☰

绘制给定节点斜率的法向量

tag-icon • tag-icon tikz-arrows tikz-styles arrow-curve tangent
绘制给定节点斜率的法向量

我使用以下代码绘制了两条彼此相切的曲线（不完全是，只是目测），有没有办法在点 $P$ 处绘制法线向量（向内和向外），如下所示？

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
    \draw[blue, very thick] (-2,10.5) .. controls (5,15.3) and (3,-0.2) .. (12.5,10.5);
    \draw (-2,7.5) .. controls (5,15.5) and (4,0.5) .. (12.5,7.5)
    node[sloped, inner xsep=25mm, inner ysep=0, fill, pos=0.5, red] (P) {}
    node[ inner xsep=35mm, inner ysep=0, fill, pos=0.5, pink] (Q) {};
    \filldraw (P) circle(2pt); 
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案1

通过使用decorations.markings图书馆：

\documentclass[margin=3mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,
                bbox,   % for better clip of image
                decorations.markings}
\begin{document}
    \begin{tikzpicture}[bezier bounding box,%
decoration = {markings,% switch on markings
              mark= at position 0.5 with {
                    \node[dot];
                    \draw[red] (-3,0) -- (3,0);
                    \draw[-Straight Barb, magenta] (0,0) -- (0,2);
                                         }
            },
dot/.style = {circle, fill=black, inner sep=1.6pt,
             node contents={}},
                        ]
\draw[blue, very thick]         (0,2) .. controls ++(4,4) and ++(-7.3,-7) .. (12, 2);
\draw[postaction={decorate}]    (0,0) .. controls ++(4,4) and ++(-4.0,-4) .. (12, 0);
    \end{tikzpicture}
\end{document}

注：Ti钾Z 通过建立包含曲线端点和两个控制点的最小矩形来确定（三次）贝塞尔曲线的边界框。库bbox用于建立精确的边界框，（尽量）仅考虑曲线。

在此处输入图片描述

答案2

按照 Qrrbrbirlbel 的建议。

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[%
    vector/.pic={\draw [-latex, thick] (0,0) node [inner sep=2pt, fill, circle] {} -- (1,0);}
]
    \draw[blue, very thick] (-2,10.5) .. controls (5,15.3) and (3,-0.2) .. (12.5,10.5);
    \draw (-2,7.5) .. controls (5,15.5) and (4,0.5) .. (12.5,7.5)
    pic [pos=0.5, sloped, red, scale=2] {vector}
    pic [pos=0.5, sloped, rotate=90, magenta, scale=2] {vector};
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案3

另一种解决方案。使用倾斜P节点作为参考，从其中心到边界上的锚点绘制放大线。负片shorten会放大它们。

注意：P绘制节点是为了显示位置和方向。最终结果应取消绘制。

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
    \draw[blue, very thick] (-2,10.5) .. controls (5,15.3) and (3,-0.2) .. (12.5,10.5);
    \draw (-2,7.5) .. controls (5,15.5) and (4,0.5) .. (12.5,7.5)
    node[draw, sloped, pos=0.5, minimum size=5mm] (P) {}; %delete `draw` for final drawing
    \filldraw (P) circle(2pt); 
    \draw[-latex, thick, shorten > = -15mm, red] (P.center)--(P.north);
    \draw[-latex, thick, shorten > = -15mm, red] (P.center)--(P.east);
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案4

使用tzplot：

在此处输入图片描述

\documentclass{standalone} 

\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}
\tzbezier[blue, very thick]"AA"(-2,10.5)(5,15.3)(3,-0.2)(12.5,10.5)
\tzbezier"BB"(-2,7.5)(5,15.5)(4,0.5)(12.5,7.5)<node[pos=0.5](P){}>
\tzdot*(P)(4pt)
\tztangent[red,dashed,thick]{BB}(P)(.2,.1)[3:6.5]{tangent}[b,red]
\tznormal[->,thick,blue]{BB}(P)(.2,.1){3cm}{normal}[r]
\tznormal'[->,thick,red]{BB}(P)(.2,.1){3cm}{normal$'$}[b]
\tznormal[->,ultra thick,green,opacity=.7]{BB}(P)(.2,.1){10cm}[180]
\end{tikzpicture}

\end{document}

相关内容