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cubo 3d con una superficie

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cubo 3d con una superficie

Quiero dibujar una capa unitaria que muestre la disposición de los átomos como se muestra aquí. (Zumdahl, Principios químicos, 5ed., Houghton Mifflin, p. 773.)

Se me ocurrió el siguiente código que dibuja las caras de los átomos (los cubos de arriba). Utiliza la idea de que sólo hay que definir la cara de un cubículo una vez: luego se puede inclinar para dibujar las otras caras. Sin embargo, no tengo ni idea de cómo dibujar (matemáticamente) las sombras (las esferas recortadas). ¿Sugerencias?

Si es posible, utilice la idea de definir sólo un lado del cubículo. Es muy conveniente ya que tendré que dibujar todos los ejemplos anteriores y posiblemente más (agregué dos caras al ejemplo). No obstante, si esto no es posible, se agradecen otras soluciones. No se puede rotar la solución.

\documentclass{minimal}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\pgfmathsetmacro{\D}{4}
\pgfmathsetmacro{\halfD}{\D/2}

\newcommand{\mycubicleface}{
    \pgfmathsetmacro{\R}{\D/2}
    \draw [fill=blue!30] (0,\R) arc [start angle=90, end angle=0, radius=\R] -- +(-\R,0);
    \draw [fill=blue!30] (0,\R) arc [start angle=-90, end angle=0, radius=\R] -- +(-\R,0);
    \draw [fill=blue!30] (\D,\R) arc [start angle=-90, end angle=-180, radius=\R] -- +(\R,0);
    \draw [fill=blue!30] (\D,\R) arc [start angle=90, end angle=180, radius=\R] -- +(\R,0);
    \draw (0,0) rectangle +(\D,\D);
}

%\newcommand{\mycubicleface}{
%   \pgfmathsetmacro{\R}{\D/sqrt(8)}    
%   \draw [fill=blue!30] (\D/2,\D/2) circle [radius=\R];
%   \draw [fill=blue!30] (0,\R) arc [start angle=90, end angle=0, radius=\R] -- +(-\R,0);
%   \draw [fill=blue!30] (0,\D - \R) arc [start angle=-90, end angle=0, radius=\R] -- +(-\R,0);
%   \draw [fill=blue!30] (\D,\D - \R) arc [start angle=-90, end angle=-180, radius=\R] -- +(\R,0);
%   \draw [fill=blue!30] (\D,\R) arc [start angle=90, end angle=180, radius=\R] -- +(\R,0);
%   \draw (0,0) rectangle +(\D,\D);
%}

\begin{scope}[yslant=-.5]
    \mycubicleface
\end{scope}
\begin{scope}[xshift=\D cm, yshift=-\halfD cm, yslant=.5]
    \mycubicleface
\end{scope}
\begin{scope}[xshift=\D cm, yshift=\halfD cm, yslant=.5, xslant=-1]
    \mycubicleface
\end{scope}

\end{tikzpicture}
\end{document}

Respuesta1

Esta es la contraparte de su resultado.

La idea surge deeste ejemploque dibuja algunos meridianos/círculo de latitud en una esfera. En lugar de dibujar esos arcos, los uso como trazado de recorte.Algunas obrasSe necesitan para conectar los arcos.

\documentclass[tikz]{standalone} 
\usepackage{tikz,spath}
    \usetikzlibrary{calc,fadings}

\newcommand\pgfmathsinandcos[3]{
    \pgfmathsetmacro#1{sin(#3)}\pgfmathsetmacro#2{cos(#3)}}

\newcommand\LongitudePlane[3][current plane]{
    \pgfmathsinandcos\sinEl\cosEl{#2}\pgfmathsinandcos\sint\cost{#3}
    \tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}}

\newcommand\LatitudePlane[3][current plane]{%
    \pgfmathsinandcos\sinEl\cosEl{#2}\pgfmathsinandcos\sint\cost{#3}
    \pgfmathsetmacro\yshift{\cosEl*\sint}
    \tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}}}

\newcommand\ClipLongitudeCircle[2]{
    \LongitudePlane\angEl{#1}
    \pgfmathsetmacro\angVis{atan(sin(#1)*cos(\angEl)/sin(\angEl))}
    \path[save path=\tmppath,current plane](\angVis:\R)arc(\angVis:\angVis+180:\R);
    \pgfoonew\patha=new spath(\tmppath)
    \pgfmathsetmacro\angVis{-atan(sin(\angEl)*cos(#1)/sin(#1))}
    \path[save path=\tmppath](-90+\angVis:\R)arc(-90+\angVis:#2180-90+\angVis:\R);
    \pgfoonew\pathb=new spath(\tmppath)
    \patha.concatenate with lineto(,\pathb)\patha.close()\patha.use path with tikz(clip)}

