ( $ (bm0) + (0,0,4) $ );
\coordinate (curvebm4) at ( $ (bm4) + (0,0,6) $ );
\coordinate (curvefm4) at ( $ (fm4) + (0,0,5.7) $ );% the surface
\filldraw[ultra thick,fill=gray!25,fill opacity=0.2](curvefm0) to[out=-30,in=210] (curvefm4) to[out=-4,in=260](curvebm4) to[out=215,in=330](curvebm0) to[out=240,in=-20](curvefm0);% lines from grid to surface
\draw[very thick,name path=leftline] (curvefm0) -- (fm0);
\draw[very thick] (curvefm4) -- (fm4);
\draw[very thick,name path=rightline] (curvebm4) -- (bm4);
\draw[very thick,dashed] (curvebm0) -- (bm0);% coordinate system
\coordinate (O) at (0,0,0);
\draw[-latex] (O) -- +(5,0,0) node[above left] {$x$};
\path[name path=yaxis] (O) -- +(0,10,0) coordinate (yaxisfinal) node[above] {$y$};
\draw[-latex] (O) -- +(0,0,5) node[left] {$z$};
\path[name intersections={of=yaxis and leftline,by={yaxis1}}];
\path[name intersections={of=yaxis and rightline,by={yaxis2}}];
\draw (O) -- (yaxis1);
\draw[densely dashed,opacity=0.1] (yaxis1) -- (yaxis2);
\draw[-latex] (yaxis2) -- (yaxisfinal);% the stippling
\path[postaction={stipple={amplitude=1cm,stipple density=0.15}}]( $ (fm4) + (0,0,4.7) $ ) -- (fm4);
\path[postaction={stipple={amplitude=1cm,stipple density=0.05}}]( $ (lm4) + (0,0,4.7) $ ) -- (lm4);% for debugging
%\foreach \Name in {bm0,fm0,lm0,fm1,fm2,fm3,fm4,bm4,lm4,bm1,bm2,bm3,lm1,lm2,lm3,%
%curvefm0,curvebm0,curvebm4,curvefm4}
%  \node at (\Name) {\Name};
\end{tikzpicture}\end{document}