使用 Tikz 的 3D 实体-或者其他替代方案？

Question 1

这是使用 Asymptote 的替代方法。它可以满足您的大多数请求；例如，颜色在序言中定义（但在 Asymptote 代码中而不是 TeX 代码中，因此您可能需要单独定义 TeX 版本）。

% To run: pdflatex --shell-escape filename.tex

\documentclass[margin=10pt,convert]{standalone}
\usepackage{asypictureB}

\begin{asyheader}
pen c1 = rgb(0.2,0.4,0.6); // Blue-ish
pen c2 = rgb(1.0,0.0,0.6); // Pink-ish
pen c3 = rgb(0.6,0.0,0.0); // Red

texpreamble("\newbox\BoxForRules
\newcommand{\boxToRule}[1]{%
    \setbox\BoxForRules=\hbox{\hspace{2pt}#1\hspace{2pt}}%
    $\rlap{\rule[\dimexpr-\dp\BoxForRules-2pt]{\wd\BoxForRules}{\dimexpr\ht\BoxForRules+\dp\BoxForRules+4pt}}\mbox{\hspace{2pt}#1\hspace{2pt}}$%
}");

import three;

void framed_label(string s, triple position, pen p = currentpen) {
    label("\boxToRule{" + s + "}", position=position, p=white + opacity(0.6));
    label(s, position=position, p=p);
}
\end{asyheader}

\begin{document}
\begin{asypicture}{name=cylinder}
    settings.outformat = "pdf";
    settings.render = 0;

    real unit = 4cm;
    unitsize(unit);

    currentprojection = orthographic((-4,2.8,-2), up=Y);

    real d = 1;
    real r = 0.45 d;
    real af = 0.5 d;

    pen cubedraw = linewidth(0.8pt) + gray;
    pen cubefill = opacity(0.5) + c1;
    pen axis = linewidth(1.0 pt) + c3;

    //Draw backside of cube
    draw( surface((0,0,d) -- (0,d,d) -- (d,d,d) -- (d,0,d) -- cycle), 
        meshpen = cubedraw, 
        surfacepen = emissive(cubefill));
    draw( surface((0,0,0) -- (0,0,d) -- (d,0,d) -- (d,0,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));
    draw( surface((d,0,0) -- (d,0,d) -- (d,d,d) -- (d,d,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));

    //Draw cylinder as surface of revolution
    path3 cyl_center = shift(d/2,0,d/2) * (O -- d*Y);
    path3 cyl_edge = shift(r*X) * cyl_center;
    int n = 10;
    guide3 to_revolve = point(cyl_edge, 0);
    for (int i = 1; i <= n; ++i)
        to_revolve = to_revolve -- point(cyl_edge, i/n);
    surface cylinder = surface(to_revolve, c=(d/2,0,d/2), axis=Y);
    draw(cylinder, meshpen = 0.3 c2 + 0.5 gray, 
            surfacepen = material(c2 + opacity(0.7), emissivepen = 0.2 c2));


    //Draw the radius arrow and center line
    draw(cyl_center, 0.8 c2);
    //draw(circle(c=(d/2,d/2,d/2), r=r, normal=Y), 0.8 c2);
    draw( (d/2,d,d/2) -- (d/2,d,d/2+r), c2 + linewidth(0.8), arrow=Arrows3(TeXHead2));
    framed_label("$r$", position=(d/2, d, d/2 + r/2), p=c2);

    //Draw front of cube
    draw( (0,0,0) -- (0,d,0) ^^ (d,d,0) -- (0,d,0) ^^ (0,d,d) -- (0,d,0), cubedraw);

    //Draw the axis arrows and annotations
    draw(O -- af*X, axis, arrow=Arrow3(TeXHead2));
    framed_label("$x$", position=(1 + 18pt/unit)*af*X, p=axis);
    draw(O -- af*Y, axis, arrow=Arrow3(TeXHead2));
    framed_label("$y$", position=(1 + 12pt/unit)*af*Y, p=axis);
    draw(O -- af*Z, axis, arrow=Arrow3(TeXHead2));
    framed_label("$z$", position=(1 + 10pt/unit)*af*Z, p=axis);

    //Draw cube lattice length measures
    draw((0,0,d*5/6) -- (0,d,d*5/6), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (0,d/2,d*5/6), c1);
    draw((d*5/6,0,0) -- (d*5/6,d,0), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d/2, 0), c1);
    draw((d*5/6, d, 0) -- (d*5/6, d, d), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d, d/2), c1);