\newcommand\ClipLatitudeCircle[2]{
    \LatitudePlane{\angEl}{#1}
    \path[save path=\tmppath,current plane](-180:\R)arc(-180:0:\R);
    \pgfoonew\patha=new spath(\tmppath)
    \path[save path=\tmppath](0:\R)arc(0:#2180:\R);
    \pgfoonew\pathb=new spath(\tmppath)
    \patha.concatenate with lineto(,\pathb)\patha.close()\patha.use path with tikz(clip)}

\newcommand\EighthSphere[3]{
    \ClipLongitudeCircle{45-\angPh}{#1}
    \ClipLongitudeCircle{135-\angPh}{#2}
    \ClipLatitudeCircle{0}{#3}
    \fill[ball color=white](0,0)circle(\R);}

\begin{document}
\def\R{6} % sphere radius
\def\angEl{20} % elevation angle in interval [1,89]
\def\angPh{10} % phase angle in interval [-44,44]
\pgfmathsetmacro\uofx{cos(-135-\angPh)}
\pgfmathsetmacro\vofx{sin(-135-\angPh)*sin(\angEl)}
\pgfmathsetmacro\uofy{cos(-45-\angPh)}
\pgfmathsetmacro\vofy{sin(-45-\angPh)*sin(\angEl)}
\pgfmathsetmacro\uofz{0}
\pgfmathsetmacro\vofz{cos(\angEl)}
\begin{tikzpicture}
    \begin{scope}[x={(\uofx cm,\vofx cm)},y={(\uofy cm,\vofy cm)},z={(\uofz cm,\vofz cm)}]
        \path(-6,-6,-6)coordinate(A){}(6,6,6)coordinate(B){};
        \path(6,-6,-6)coordinate(P){}(6,6,-6)coordinate(Q){}(-6,6,-6)coordinate(R){}
             (-6,6,6)coordinate(S){}(-6,-6,6)coordinate(T){}(6,-6,6)coordinate(U){};
    \end{scope}
    \path(-12,-12)(12,12);
    \draw(P)--(Q)--(R)--(S)--(T)--(U)--cycle;
    \clip(P)--(Q)--(R)--(S)--(T)--(U)--cycle;
    \begin{scope}[transform canvas={shift=(A)}]
        \EighthSphere{+}{-}{+}
    \end{scope}
    \begin{scope}[transform canvas={shift=(P)}]
        \EighthSphere{+}{+}{+}
    \end{scope}
    \begin{scope}[transform canvas={shift=(R)}]
        \EighthSphere{-}{-}{+}
    \end{scope}
    \begin{scope}[transform canvas={shift=(T)}]
        \EighthSphere{+}{-}{-}
    \end{scope}
    \begin{scope}[transform canvas={shift=(Q)}]
        \EighthSphere{-}{+}{+}
    \end{scope}
    \begin{scope}[transform canvas={shift=(S)}]
        \EighthSphere{-}{-}{-}
    \end{scope}
    \begin{scope}[transform canvas={shift=(U)}]
        \EighthSphere{+}{+}{-}
    \end{scope}
\end{tikzpicture}
\end{document}

Respuesta2

¡Aquí está finalmente! Puede producir los tres cubos comentando y descomentando el siguiente código.

La respuesta es básicamentela respuesta del símbolo 1, sólo modificado. Tenga en cuenta que necesita instalar spathel paquete manualmentecomo se informa aquí.

Las secciones comentadas en el código son para depurar (dibujar las rutas que se van a recortar).

