如何为圆和直线创建三角曲线和虚线？

Question 1

以下是我想到的办法。有更好的办法，但看起来不错：

最困难的部分是填充青色管段。

为了回答你的问题，我粘贴了我上面的评论

问题是关于正弦波频率。任何正弦函数都可以定义为：A sin（2 pi ft + phi）。A 是振幅，pi 是 3.14。f 是频率，t 是时间（在绘图的情况下为 x），phi 是原点的相位。您可以通过修改 f 和 phi 来修改正弦（余弦）波：
\draw[-,thick,domain=0:5,samples=100] 
plot (\x, {sin(25*2*3.14*\x)-(cos(25*2*3.14*\x))^2-\x});
我还添加/替换了 x 以使正弦波上升/下降。

\documentclass[12pt]{article}
\usepackage{tikz}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}

\begin{document}
    \begin{tikzpicture}[scale=1,>=latex,x=1.5cm,y=0.8cm]
    \fill[fill=white,opacity=0.5] (1,0) -- plot[domain=1:4] (\x,{sqrt(2*(\x)+1))}) -- (4,0);
    \fill[fill=white,opacity=0.5] (1,0) -- plot[domain=1:4] (\x,{-sqrt(2*(\x)+1))}) -- (4,0);
    
    \draw[name path = A ,-,thick,domain=0:4.501,samples=100] plot (\x,{sin(25*1*3.14*\x)+(cos(5*1*3.14*\x))^2+\x});
    \draw[name path = B, -,thick,domain=0:4.501,samples=100] plot (\x,{-sin(25*1*3.14*\x)-(cos(5*1*3.14*\x))^2-\x});


%   \draw[dashed] (0.1,-1.1) arc (-90:90:0.17 and 1.1);% half circle facing left
%   \draw(0.1,-1.1) arc (-90:90:-0.17 and 1.1);% 
    
% circle left
    \path[name path = up1] (0,0) -- (0,5);
    \path[name intersections= {of = {up1 and A}, by =p1}];
    \draw let \p1=(p1) in (0,0) circle [y radius=\y1, x radius =\y1/6] ;

%% circle mid
%   \coordinate (y0) at (2,0);
%   \path[name path = up2] (y0) -- (2,11);
%   \path[name intersections= {of = {up2 and A}, by =p2}];
%%  \draw let \p1=(p2) in (y0) circle [y radius=\y1, x radius =\y1/6] ;
%
%   
% circle before 
    \coordinate (y1) at (1.9,0);    
    \path[name path = up3] (y1) -- (1.9,11);
    \path[name path = down3] (y1) -- (1.9,-11);
    \path[name intersections= {of = {up3 and A}, by =p3}];
    \path[name intersections= {of = {down3 and B}, by =p3s}];
    \draw let \p1=(p3) in (y1) circle [y radius=\y1, x radius =\y1/6] ;

    
% circle after 
    \coordinate (y2) at (2.1,0);    
    \path[name path = up4] (y2) -- (2.1,11);
    \path[name path = down4] (y2) -- (2.1,-11);
    \path[name intersections= {of = {up4 and A}, by =p4}];
    \path[name intersections= {of = {down4 and B}, by =p4s}];

% fill mid cone:
\fill[cyan,opacity=0.3] let \p1=(p3) in   (p3) --(p4) --  (p4s) -- (p3s) arc (-90:-270:\y1/6 and \y1) -- cycle  ;
    \draw [fill=white]let \p1=(p4) in (y2) circle [y radius=\y1, x radius =\y1/6] ;
%
    \draw[<->] (y2) -- (p4) node[right, midway]  {\footnotesize $y_{1}$};

% circle  
    \coordinate (y3) at (4.5,0);    
    \path[name path = up5] (y3) -- (4.5, 7);
    \path[name intersections= {of = {up5 and A}, by =p5}];
    \draw let \p1=(p5) in (y3) circle [y radius=\y1, x radius =\y1/6] ;

    
%%%%%%%%%%%%%%% Axis and Delta x
\draw[<->] ($(p3)+(0,0.25)$) -- ($(p4)+(0,0.25)$) node [above]  {\footnotesize $\triangle x_{i}$};
\draw[->,thick] (-1,0) -- (5,0) node[above] {\footnotesize $x$};
    \end{tikzpicture}
\end{document}

