如何将 3D 中的 2D 文本添加到平面上？

Question 1

这真的只是（也仅仅是；-）为了好玩。我在 Ti 中玩过类似的任务。钾Z.以下代码需要3dtools 库project on plane，以及的某个版本orthonormal basis vectors of plane将在某个时候添加到此库中。给定三个点A、B和C，这些工具允许您切换到包含这些点的平面。此平面的基向量是正交的，并且第一个基向量与平行A--B。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
\tikzset{project on plane/.code n args={3}{%
\pgfmathsetmacro{\myn}{TD("(#2)x(#3)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myn)o(\myn)")}
\pgfmathsetmacro{\myn}{TD("\mynormalization*(\myn)")}
\pgfmathsetmacro{\myproj}{-1*TD("(#1)o(\myn)")}
\pgfmathsetmacro{\myprojcoord}{TD("(#1)+\myproj*(\myn)")}
\tikzset{insert path={(\myprojcoord)}}
},orthonormal basis vectors of plane/.code n args={3}{%
\pgfmathsetmacro{\mya}{TD("(#2)-(#1)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\mya)o(\mya)")}
\pgfmathsetmacro{\mya}{TD("\mynormalization*(\mya)")}
\pgfmathsetmacro{\myb}{TD("(#3)-(#1)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myb)o(\myb)")}
\pgfmathsetmacro{\myb}{TD("\mynormalization*(\myb)")}
\pgfmathsetmacro{\myn}{TD("(\mya)x(\myb)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myn)o(\myn)")}
\pgfmathsetmacro{\myn}{TD("\mynormalization*(\myn)")}
\pgfmathsetmacro{\myc}{TD("(\myn)x(\mya)")}
\tikzset{insert path={
 (\mya) coordinate(\pgfkeysvalueof{/tikz/3d/projections/planex})
 (\myc) coordinate(\pgfkeysvalueof{/tikz/3d/projections/planey})
 }}},
3d/projections/.cd,planex/.initial=planex,planey/.initial=planey}

\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[tdplot_main_coords,bullet/.style={draw,fill,black,inner
    sep=1.5pt,circle,opacity=1},font=\sffamily]
 \path (4,0,0) coordinate (v1) 
       (0,6,0) coordinate (v2) 
       (-2,-3,0) coordinate (p0);
 \draw[fill=orange] (p0)  -- ++ (v1) -- ++ (v2) -- ++ ($-1*(v1)$) -- cycle;
 \draw[thick,blue,-stealth] (p0) -- ++ (v1) node[left]{$v_1$};
 \draw[thick,blue,-stealth] (p0) -- ++ (v2) node[above]{$v_2$};
 \path        (1,2,4) coordinate (pA)
  [project on plane={pA}{v1}{v2}] coordinate (pB)
  [3d coordinate={(pC)=(p0)+0.2*(v1)+0.2*(v2)}];
 \draw[thick,blue,fill=black,fill opacity=0.3,text opacity=1,text=black] 
  (pA)  node[bullet,label=right:$A$]  {}
  -- (pB) node[bullet,label=right:$B$] {} 
  -- (pC) node[bullet,label=left:$C$] {} -- cycle;
 \path[orthonormal basis vectors of plane={pC}{pB}{pA}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pC)!0.5!(pB)$) node[above,yellow] {from $C$ to $B$};
 \end{scope}
 \path[orthonormal basis vectors of plane={pB}{pA}{pC}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pB)!0.5!(pA)$) node[above,yellow] {from $B$ to $A$};
 \end{scope}
 \path[orthonormal basis vectors of plane={pA}{pC}{pB}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pA)!0.5!(pC)$) node[above,yellow] {from $A$ to $C$};
 \end{scope}
\end{tikzpicture}
\end{document}

