我怎样才能将法线向量放在外面的蓝色网格上？
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage{amsmath}
\usetikzlibrary{arrows}
\usepackage{pgfplots}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\newcommand\pgfmathsinandcos[3]{%
\pgfmathsetmacro#1{sin(#3)}%
\pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % azimuth
\tikzset{#1/.estyle = {cm = {\cost, \sint*\sinEl, 0, \cosEl, (0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % latitude
\pgfmathsetmacro\yshift{\cosEl*\sint}
\tikzset{#1/.estyle = {cm = {\cost, 0, 0, \cost*\sinEl, (0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style = {scale = #1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane] (\angVis:1) arc (\angVis:\angVis + 180:1);
\draw[current plane, dashed] (\angVis - 180:1) arc (\angVis - 180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style = {scale = #1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane] (\angVis:1) arc (\angVis:-\angVis - 180:1);
\draw[current plane, dashed] (180 - \angVis:1) arc (180 - \angVis:\angVis:1);
}
\newcommand\DrawLongitudeCirclered[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, blue, thick] (150:1) arc (150:180:1);
% \draw[current plane,dashed] (-50:1) arc (-50:-35:1);
}%for drawing the grid
\newcommand\DLongredd[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, black, dashed, ultra thick] (150:1) arc (150:180:1);
}
\newcommand\DLatred[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane, dashed, black, ultra thick] (-50:1) arc (-50:-35:1);
}
\newcommand \fillred[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, blue, thin] (\angVis:1) arc (\angVis:\angVis+180:1);
}
\newcommand\DrawLatitudeCirclered[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
% \draw[current plane,red,thick] (-\angVis-50:1) arc (-\angVis-50:-\angVis-20:1);
\draw[current plane, blue, thick] (-50:1) arc (-50:-35:1);
}
\tikzset{%
>=latex, % option for nice arrows
inner sep = 0pt,%
outer sep = 2pt,%
mark coordinate/.style = {inner sep = 0pt, outer sep = 0pt, minimum size = 3pt,
fill = black, circle}%
}
\begin{document}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\def\R{2} % sphere radius
\def\angEl{25} % elevation angle
\def\angAz{-100} % azimuth angle
\def\angPhiOne{-50} % longitude of point P
\def\angPhiTwo{-35} % longitude of point Q
\def\angBeta{30} % latitude of point P and Q
%% working planes
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhiOne}
\LongitudePlane[qzplane]{\angEl}{\angPhiTwo}
\LatitudePlane[equator]{\angEl}{0}
\fill[ball color = green!10] (0,0) circle (\R); % 3D lighting effect
\coordinate (O) at (0,0);
\coordinate[mark coordinate] (N) at (0,\H);
\coordinate[mark coordinate] (S) at (0,-\H);
\path[xzplane] (\R,0) coordinate (XE);
%defining points outsided the area bounded by the sphere
\path[qzplane] (\angBeta:\R+3) coordinate (XEd);
\path[pzplane] (\angBeta:\R) coordinate (P);
\path[pzplane] (\angBeta:\R+3) coordinate (Pd);
\path[pzplane] (\angBeta:\R+5.2376) coordinate (Td);
\path[pzplane] (\R,0) coordinate (PE);
\path[pzplane] (\R+3,0) coordinate (PEd);
\path[qzplane] (\angBeta:\R) coordinate (Q);
\path[qzplane] (\angBeta:\R) coordinate (Qd);
\path[qzplane] (\R,0) coordinate (QE);
\path[qzplane] (\R+3,0) coordinate (QEd);
\DrawLongitudeCircle[\R]{\angPhiOne} % pzplane