Answer

以下是我想到的办法。有更好的办法，但看起来不错：

最困难的部分是填充青色管段。

为了回答你的问题，我粘贴了我上面的评论

问题是关于正弦波频率。任何正弦函数都可以定义为：A sin（2 pi ft + phi）。A 是振幅，pi 是 3.14。f 是频率，t 是时间（在绘图的情况下为 x），phi 是原点的相位。您可以通过修改 f 和 phi 来修改正弦（余弦）波：
\draw[-,thick,domain=0:5,samples=100] 
plot (\x, {sin(25*2*3.14*\x)-(cos(25*2*3.14*\x))^2-\x});
我还添加/替换了 x 以使正弦波上升/下降。

\documentclass[12pt]{article}
\usepackage{tikz}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}

\begin{document}
    \begin{tikzpicture}[scale=1,>=latex,x=1.5cm,y=0.8cm]
    \fill[fill=white,opacity=0.5] (1,0) -- plot[domain=1:4] (\x,{sqrt(2*(\x)+1))}) -- (4,0);
    \fill[fill=white,opacity=0.5] (1,0) -- plot[domain=1:4] (\x,{-sqrt(2*(\x)+1))}) -- (4,0);
    
    \draw[name path = A ,-,thick,domain=0:4.501,samples=100] plot (\x,{sin(25*1*3.14*\x)+(cos(5*1*3.14*\x))^2+\x});
    \draw[name path = B, -,thick,domain=0:4.501,samples=100] plot (\x,{-sin(25*1*3.14*\x)-(cos(5*1*3.14*\x))^2-\x});


%   \draw[dashed] (0.1,-1.1) arc (-90:90:0.17 and 1.1);% half circle facing left
%   \draw(0.1,-1.1) arc (-90:90:-0.17 and 1.1);% 
    
% circle left
    \path[name path = up1] (0,0) -- (0,5);
    \path[name intersections= {of = {up1 and A}, by =p1}];
    \draw let \p1=(p1) in (0,0) circle [y radius=\y1, x radius =\y1/6] ;

%% circle mid
%   \coordinate (y0) at (2,0);
%   \path[name path = up2] (y0) -- (2,11);
%   \path[name intersections= {of = {up2 and A}, by =p2}];
%%  \draw let \p1=(p2) in (y0) circle [y radius=\y1, x radius =\y1/6] ;
%
%   
% circle before 
    \coordinate (y1) at (1.9,0);    
    \path[name path = up3] (y1) -- (1.9,11);
    \path[name path = down3] (y1) -- (1.9,-11);
    \path[name intersections= {of = {up3 and A}, by =p3}];
    \path[name intersections= {of = {down3 and B}, by =p3s}];
    \draw let \p1=(p3) in (y1) circle [y radius=\y1, x radius =\y1/6] ;

    
% circle after 
    \coordinate (y2) at (2.1,0);    
    \path[name path = up4] (y2) -- (2.1,11);
    \path[name path = down4] (y2) -- (2.1,-11);
    \path[name intersections= {of = {up4 and A}, by =p4}];
    \path[name intersections= {of = {down4 and B}, by =p4s}];

% fill mid cone:
\fill[cyan,opacity=0.3] let \p1=(p3) in   (p3) --(p4) --  (p4s) -- (p3s) arc (-90:-270:\y1/6 and \y1) -- cycle  ;
    \draw [fill=white]let \p1=(p4) in (y2) circle [y radius=\y1, x radius =\y1/6] ;
%
    \draw[<->] (y2) -- (p4) node[right, midway]  {\footnotesize $y_{1}$};

% circle  
    \coordinate (y3) at (4.5,0);    
    \path[name path = up5] (y3) -- (4.5, 7);
    \path[name intersections= {of = {up5 and A}, by =p5}];
    \draw let \p1=(p5) in (y3) circle [y radius=\y1, x radius =\y1/6] ;

    
%%%%%%%%%%%%%%% Axis and Delta x
\draw[<->] ($(p3)+(0,0.25)$) -- ($(p4)+(0,0.25)$) node [above]  {\footnotesize $\triangle x_{i}$};
\draw[->,thick] (-1,0) -- (5,0) node[above] {\footnotesize $x$};
    \end{tikzpicture}
\end{document}

Question 2

另一种方法是使用渐近线。你可以使用http://asymptote.ualberta.ca/和/或使用asymptote文档 asymptote.pdf 第 7 章：LaTeX 用法中的包。

代码

    //http://asymptote.ualberta.ca/
    //
    //Basic settings
    settings.prc=false;
    settings.render = 8;

    import solids;
    currentprojection = perspective(3,2,6,up=Y);
    unitsize(4cm);// it will be necessary to enlarge to scale 4 the text