El resultado final es satisfactorio. Sin embargo, tenga en cuenta el apilamiento y el sombreado incorrectos en la imagen del medio con las dos medias esferas.

ingrese la descripción de la imagen aquí

\documentclass[tikz]{standalone} 
\usepackage{spath}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{fadings}

\begin{document}

% Source: LaTeX-Community.org 
%         <http://www.latex-community.org/viewtopic.php?f=4&t=2111>
\begin{tikzpicture}
\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/.style={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/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}}
}

%\newcommand\DrawLongitudeCircle[2][4]{
%  \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] (\angVis:\R) arc (\angVis:\angVis+180:\R);
%  \draw[current plane, blue] (\angVis-180:\R) arc (\angVis-180:\angVis:\R);
%}

%\newcommand\DrawLatitudeCircle[2][5]{
%  \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] (\angVis:\R) arc (\angVis:-\angVis-180:\R);
%  \draw[current plane, red] (180-\angVis:\R) arc (180-\angVis:\angVis:\R);
%}

\newcommand\ClipLongitudeCircle[2]{
    \LongitudePlane{\angEl}{#1}
    \pgfmathsetmacro\angVis{atan(sin(#1)*cos(\angEl)/sin(\angEl))}
    \path[save path=\tmppath, current plane] (\angVis:\R) arc (\angVis:\angVis+180:\R); % current plane transformation
    \pgfoonew\patha=new spath(\tmppath)
    \pgfmathsetmacro\angVis{-atan(sin(\angEl)*cos(#1)/sin(#1))}
    \path[save path=\tmppath] (-90+\angVis:\R) arc (-90+\angVis:#2 180-90+\angVis:\R); % no coordinate transform (no current plane)
    \pgfoonew\pathb=new spath(\tmppath)
    \patha.concatenate with lineto(,\pathb)
    \patha.close()
    \patha.use path with tikz(clip)
%   \patha.use path with tikz(fill=magenta, opacity=.2)
%   \patha.use path with tikz(draw=magenta, very thick)
}

\newcommand\ClipLatitudeCircle[2]{
    \LatitudePlane{\angEl}{#1}
    \path[save path=\tmppath,current plane] (-180:\R) arc (-180:0:\R);
    \pgfoonew\patha=new spath(\tmppath)
    \path[save path=\tmppath] (0:\R) arc (0:#2 180:\R);
    \pgfoonew\pathb=new spath(\tmppath)
    \patha.concatenate with lineto(,\pathb)
    \patha.close()
    \patha.use path with tikz(clip)
%   \patha.use path with tikz(fill=cyan, opacity=.2)
%   \patha.use path with tikz(draw=cyan, very thick)
}

\newcommand\ClippedEightSphere[4]{
\begin{scope}[transform canvas={shift=(#4)}]
    \ClipLongitudeCircle{45-\angPh}{#1}
    \ClipLongitudeCircle{135-\angPh}{#2}
    \ClipLatitudeCircle{0}{#3}
    \fill[ball color=white] (0,0) circle (\R);
\end{scope}}

\newcommand\ClippedLatitudeSphere[3]{
\begin{scope}[transform canvas={shift=(#1)}]
    \LatitudePlane{\angEl}{#2}
    \ClipLatitudeCircle{0}{#3}
    \fill[ball color=white] (0,0) circle [radius=\R];
\end{scope}}

\newcommand\ClippedLongitudeSphere[3]{
\begin{scope}[transform canvas={shift=(#1)}]
    \LongitudePlane{\angEl}{#2}
    \ClipLongitudeCircle{#2}{#3}
    \fill[ball color=white] (0,0) circle [radius=\R];
\end{scope}}

\newcommand\DrawLongitudeArc[4]{
    \LongitudePlane{\angEl}{#2}
    \begin{scope}[current plane, transform canvas={shift=(#1)}]
    \fill [cyan] (0,0) -- ++(#3:\R) arc [start angle=#3, delta angle=#4, radius=\R] -- cycle;
    \draw ++(#3:\R) arc [start angle=#3, delta angle=#4, radius=\R];
    \end{scope}}

\newcommand\DrawLatitudeArc[4]{
    \LatitudePlane{\angEl}{#2}
    \begin{scope}[current plane, transform canvas={shift=(#1)}]
    \fill [cyan] (0,0) -- ++(#3:\R) arc [start angle=#3, delta angle=#4, radius=\R] -- cycle;
    \draw ++(#3:\R) arc [start angle=#3, delta angle=#4, radius=\R];
    \end{scope}}