\DrawLongitudeCircle[\R]{\angPhiTwo} % qzplane
\DrawLatitudeCircle[\R]{\angBeta}
\DrawLatitudeCircle[\R]{0} % equator
% labelling north and south
\node[above = 8pt] at (N) {$\mathbf{N}$};
\node[below = 8pt] at (S) {$\mathbf{S}$};
\draw[-, dashed, thick] (N) -- (S);
%\draw[->] (O) -- (P);
%\draw[dashed] (XE) -- (O) -- (PE);
\draw[dashed] (O) -- (QE);
% connecting Points outside the sphere
\draw[-, dashed, black, very thick] (O) -- (Pd);
\draw[-, dashed, black, very thick] (O) -- (PEd);
\draw[-, dashed, black, very thick] (O) -- (QEd);
\draw[-, dashed, black, very thick] (O) -- (XEd);
\path[pzplane] (0.5*\angBeta:\R) node[right] {$$};
\path[qzplane] (0.5*\angBeta:\R) node[right] {$$};
\path[xzplane] (0:\R) node[below] {$$};
\path[xzplane] (\angBeta:\R) node[below left] {$$};
\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R]{\t} }
\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R]{\t} }
% drawing grids on the spere invoking DLongredd and DrawLongitudeCirclered
\foreach \t in {130,145,...,145} { \DLongredd[\R+3]{\t} }
\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R+3]{\t} }
\foreach \t in {0,30,...,30} { \DLatred[\R+3]{\t} }
\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R+3]{\t} }
\end{tikzpicture}
\caption{The normal pressure force of the surrounding water on $m$.}
\end{figure}
\end{document}
答案1
我使用不太最小的 MWE 中已定义的原语创建了一个解决方案。:-)
新增内容
由于代码较长，我将逐行解释我的添加内容；完整的代码如下。
\def\angPhiAvg{-42.5}
定义矢量要跟随的角度 phi（在本例中为网格范围的平均值）。
\LongitudePlane[myplane]{\angEl}{\angPhiAvg}
定义矢量所在的附加工作平面。
\path[myplane] (\angBeta/2:\R+3) coordinate (Ts);
\path[myplane] (\angBeta/2:\R+4) coordinate (Tf);
定义向量的开始和结束；在本例中为单位长度。
\draw[->, green, very thick] (Ts) -- (Tf) node[right] {$\mathbf{\hat{n}}$};
绘制并标记法线矢量。
完整代码
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage{amsmath}
\usetikzlibrary{arrows}
\usepackage{pgfplots}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\newcommand\pgfmathsinandcos[3]{%
\pgfmathsetmacro#1{sin(#3)}%
\pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % azimuth
\tikzset{#1/.estyle = {cm = {\cost, \sint*\sinEl, 0, \cosEl, (0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % latitude
\pgfmathsetmacro\yshift{\cosEl*\sint}
\tikzset{#1/.estyle = {cm = {\cost, 0, 0, \cost*\sinEl, (0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style = {scale = #1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane] (\angVis:1) arc (\angVis:\angVis + 180:1);
\draw[current plane, dashed] (\angVis - 180:1) arc (\angVis - 180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style = {scale = #1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane] (\angVis:1) arc (\angVis:-\angVis - 180:1);
\draw[current plane, dashed] (180 - \angVis:1) arc (180 - \angVis:\angVis:1);
}
\newcommand\DrawLongitudeCirclered[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, blue, thick] (150:1) arc (150:180:1);
% \draw[current plane,dashed] (-50:1) arc (-50:-35:1);
}%for drawing the grid
\newcommand\DLongredd[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, black, dashed, ultra thick] (150:1) arc (150:180:1);
}
\newcommand\DLatred[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane, dashed, black, ultra thick] (-50:1) arc (-50:-35:1);
}
\newcommand \fillred[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane, blue, thin] (\angVis:1) arc (\angVis:\angVis+180:1);