    // the axes
    draw((0,0,0)--(11,0,0), blue,L=Label(scale(4)*"$x$", position=EndPoint),arrow=Arrows3(5mm)); //x-axis
    draw((0,0,0)--(0,5,0), green,L=Label(scale(4)*"$y$", position=EndPoint),arrow=Arrows3(5mm)); //y-axis
    draw((0,0,0)--(0,0,5), red,L=Label(scale(4)*"$z$", position=EndPoint),arrow=Arrows3); //z-axis
    ////////////////////////////////////////////////////
    triple pO=(0,0,0);
    path3 gene=
    (0,1,0)..(4.5,3,0)
    ..(5.5,2.5,0)
    ..(8,4,0)
    ..(10,4.5,0);
    //   We place two points on the generatrix
    triple p1=point(gene, 1);
    triple p2=point(gene, 1.1);
    // We define a projection on the x axis
    transform3 pr=planeproject(Y,O);
    triple pp1=pr*p1;
    triple pp2=pr*p2;


    // We define and draw the surfaces of revolution
    revolution sur=revolution(pO,gene,X,0,360);
    draw(surface(sur),surfacepen=material(yellow+opacity(0.5)));
    //
    path3 ray=(0,0,0)--(0,1,0);
    revolution disque=revolution(pO,ray,X,0,360);
    draw(surface(disque),yellow+opacity(0.5));
    //
    path3 delta=(p1)--(p2);
    revolution surdelta=revolution(pO,delta,X,0,360);
    draw(surface(surdelta),surfacepen=material(blue));

    //We define two points to display the label delta xi
    triple ph1=pp1+(0,3.5,0);
    triple ph2=pp2+(0,3.5,0);
    //
    draw (p1--ph1,bp+dashed);
    draw (p2--ph2,bp+dashed);
    // The text is enlarged to scale 4
    draw (Label(scale(4)*"$\Delta x_i$",position=MidPoint,align=N),ph1--ph2,2bp+blue);
    draw(Label(scale(4)*"$y_i$",position=MidPoint,align=E),p2--pp2,2bp+dashed+red,arrow=Arrows3(5mm));

Answer

另一种方法是使用渐近线。你可以使用http://asymptote.ualberta.ca/和/或使用asymptote文档 asymptote.pdf 第 7 章：LaTeX 用法中的包。

代码

    //http://asymptote.ualberta.ca/
    //
    //Basic settings
    settings.prc=false;
    settings.render = 8;

    import solids;
    currentprojection = perspective(3,2,6,up=Y);
    unitsize(4cm);// it will be necessary to enlarge to scale 4 the text

    // the axes
    draw((0,0,0)--(11,0,0), blue,L=Label(scale(4)*"$x$", position=EndPoint),arrow=Arrows3(5mm)); //x-axis
    draw((0,0,0)--(0,5,0), green,L=Label(scale(4)*"$y$", position=EndPoint),arrow=Arrows3(5mm)); //y-axis
    draw((0,0,0)--(0,0,5), red,L=Label(scale(4)*"$z$", position=EndPoint),arrow=Arrows3); //z-axis
    ////////////////////////////////////////////////////
    triple pO=(0,0,0);
    path3 gene=
    (0,1,0)..(4.5,3,0)
    ..(5.5,2.5,0)
    ..(8,4,0)
    ..(10,4.5,0);
    //   We place two points on the generatrix
    triple p1=point(gene, 1);
    triple p2=point(gene, 1.1);
    // We define a projection on the x axis
    transform3 pr=planeproject(Y,O);
    triple pp1=pr*p1;
    triple pp2=pr*p2;


    // We define and draw the surfaces of revolution
    revolution sur=revolution(pO,gene,X,0,360);
    draw(surface(sur),surfacepen=material(yellow+opacity(0.5)));
    //
    path3 ray=(0,0,0)--(0,1,0);
    revolution disque=revolution(pO,ray,X,0,360);
    draw(surface(disque),yellow+opacity(0.5));
    //
    path3 delta=(p1)--(p2);
    revolution surdelta=revolution(pO,delta,X,0,360);
    draw(surface(surdelta),surfacepen=material(blue));

    //We define two points to display the label delta xi
    triple ph1=pp1+(0,3.5,0);
    triple ph2=pp2+(0,3.5,0);
    //
    draw (p1--ph1,bp+dashed);
    draw (p2--ph2,bp+dashed);
    // The text is enlarged to scale 4
    draw (Label(scale(4)*"$\Delta x_i$",position=MidPoint,align=N),ph1--ph2,2bp+blue);
    draw(Label(scale(4)*"$y_i$",position=MidPoint,align=E),p2--pp2,2bp+dashed+red,arrow=Arrows3(5mm));

Question 3

我不知道你的曲线方程，所以这是一个近似值，但高度可定制。

我正在画圆。这种方法很容易将切点放置在您想要的任何位置。但由于圆在透视图中被视为椭圆，因此我更改了 xscale。

第一部分是放置所有点。对于每个圆，我们需要中心和切点。然后我们需要极坐标，这样我们就知道切线的角度了。

其余的：一对或弧线和曲线，如

(A1) to[out=\aa-90,in=\ab+90] (B1) ...