我当然不是声称这可以与之竞争asymptote。

Answer

这真的只是（也仅仅是；-）为了好玩。我在 Ti 中玩过类似的任务。钾Z.以下代码需要3dtools 库project on plane，以及的某个版本orthonormal basis vectors of plane将在某个时候添加到此库中。给定三个点A、B和C，这些工具允许您切换到包含这些点的平面。此平面的基向量是正交的，并且第一个基向量与平行A--B。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
\tikzset{project on plane/.code n args={3}{%
\pgfmathsetmacro{\myn}{TD("(#2)x(#3)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myn)o(\myn)")}
\pgfmathsetmacro{\myn}{TD("\mynormalization*(\myn)")}
\pgfmathsetmacro{\myproj}{-1*TD("(#1)o(\myn)")}
\pgfmathsetmacro{\myprojcoord}{TD("(#1)+\myproj*(\myn)")}
\tikzset{insert path={(\myprojcoord)}}
},orthonormal basis vectors of plane/.code n args={3}{%
\pgfmathsetmacro{\mya}{TD("(#2)-(#1)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\mya)o(\mya)")}
\pgfmathsetmacro{\mya}{TD("\mynormalization*(\mya)")}
\pgfmathsetmacro{\myb}{TD("(#3)-(#1)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myb)o(\myb)")}
\pgfmathsetmacro{\myb}{TD("\mynormalization*(\myb)")}
\pgfmathsetmacro{\myn}{TD("(\mya)x(\myb)")}
\pgfmathsetmacro{\mynormalization}{1/sqrt(TD("(\myn)o(\myn)")}
\pgfmathsetmacro{\myn}{TD("\mynormalization*(\myn)")}
\pgfmathsetmacro{\myc}{TD("(\myn)x(\mya)")}
\tikzset{insert path={
 (\mya) coordinate(\pgfkeysvalueof{/tikz/3d/projections/planex})
 (\myc) coordinate(\pgfkeysvalueof{/tikz/3d/projections/planey})
 }}},
3d/projections/.cd,planex/.initial=planex,planey/.initial=planey}

\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[tdplot_main_coords,bullet/.style={draw,fill,black,inner
    sep=1.5pt,circle,opacity=1},font=\sffamily]
 \path (4,0,0) coordinate (v1) 
       (0,6,0) coordinate (v2) 
       (-2,-3,0) coordinate (p0);
 \draw[fill=orange] (p0)  -- ++ (v1) -- ++ (v2) -- ++ ($-1*(v1)$) -- cycle;
 \draw[thick,blue,-stealth] (p0) -- ++ (v1) node[left]{$v_1$};
 \draw[thick,blue,-stealth] (p0) -- ++ (v2) node[above]{$v_2$};
 \path        (1,2,4) coordinate (pA)
  [project on plane={pA}{v1}{v2}] coordinate (pB)
  [3d coordinate={(pC)=(p0)+0.2*(v1)+0.2*(v2)}];
 \draw[thick,blue,fill=black,fill opacity=0.3,text opacity=1,text=black] 
  (pA)  node[bullet,label=right:$A$]  {}
  -- (pB) node[bullet,label=right:$B$] {} 
  -- (pC) node[bullet,label=left:$C$] {} -- cycle;
 \path[orthonormal basis vectors of plane={pC}{pB}{pA}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pC)!0.5!(pB)$) node[above,yellow] {from $C$ to $B$};
 \end{scope}
 \path[orthonormal basis vectors of plane={pB}{pA}{pC}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pB)!0.5!(pA)$) node[above,yellow] {from $B$ to $A$};
 \end{scope}
 \path[orthonormal basis vectors of plane={pA}{pC}{pB}]; 
 \begin{scope}[x={(planex)},y={(planey)},canvas is xy plane at z=0,
    transform shape]
  \path ($(pA)!0.5!(pC)$) node[above,yellow] {from $A$ to $C$};
 \end{scope}
\end{tikzpicture}
\end{document}

我当然不是声称这可以与之竞争asymptote。

Question 2

这是我的尝试：

// run asy -f pdf <name>.asy
settings.outformat="pdf"; 
settings.prc=false;
settings.render=0;

usepackage("amssymb");

import three;
unitsize(1cm);
defaultpen(fontsize(12pt));
defaultpen(linewidth(1bp));
size(10cm,0);
currentprojection=orthographic(1.5,0.8,0.5);
triple v1=(4,0,0),v2=(0,6,0),p0=(-2,-3,0);
path3 pl=plane(v1,v2,p0);
transform3 proj=planeproject(pl);
triple pA=(1,2,3.5), pB=proj*pA, pC=p0+.2*v1+.2*v2, 
vnP=unit(cross(v1,v2)),pD=rotate(90,pC,pC+vnP)*pB; 
draw(surface(pl),orange+opacity(.5));
draw(Label("$\vec{v}_1$"),p0--p0+v1,1bp+green,Arrow3(size=8));
draw(Label("$\vec{v}_2$",position=Relative(0.7)),p0--p0+v2,N,1bp+green,Arrow3(size=8));
layer();
draw(surface(pA--pB--pC--cycle),opacity(0.5)+gray,1bp+.8blue);

dot("$A$",pA); dot("$B$",pB); dot("$C$",pC,dir(pC-pB));
dot("$p_0$",p0,NW);