}
\newcommand\DrawLatitudeCirclered[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
% \draw[current plane,red,thick] (-\angVis-50:1) arc (-\angVis-50:-\angVis-20:1);
\draw[current plane, blue, thick] (-50:1) arc (-50:-35:1);
}
\tikzset{%
>=latex, % option for nice arrows
inner sep = 0pt,%
outer sep = 2pt,%
mark coordinate/.style = {inner sep = 0pt, outer sep = 0pt, minimum size = 3pt,
fill = black, circle}%
}
\begin{document}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\def\R{2} % sphere radius
\def\angEl{25} % elevation angle
\def\angAz{-100} % azimuth angle
\def\angPhiOne{-50} % longitude of point P
\def\angPhiTwo{-35} % longitude of point Q
\def\angPhiAvg{-42.5} % longitude of normal vector ******
\def\angBeta{30} % latitude of point P and Q
%% working planes
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhiOne}
\LongitudePlane[qzplane]{\angEl}{\angPhiTwo}
\LongitudePlane[myplane]{\angEl}{\angPhiAvg} % ******
\LatitudePlane[equator]{\angEl}{0}
\fill[ball color = green!10] (0,0) circle (\R); % 3D lighting effect
\coordinate (O) at (0,0);
\coordinate[mark coordinate] (N) at (0,\H);
\coordinate[mark coordinate] (S) at (0,-\H);
\path[xzplane] (\R,0) coordinate (XE);
%defining points outsided the area bounded by the sphere
\path[qzplane] (\angBeta:\R+3) coordinate (XEd);
\path[pzplane] (\angBeta:\R) coordinate (P);
\path[pzplane] (\angBeta:\R+3) coordinate (Pd);
\path[myplane] (\angBeta/2:\R+3) coordinate (Ts); % ******
\path[myplane] (\angBeta/2:\R+4) coordinate (Tf); % ******
\path[pzplane] (\R,0) coordinate (PE);
\path[pzplane] (\R+3,0) coordinate (PEd);
\path[qzplane] (\angBeta:\R) coordinate (Q);
\path[qzplane] (\angBeta:\R) coordinate (Qd);
\path[qzplane] (\R,0) coordinate (QE);
\path[qzplane] (\R+3,0) coordinate (QEd);
\DrawLongitudeCircle[\R]{\angPhiOne} % pzplane
\DrawLongitudeCircle[\R]{\angPhiTwo} % qzplane
\DrawLatitudeCircle[\R]{\angBeta}
\DrawLatitudeCircle[\R]{0} % equator
% labelling north and south
\node[above = 8pt] at (N) {$\mathbf{N}$};
\node[below = 8pt] at (S) {$\mathbf{S}$};
\draw[-, dashed, thick] (N) -- (S);
%\draw[->] (O) -- (P);
%\draw[dashed] (XE) -- (O) -- (PE);
\draw[dashed] (O) -- (QE);
% connecting Points outside the sphere
\draw[-, dashed, black, very thick] (O) -- (Pd);
\draw[-, dashed, black, very thick] (O) -- (PEd);
\draw[-, dashed, black, very thick] (O) -- (QEd);
\draw[-, dashed, black, very thick] (O) -- (XEd);
\path[pzplane] (0.5*\angBeta:\R) node[right] {$$};
\path[qzplane] (0.5*\angBeta:\R) node[right] {$$};
\path[xzplane] (0:\R) node[below] {$$};
\path[xzplane] (\angBeta:\R) node[below left] {$$};
\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R]{\t} }
\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R]{\t} }
\draw[->, green, very thick] (Ts) -- (Tf) node[right] {$\mathbf{\hat{n}}$}; % ******
% drawing grids on the spere invoking DLongredd and DrawLongitudeCirclered
\foreach \t in {130,145,...,145} { \DLongredd[\R+3]{\t} }
\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R+3]{\t} }
\foreach \t in {0,30,...,30} { \DLatred[\R+3]{\t} }
\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R+3]{\t} }
\end{tikzpicture}
\caption{The normal pressure force of the surrounding water on $m$.}
\end{figure}
\end{document}