上述代码绘制了一条曲线，该曲线以一个角度\aa-90（与第一个圆相切）离开点（A1），并以一个\ab+90与第二个圆相切的角度到达点（B1）。

完整示例：

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,xscale=0.5]
% DIMENSIONS AND COORDINATES
% first circle from the left
\def\xa{0}   % position
\def\ra{1}   % radius
\def\aa{95}  % angle
\coordinate (A0) at (\xa,0);             % center
\coordinate (A1) at ($(A0)+( \aa:\ra)$); % tangent point above
\coordinate (A2) at ($(A0)+(-\aa:\ra)$); % tangent point below
% second circle
\def\xb{6}   % position
\def\rb{2}   % radius
\def\ab{80}  % angle
\coordinate (B0) at (\xb,0);             % center
\coordinate (B1) at ($(B0)+( \ab:\rb)$); % tangent point above
\coordinate (B2) at ($(B0)+(-\ab:\rb)$); % tangent point below
% third circle
\def\xc{6.5} % position
\def\rc{1.9} % radius
\def\ac{80}  % angle
\coordinate (C0) at (\xc,0);             % center
\coordinate (C1) at ($(C0)+( \ac:\rc)$); % tangent point above
\coordinate (C2) at ($(C0)+(-\ac:\rc)$); % tangent point below
% fourth circle
\def\xd{13}  % position
\def\rd{2.9} % radius
\def\ad{80}  % angle
\coordinate (D0) at (\xd,0);             % center
\coordinate (D1) at ($(D0)+( \ad:\rd)$); % tangent point above
\coordinate (D2) at ($(D0)+(-\ad:\rd)$); % tangent point below
% DRAWING
% section
\fill[cyan!10] (B1) to[out=\ab-90,in=\ac+90]  (C1) arc (\ac:-\ac:\rc)
                    to[out=270-\ac,in=90-\ab] (B2) arc (-\ab:\ab:\rb);
\fill[cyan!60] (C1) to[out=\ab-90,in=\ac+90]  (B1) arc (\ab:360-\ab:\rb)
                    to[out=270-\ab,in=90-\ac] (C2) arc (360-\ac:\ac:\rc);
% first circle
\draw         (A1) arc (\aa:360-\aa:\ra);
\draw[dashed] (A1) arc (\aa:-\aa:\ra);
% rest of the circles
\foreach\i/\j in {B/\rb,C/\rc,D/\rd}
  \draw (\i0) circle (\j);
% surface
\draw[thick,cyan] (A1) to[out=\aa-90,in=\ab+90] (B1) to[out=\ab-90,in=\ac+90]
                  (C1) to[out=\ac-90,in=\ad+90] (D1);
\draw[yscale=-1]  (A2) to[out=\aa-90,in=\ab+90] (B2) to[out=\ab-90,in=\ac+90]
                  (C2) to[out=\ac-90,in=\ad+90] (D2);
% axis
\draw[thick]  (-\ra,0) --++ (-1,0);
\draw[dashed] (-\ra,0) --   (D0);
\draw[thick]  (D0)  --   (\xd+\rd+1,0);
\foreach\i in {A,B,C,D}
  \fill (\i0) ellipse (0.8mm and 0.4mm);
% labels
\draw[latex-latex]            (C0) --++ (0,\rc)     node[midway,right] {$y_1$};
\draw         (B0) ++  (0,\rb+0.1) --++ (0,1);
\draw         (C0) ++  (0,\rc+0.1) --++ (0,1+\rb-\rc);
\draw[-latex] (B0) ++ (-0.5,\rb+1) --++ (0.5,0);
\draw[-latex] (C0) ++  (0.5,\rb+1) --++ (-0.5,0);
\draw         (B0) ++    (0,\rb+1) --++ (\xc-\xb,0) node[midway,yshift=3mm] {$\Delta x$};
\end{tikzpicture}
\end{document}

Answer