    \def\D{8} % cubic side length
%   \pgfmathsetmacro\R{\D/2} % sphere radius
    \pgfmathsetmacro\R{sqrt(2)/4*\D} % sphere radius
%   \pgfmathsetmacro\R{sqrt(3)/4*\D} % sphere radius
    \def\angEl{20} % elevation angle in interval [1,89]
    \def\angPh{10} % phase angle in interval [-44,44]
    \pgfmathsetmacro\uofx{cos(-135-\angPh)}
    \pgfmathsetmacro\vofx{sin(-135-\angPh)*sin(\angEl)}
    \pgfmathsetmacro\uofy{cos(-45-\angPh)}
    \pgfmathsetmacro\vofy{sin(-45-\angPh)*sin(\angEl)}
    \pgfmathsetmacro\uofz{0}
    \pgfmathsetmacro\vofz{cos(\angEl)}

    % The coordinates of the cube
    \begin{scope}[x={(\uofx cm,\vofx cm)}, y={(\uofy cm,\vofy cm)}, z={(\uofz cm,\vofz cm)}]
    \coordinate (C1) at (\D,0,0);
    \coordinate (C2) at (\D,0,\D);
    \coordinate (C3) at (0,0,\D);
    \coordinate (C4) at (0,\D,\D);
    \coordinate (C5) at (0,\D,0);
    \coordinate (C6) at (\D,\D,0);
    \coordinate (C7) at (0,0,0);
    \coordinate (C8) at (\D,\D,\D);
%    \foreach \n in {1,2,...,8} \node at (C\n) {C\n};

    \coordinate (C0) at ($(C2)!.5!(C5)$);
    \coordinate (S1) at ($(C2)!.5!(C6)$);
    \coordinate (S2) at ($(C2)!.5!(C4)$);
    \coordinate (S3) at ($(C8)!.5!(C5)$);
    \coordinate (S4) at ($(C6)!.5!(C7)$);
    \coordinate (S5) at ($(C1)!.5!(C3)$);
    \coordinate (S6) at ($(C5)!.5!(C3)$);
    \end{scope}

    % Draw the clipped spheres
    \ClippedEightSphere{+}{-}{+}{C7}
    \ClippedLongitudeSphere{S5}{45-\angPh}{+}
    \ClippedLongitudeSphere{S6}{135-\angPh}{-}
    \ClippedLatitudeSphere{S4}{0}{+}

    \ClippedEightSphere{-}{+}{-}{C8}
    \ClippedEightSphere{+}{-}{-}{C3}
    \ClippedEightSphere{+}{+}{-}{C2}
%   \fill[ball color=white] (C0) circle [radius=\R];
    \ClippedEightSphere{-}{-}{-}{C4}
    \ClippedEightSphere{+}{+}{+}{C1}
    \ClippedEightSphere{-}{-}{+}{C5}
    \ClippedEightSphere{-}{+}{+}{C6}

    % Draw the half spheres
    \ClippedLatitudeSphere{S2}{0}{-}
    \ClippedLongitudeSphere{S3}{45-\angPh}{-}
    \ClippedLongitudeSphere{S1}{135-\angPh}{+}
    \DrawLatitudeArc{S2}{0}{0}{360}
    \DrawLongitudeArc{S1}{135-\angPh}{0}{360}
    \DrawLongitudeArc{S3}{45-\angPh}{0}{360}

    % Draw the Arcs
    \DrawLongitudeArc{C1}{135-\angPh}{90}{90}
    \DrawLongitudeArc{C2}{135-\angPh}{-90}{-90}
    \DrawLongitudeArc{C4}{45-\angPh}{-90}{-90}
    \DrawLongitudeArc{C5}{45-\angPh}{90}{90}
    \DrawLongitudeArc{C6}{135-\angPh}{90}{-90}
    \DrawLongitudeArc{C6}{45-\angPh}{90}{-90}
    \DrawLongitudeArc{C8}{135-\angPh}{-90}{90}
    \DrawLongitudeArc{C8}{45-\angPh}{-90}{90}
    \DrawLatitudeArc{C2}{0}{45-\angPh}{-90}
    \DrawLatitudeArc{C3}{0}{-45-\angPh}{-90}
    \DrawLatitudeArc{C4}{0}{135-\angPh}{90}
    \DrawLatitudeArc{C8}{0}{135-\angPh}{-90}

    % Draw the cube
    \draw (C1)--(C2)--(C3)--(C4)--(C5)--(C6)--cycle;
    \draw (C2)--(C8)--(C6);
    \draw (C8)--(C4);

    % Radius node
    \coordinate (r) at ($(C2) - (\R/10,0)$);
    \LongitudePlane{\angEl}{135-\angPh}
    \draw [<->, current plane] (r) -- node [left] {$r$} +(-90:\R);

\end{tikzpicture}

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