切线与曲线相交

Question

为什么程序只读取一个交点？解决方法是将其分成两部分，用不同长度的切线绘制。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\usetikzlibrary{decorations.markings}
\begin{document}
\pgfkeys{tikz/.cd,
 tangent length/.store in=\TangentLength,
 tangent length=3.14cm,
 normal length/.store in=\NormalLength,
 normal length=7mm}
 \newcounter{tangent}
 \newcounter{normal}
 \tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
 tangent at/.style={postaction={decorate,decoration={markings,
 mark=at position #1 with {\stepcounter{tangent}
 \draw[tangent,name path=tangent-\thetangent] (-\TangentLength,0) -- 
 (9cm,0);
 \fill[tangent] (0,0) circle (2pt);}}}},
  normal at/.style={postaction={decorate,decoration={markings,
   mark=at position #1 with {\stepcounter{normal}
 \draw[normal,name path=normal-\thenormal] (0,-\NormalLength) -- 
 (0,\NormalLength);
 \fill[normal] (0,0) circle (2pt);}}}}, 
 }
 \begin{tikzpicture}
 % Axes
 \draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
 \draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
 % Origin
 \node at (0,0) [below left] {$0$};
 % Points
 \coordinate (start) at (1,-0.8);
 \coordinate (c1) at (3,3);
 \coordinate (c2) at (5.5,1.5);
 \coordinate (c3) at (8,4);
 \coordinate (end) at (10.5,-0.8);
 % show the points
 % \foreach \n in {start,c1,c2,c3,end} \fill [black] (\n)
 %     circle (2pt) node [below] {}; 
 %  join the coordinates
\draw [name path=curve,thick,tangent at/.list={0.3,0.3},
  normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
  (c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
 \fill[name intersections={of=curve and tangent-2,total=\t},cyan]
 (intersection-\t) circle (2pt);
  \fill[name intersections={of=curve and tangent-1,total=\t},cyan]
  (intersection-\t) circle (2pt);
 \end{tikzpcicture}
 \end{document}

输出：

Answer 1

样式tangent at=<pos>在位置处附加一条切线pos。因此tangent at/.list={0.3,0.3}只会创建两条相同的切线。但是，这与交点无关。相反，您想标记切线与曲线的最后两个交点。（Ti钾Z 找到更多的交点，因为切线当然非常接近曲线，所以一些额外的交点不是真正的交点，而是由于数值不准确造成的。）

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}
\usetikzlibrary{decorations.markings}
\begin{document}
\pgfkeys{tikz/.cd,
 tangent length/.store in=\TangentLength,
 tangent length=3.14cm,
 normal length/.store in=\NormalLength,
 normal length=7mm}
 \newcounter{tangent}
 \newcounter{normal}
 \tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
 tangent at/.style={postaction={decorate,decoration={markings,
 mark=at position #1 with {\stepcounter{tangent}
 \draw[tangent,name path=tangent-\thetangent] (-\TangentLength,0) -- 
 (9cm,0);
 \fill[tangent] (0,0) circle (2pt);}}}},
  normal at/.style={postaction={decorate,decoration={markings,
   mark=at position #1 with {\stepcounter{normal}
 \draw[normal,name path=normal-\thenormal] (0,-\NormalLength) -- 
 (0,\NormalLength);
 \fill[normal] (0,0) circle (2pt);}}}}, 
 }
 \begin{tikzpicture}
 % Axes
 \draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
 \draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
 % Origin
 \node at (0,0) [below left] {$0$};
 % Points
 \coordinate (start) at (1,-0.8);
 \coordinate (c1) at (3,3);
 \coordinate (c2) at (5.5,1.5);
 \coordinate (c3) at (8,4);
 \coordinate (end) at (10.5,-0.8);
 % show the points
 % \foreach \n in {start,c1,c2,c3,end} \fill [black] (\n)
 %     circle (2pt) node [below] {}; 
 %  join the coordinates
\draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
  (c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
 \fill[name intersections={of=curve and tangent-1,total=\t},cyan]
 \pgfextra{\pgfmathtruncatemacro{\prevt}{\t-1}}
 foreach \i in {\prevt,\t} {(intersection-\i) circle (2pt)};
\end{tikzpicture}
\end{document}

Answer 2

使用tzplot：

\documentclass{standalone} 

\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}
\tzhelplines(-1,-1)(11,6)
\tzaxes(-1,-1)(11,6){$x$}{$y$}
\tzshoworigin
\tzcoors(1,-0.8)(start) (3,3)(c1) (5.5,1.5)(c2) (8,4)(c3) (10.5,-0.8)(end) ;
\tztos[thick]"curve"(start)[out=70,in=180]
                    (c1)[out=0,in=180]
                    (c2)[out=0,in=180]
                    (c3)[out=0,in=150]
                    (end) ;
\tztangentat[red]"tan"{curve}{3.53}[1:11]
\tzXpoint{curve}{tan}(X)
\tzdot*[red](X)
\tzdot*[red](X-5) % trial and error
\end{tikzpicture}

\end{document}