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표면이 있는 3D 큐브

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표면이 있는 3D 큐브

여기에 표시된 대로 원자의 배열을 보여주는 단위 껍질을 그리고 싶습니다. (Zumdahl, 화학 원리, 5판, Houghton Mifflin, p. 773.)

나는 원자 면(위의 큐브)을 그리는 다음 코드를 생각해 냈습니다. 큐비클 면을 한 번만 정의하면 된다는 아이디어를 사용합니다. 그런 다음 기울어져 다른 면을 그릴 수 있습니다. 그러나 나는 음영(잘린 구)을 (수학적으로) 그리는 방법을 모릅니다. 제안?

가능하다면 큐비클 측면을 하나만 정의하는 아이디어를 사용하세요. 위의 모든 예와 더 많은 예를 그려야 하기 때문에 매우 편리합니다(예제에 두 개의 면을 추가했습니다). 그러나 이것이 가능하지 않은 경우 다른 솔루션을 사용하는 것이 좋습니다. 솔루션을 회전할 수 없습니다.

\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}

답변1

이것은 결과의 반대 부분입니다.

아이디어는 다음에서 비롯됩니다.이 예구에 자오선/위도 원을 그리는 것입니다. 해당 호를 그리는 대신 클리핑 경로로 사용합니다.일부 작품호를 서로 연결하려면 필요합니다.

\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}

답변2

드디어 왔습니다! 다음 코드에 주석을 달고 주석을 제거하여 세 개의 큐브를 모두 생성할 수 있습니다.

대답은 기본적으로기호 1의 답, 수정만 되었습니다. spath패키지를 수동으로 설치해야 합니다.여기에 알려드린 대로.

코드에서 주석 처리된 섹션은 디버깅(클리핑할 경로 그리기)을 위한 것입니다.

최종 결과는 만족스럽습니다. 그러나 두 개의 반구가 있는 가운데 이미지의 잘못된 스택 및 음영에 유의하십시오.

여기에 이미지 설명을 입력하세요

\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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