    //Material parameters label
    framed_label("$\varepsilon_c, \mu_c$", position=(d/2, d/2+r/2, d/2), p=c1);
\end{asypicture}

\begin{asypicture}{name=sphere}
    settings.outformat = "pdf";
    settings.render = 0;
    import graph3;

    real unit = 4cm;
    unitsize(unit);

    currentprojection = orthographic((-4,2.8,-2), up=Y);

    real d = 1;
    real r = 0.45 d;
    real af = 0.5 d;

    pen cubedraw = linewidth(0.8pt) + gray;
    pen cubefill = opacity(0.5) + c1;
    pen axis = linewidth(1.0 pt) + c3;

    //Draw backside of cube
    draw( surface((0,0,d) -- (0,d,d) -- (d,d,d) -- (d,0,d) -- cycle), 
        meshpen = cubedraw, 
        surfacepen = emissive(cubefill));
    draw( surface((0,0,0) -- (0,0,d) -- (d,0,d) -- (d,0,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));
    draw( surface((d,0,0) -- (d,0,d) -- (d,d,d) -- (d,d,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));

    //Draw sphere as surface of revolution
    triple centerpoint = (d/2, d/2, d/2);
    path3 centerline = (centerpoint - r*Y) -- (centerpoint + r*Y);
    path3 to_revolve = Arc(centerpoint - r*Y, centerpoint + r*Y, c=centerpoint, normal=X, n=16);
    surface sphere = surface(to_revolve, c=centerpoint, axis=Y);
    draw(sphere, meshpen = 0.3 c2 + 0.5 gray, 
            surfacepen = material(c2 + opacity(0.7), emissivepen = 0.2 c2));


    //Draw the radius arrow and helper lines
    draw(centerline, 0.8 c2);
    draw(circle(c=(d/2,d/2,d/2), r=r, normal=Y), 0.8 c2);
    draw( (d/2,d/2,d/2) -- (d/2,d/2,d/2+r), c2 + linewidth(0.8), arrow=Arrows3(TeXHead2));
    framed_label("$r$", position=(d/2, d/2, d/2 + r/2), p=c2);

    //Draw front of cube
    draw( (0,0,0) -- (0,d,0) ^^ (d,d,0) -- (0,d,0) ^^ (0,d,d) -- (0,d,0), cubedraw);

    //Draw the axis arrows and annotations
    draw(O -- af*X, axis, arrow=Arrow3(TeXHead2));
    framed_label("$x$", position=(1 + 18pt/unit)*af*X, p=axis);
    draw(O -- af*Y, axis, arrow=Arrow3(TeXHead2));
    framed_label("$y$", position=(1 + 12pt/unit)*af*Y, p=axis);
    draw(O -- af*Z, axis, arrow=Arrow3(TeXHead2));
    framed_label("$z$", position=(1 + 10pt/unit)*af*Z, p=axis);

    //Draw cube lattice length measures
    draw((0,0,d*5/6) -- (0,d,d*5/6), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (0,d/2,d*5/6), c1);
    draw((d*5/6,0,0) -- (d*5/6,d,0), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d/2, 0), c1);
    draw((d*5/6, d, 0) -- (d*5/6, d, d), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d, d/2), c1);

    //Material parameters label
    framed_label("$\varepsilon_c, \mu_c$", position=(d/2, d/2+r/2, d/2), p=c1);
\end{asypicture}

\end{document}

结果如下：

在此处输入图片描述

从技术角度来看，最困难的部分是围绕文本的白色方框；正如你所看到的，我放弃了圆角。

我还要指出的是，如果您愿意使用高分辨率光栅化图形，很多事情都会变得更容易：它会自动确定哪些对象位于其他对象之前（与绘图顺序无关），并且网格线不是必需的。

关于使用 Asymptote 的工作流程的说明：以下是一些可用选项。（所有这些都需要安装可用的 Asymptote，尽管 TeXLive 会自动安装。）

使用启用了选项的标准 latex 命令（例如pdflatex）-shell-escape。这需要asypictureB包。在任何给定的运行中，只有自上次运行以来已更改（或已删除）的图片才会被重新编译。您可以创建一个“公共前言”，该前言在所有 Asymptote 文件（例如颜色定义）之间共享，但 TeX 前言中的定义不会自动延续。
这是我上面建议使用的选项。
使用latexmk脚本，并按照说明扩充配置文件在本文档中。为此，您可能应该使用asymptote包而不是asypictureB，因为包并非设计为以这种方式使用。您仍然可以选择通用的 Asymptote 前言。使用包inline选项asymptote，您还可以访问标签中主文档的所有包和宏。
使用asymptote或asypictureB多次运行分别编译图片。命令序列
pdflatex filename
asy filename-*.asy
pdflatex filename
通常适用于任一包（或两者），尽管每个图像都会重新编译 - 包括自上次运行以来未更改的图像。该包提供了一种比中间行更有效的替代方案asypictureB；请参阅软件包文档，第 2.1 节，第 4 页。