// draw a dimension arrow from A to B to d mm above the segment with the text (gg dich)
// https://melusine.eu.org/syracuse/asymptote/comin/geoespace.asy
void cote(triple A1,triple B1, string text, real d,bool line=true,
real pos=.5, real a=1, bool trait=false,pen sty=black, pen joinpen=dotted,
align alignLabel=RightSide ){
pair M,N;
pair A=project(A1);
pair B=project(B1);
M=A+d/10*dir(degrees(B-A)+90);
N=B+d/10*dir(degrees(B-A)+90);
if(line==false)
label(Label(text,Rotate(dir(degrees(a*(N-M)))),position=Relative(pos),align=alignLabel),N--M); 
else {
label(Label(text,Rotate(dir(degrees(a*(N-M)))),position=Relative(pos),align=alignLabel),N--M);
draw(N--M,Arrows(size=5),p=sty);}
if(trait==true){ draw(A--M^^B--N,joinpen); }
}
cote(pC,pA,"\footnotesize distance $AC$",-3.5,line=false);
cote(pC,pB,"\footnotesize distance $BC$",0,line=false);
cote(pA,pB,"\footnotesize distance $AB$",-3.5,line=false);
cote(pC,(pA+pB)/2,"${\vartriangle}ABC$",-2,line=false,pos=.4);

shipout(bbox(2mm,Fill(white)));

Answer

这是我的尝试：

// run asy -f pdf <name>.asy
settings.outformat="pdf"; 
settings.prc=false;
settings.render=0;

usepackage("amssymb");

import three;
unitsize(1cm);
defaultpen(fontsize(12pt));
defaultpen(linewidth(1bp));
size(10cm,0);
currentprojection=orthographic(1.5,0.8,0.5);
triple v1=(4,0,0),v2=(0,6,0),p0=(-2,-3,0);
path3 pl=plane(v1,v2,p0);
transform3 proj=planeproject(pl);
triple pA=(1,2,3.5), pB=proj*pA, pC=p0+.2*v1+.2*v2, 
vnP=unit(cross(v1,v2)),pD=rotate(90,pC,pC+vnP)*pB; 
draw(surface(pl),orange+opacity(.5));
draw(Label("$\vec{v}_1$"),p0--p0+v1,1bp+green,Arrow3(size=8));
draw(Label("$\vec{v}_2$",position=Relative(0.7)),p0--p0+v2,N,1bp+green,Arrow3(size=8));
layer();
draw(surface(pA--pB--pC--cycle),opacity(0.5)+gray,1bp+.8blue);

dot("$A$",pA); dot("$B$",pB); dot("$C$",pC,dir(pC-pB));
dot("$p_0$",p0,NW);

// draw a dimension arrow from A to B to d mm above the segment with the text (gg dich)
// https://melusine.eu.org/syracuse/asymptote/comin/geoespace.asy
void cote(triple A1,triple B1, string text, real d,bool line=true,
real pos=.5, real a=1, bool trait=false,pen sty=black, pen joinpen=dotted,
align alignLabel=RightSide ){
pair M,N;
pair A=project(A1);
pair B=project(B1);
M=A+d/10*dir(degrees(B-A)+90);
N=B+d/10*dir(degrees(B-A)+90);
if(line==false)
label(Label(text,Rotate(dir(degrees(a*(N-M)))),position=Relative(pos),align=alignLabel),N--M); 
else {
label(Label(text,Rotate(dir(degrees(a*(N-M)))),position=Relative(pos),align=alignLabel),N--M);
draw(N--M,Arrows(size=5),p=sty);}
if(trait==true){ draw(A--M^^B--N,joinpen); }
}
cote(pC,pA,"\footnotesize distance $AC$",-3.5,line=false);
cote(pC,pB,"\footnotesize distance $BC$",0,line=false);
cote(pA,pB,"\footnotesize distance $AB$",-3.5,line=false);
cote(pC,(pA+pB)/2,"${\vartriangle}ABC$",-2,line=false,pos=.4);

shipout(bbox(2mm,Fill(white)));

如何将 3D 中的 2D 文本添加到平面上？

答案1

答案2

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