就我个人而言，我更喜欢第一种选择，因为它提供了最好的调试支持。同时，我建议 LaTeX 用户熟悉使用latexmk，因为它可用于自动化整个工作流程，包括制作索引（如果需要）和多次运行以定义标签和目录（同样，仅在必要时；latexmk擅长检测这一点）。

Answer

这是使用 Asymptote 的替代方法。它可以满足您的大多数请求；例如，颜色在序言中定义（但在 Asymptote 代码中而不是 TeX 代码中，因此您可能需要单独定义 TeX 版本）。

% To run: pdflatex --shell-escape filename.tex

\documentclass[margin=10pt,convert]{standalone}
\usepackage{asypictureB}

\begin{asyheader}
pen c1 = rgb(0.2,0.4,0.6); // Blue-ish
pen c2 = rgb(1.0,0.0,0.6); // Pink-ish
pen c3 = rgb(0.6,0.0,0.0); // Red

texpreamble("\newbox\BoxForRules
\newcommand{\boxToRule}[1]{%
    \setbox\BoxForRules=\hbox{\hspace{2pt}#1\hspace{2pt}}%
    $\rlap{\rule[\dimexpr-\dp\BoxForRules-2pt]{\wd\BoxForRules}{\dimexpr\ht\BoxForRules+\dp\BoxForRules+4pt}}\mbox{\hspace{2pt}#1\hspace{2pt}}$%
}");

import three;

void framed_label(string s, triple position, pen p = currentpen) {
    label("\boxToRule{" + s + "}", position=position, p=white + opacity(0.6));
    label(s, position=position, p=p);
}
\end{asyheader}

\begin{document}
\begin{asypicture}{name=cylinder}
    settings.outformat = "pdf";
    settings.render = 0;

    real unit = 4cm;
    unitsize(unit);

    currentprojection = orthographic((-4,2.8,-2), up=Y);

    real d = 1;
    real r = 0.45 d;
    real af = 0.5 d;

    pen cubedraw = linewidth(0.8pt) + gray;
    pen cubefill = opacity(0.5) + c1;
    pen axis = linewidth(1.0 pt) + c3;

    //Draw backside of cube
    draw( surface((0,0,d) -- (0,d,d) -- (d,d,d) -- (d,0,d) -- cycle), 
        meshpen = cubedraw, 
        surfacepen = emissive(cubefill));
    draw( surface((0,0,0) -- (0,0,d) -- (d,0,d) -- (d,0,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));
    draw( surface((d,0,0) -- (d,0,d) -- (d,d,d) -- (d,d,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));

    //Draw cylinder as surface of revolution
    path3 cyl_center = shift(d/2,0,d/2) * (O -- d*Y);
    path3 cyl_edge = shift(r*X) * cyl_center;
    int n = 10;
    guide3 to_revolve = point(cyl_edge, 0);
    for (int i = 1; i <= n; ++i)
        to_revolve = to_revolve -- point(cyl_edge, i/n);
    surface cylinder = surface(to_revolve, c=(d/2,0,d/2), axis=Y);
    draw(cylinder, meshpen = 0.3 c2 + 0.5 gray, 
            surfacepen = material(c2 + opacity(0.7), emissivepen = 0.2 c2));


    //Draw the radius arrow and center line
    draw(cyl_center, 0.8 c2);
    //draw(circle(c=(d/2,d/2,d/2), r=r, normal=Y), 0.8 c2);
    draw( (d/2,d,d/2) -- (d/2,d,d/2+r), c2 + linewidth(0.8), arrow=Arrows3(TeXHead2));
    framed_label("$r$", position=(d/2, d, d/2 + r/2), p=c2);

    //Draw front of cube
    draw( (0,0,0) -- (0,d,0) ^^ (d,d,0) -- (0,d,0) ^^ (0,d,d) -- (0,d,0), cubedraw);

    //Draw the axis arrows and annotations
    draw(O -- af*X, axis, arrow=Arrow3(TeXHead2));
    framed_label("$x$", position=(1 + 18pt/unit)*af*X, p=axis);
    draw(O -- af*Y, axis, arrow=Arrow3(TeXHead2));
    framed_label("$y$", position=(1 + 12pt/unit)*af*Y, p=axis);
    draw(O -- af*Z, axis, arrow=Arrow3(TeXHead2));
    framed_label("$z$", position=(1 + 10pt/unit)*af*Z, p=axis);

    //Draw cube lattice length measures
    draw((0,0,d*5/6) -- (0,d,d*5/6), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (0,d/2,d*5/6), c1);
    draw((d*5/6,0,0) -- (d*5/6,d,0), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d/2, 0), c1);
    draw((d*5/6, d, 0) -- (d*5/6, d, d), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d, d/2), c1);

    //Material parameters label
    framed_label("$\varepsilon_c, \mu_c$", position=(d/2, d/2+r/2, d/2), p=c1);
\end{asypicture}

\begin{asypicture}{name=sphere}
    settings.outformat = "pdf";
    settings.render = 0;
    import graph3;

    real unit = 4cm;
    unitsize(unit);

    currentprojection = orthographic((-4,2.8,-2), up=Y);

    real d = 1;
    real r = 0.45 d;
    real af = 0.5 d;

    pen cubedraw = linewidth(0.8pt) + gray;
    pen cubefill = opacity(0.5) + c1;
    pen axis = linewidth(1.0 pt) + c3;

    //Draw backside of cube
    draw( surface((0,0,d) -- (0,d,d) -- (d,d,d) -- (d,0,d) -- cycle), 
        meshpen = cubedraw, 
        surfacepen = emissive(cubefill));
    draw( surface((0,0,0) -- (0,0,d) -- (d,0,d) -- (d,0,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));
    draw( surface((d,0,0) -- (d,0,d) -- (d,d,d) -- (d,d,0) -- cycle), meshpen = cubedraw, surfacepen = emissive(cubefill));

    //Draw sphere as surface of revolution
    triple centerpoint = (d/2, d/2, d/2);
    path3 centerline = (centerpoint - r*Y) -- (centerpoint + r*Y);
    path3 to_revolve = Arc(centerpoint - r*Y, centerpoint + r*Y, c=centerpoint, normal=X, n=16);
    surface sphere = surface(to_revolve, c=centerpoint, axis=Y);
    draw(sphere, meshpen = 0.3 c2 + 0.5 gray, 
            surfacepen = material(c2 + opacity(0.7), emissivepen = 0.2 c2));


    //Draw the radius arrow and helper lines
    draw(centerline, 0.8 c2);
    draw(circle(c=(d/2,d/2,d/2), r=r, normal=Y), 0.8 c2);
    draw( (d/2,d/2,d/2) -- (d/2,d/2,d/2+r), c2 + linewidth(0.8), arrow=Arrows3(TeXHead2));
    framed_label("$r$", position=(d/2, d/2, d/2 + r/2), p=c2);

    //Draw front of cube
    draw( (0,0,0) -- (0,d,0) ^^ (d,d,0) -- (0,d,0) ^^ (0,d,d) -- (0,d,0), cubedraw);

    //Draw the axis arrows and annotations
    draw(O -- af*X, axis, arrow=Arrow3(TeXHead2));
    framed_label("$x$", position=(1 + 18pt/unit)*af*X, p=axis);
    draw(O -- af*Y, axis, arrow=Arrow3(TeXHead2));
    framed_label("$y$", position=(1 + 12pt/unit)*af*Y, p=axis);
    draw(O -- af*Z, axis, arrow=Arrow3(TeXHead2));
    framed_label("$z$", position=(1 + 10pt/unit)*af*Z, p=axis);

    //Draw cube lattice length measures
    draw((0,0,d*5/6) -- (0,d,d*5/6), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (0,d/2,d*5/6), c1);
    draw((d*5/6,0,0) -- (d*5/6,d,0), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d/2, 0), c1);
    draw((d*5/6, d, 0) -- (d*5/6, d, d), p=linewidth(0.8pt) + c1, arrow=Arrows3(TeXHead2));
    framed_label("$d$", (d*5/6, d, d/2), c1);

    //Material parameters label
    framed_label("$\varepsilon_c, \mu_c$", position=(d/2, d/2+r/2, d/2), p=c1);
\end{asypicture}

\end{document}

结果如下：

在此处输入图片描述

从技术角度来看，最困难的部分是围绕文本的白色方框；正如你所看到的，我放弃了圆角。

我还要指出的是，如果您愿意使用高分辨率光栅化图形，很多事情都会变得更容易：它会自动确定哪些对象位于其他对象之前（与绘图顺序无关），并且网格线不是必需的。

关于使用 Asymptote 的工作流程的说明：以下是一些可用选项。（所有这些都需要安装可用的 Asymptote，尽管 TeXLive 会自动安装。）

使用启用了选项的标准 latex 命令（例如pdflatex）-shell-escape。这需要asypictureB包。在任何给定的运行中，只有自上次运行以来已更改（或已删除）的图片才会被重新编译。您可以创建一个“公共前言”，该前言在所有 Asymptote 文件（例如颜色定义）之间共享，但 TeX 前言中的定义不会自动延续。
这是我上面建议使用的选项。
使用latexmk脚本，并按照说明扩充配置文件在本文档中。为此，您可能应该使用asymptote包而不是asypictureB，因为包并非设计为以这种方式使用。您仍然可以选择通用的 Asymptote 前言。使用包inline选项asymptote，您还可以访问标签中主文档的所有包和宏。
使用asymptote或asypictureB多次运行分别编译图片。命令序列
pdflatex filename
asy filename-*.asy
pdflatex filename
通常适用于任一包（或两者），尽管每个图像都会重新编译 - 包括自上次运行以来未更改的图像。该包提供了一种比中间行更有效的替代方案asypictureB；请参阅软件包文档，第 2.1 节，第 4 页。

就我个人而言，我更喜欢第一种选择，因为它提供了最好的调试支持。同时，我建议 LaTeX 用户熟悉使用latexmk，因为它可用于自动化整个工作流程，包括制作索引（如果需要）和多次运行以定义标签和目录（同样，仅在必要时；latexmk擅长检测这一点）。

Question 2

球体和立方体的中心位于 (0,0,0)。取消注释以查看内部坐标系。使用或\axesIIID运行示例，或者使用需要的 pdflatex 。xelatexlatex->dvisps->ps2pdf\usepackage[crop=off]{auto-pst-pdf}

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\begin{document}

\psset{viewpoint=30 40 20 rtp2xyz,Decran=30}
  \begin{pspicture}(-3.5,-3.5)(3.5,3.5)
%  \axesIIID(2,2,2)(4,4,4)
   \psSolid[object=cube,a=4,fillcolor=blue,opacity=0.2,action=draw*]%
   \psSolid[object=sphere,r=1.5,linewidth=0.1pt,ngrid=20 20,fillcolor=red,opacity=0.2,action=draw*]%
   \psSolid[object=vecteur,args=0 -2 0](2,2,-2)
   \psSolid[object=vecteur,args=-2 0 0](2,2,-2)
   \psSolid[object=vecteur,args=0 0 2](2,2,-2)
   \psPoint(2,2,0.2){Z}\rput(Z){z}\psPoint(2,-0.2,-2){X}\rput(X){x}\psPoint(-0.2,2,-2){Y}\rput(Y){y}
   \psPoint(2,-1.6,-2){a1}\psPoint(2,-1.6,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(2,-1.6,2){a1}\psPoint(-2,-1.6,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(-1.6,2,-2){a1}\psPoint(-1.6,2,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(0,0,0){a1}\psPoint(1,-1,0){a2}\pcline{->}(a1)(a2)\ncput*{r}
  \end{pspicture}

\end{document}

在此处输入图片描述

Answer

球体和立方体的中心位于 (0,0,0)。取消注释以查看内部坐标系。使用或\axesIIID运行示例，或者使用需要的 pdflatex 。xelatexlatex->dvisps->ps2pdf\usepackage[crop=off]{auto-pst-pdf}

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\begin{document}

\psset{viewpoint=30 40 20 rtp2xyz,Decran=30}
  \begin{pspicture}(-3.5,-3.5)(3.5,3.5)
%  \axesIIID(2,2,2)(4,4,4)
   \psSolid[object=cube,a=4,fillcolor=blue,opacity=0.2,action=draw*]%
   \psSolid[object=sphere,r=1.5,linewidth=0.1pt,ngrid=20 20,fillcolor=red,opacity=0.2,action=draw*]%
   \psSolid[object=vecteur,args=0 -2 0](2,2,-2)
   \psSolid[object=vecteur,args=-2 0 0](2,2,-2)
   \psSolid[object=vecteur,args=0 0 2](2,2,-2)
   \psPoint(2,2,0.2){Z}\rput(Z){z}\psPoint(2,-0.2,-2){X}\rput(X){x}\psPoint(-0.2,2,-2){Y}\rput(Y){y}
   \psPoint(2,-1.6,-2){a1}\psPoint(2,-1.6,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(2,-1.6,2){a1}\psPoint(-2,-1.6,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(-1.6,2,-2){a1}\psPoint(-1.6,2,2){a2}\pcline{<->}(a1)(a2)\ncput*{d}
   \psPoint(0,0,0){a1}\psPoint(1,-1,0){a2}\pcline{->}(a1)(a2)\ncput*{r}
  \end{pspicture}

\end{document}

在此处输入图片描述

使用 Tikz 的 3D 实体-或者其他替代方案？

答案1

答案2

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