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Tikz：如何控制 3D 图片的长度？

tag-icon • tag-icon tikz-pgf 3d
Tikz：如何控制 3D 图片的长度？

我尝试使用带有等距投影或斜投影（法语中为 perpective cavalière）的 tikz 绘制一个球体。

对于斜投影，您必须在 x 轴上放置一个距离的缩放因子（scal < 1）。但如果我希望我的球体看起来像一个不扭曲的球体，我必须将缩放比例设为零。因此，我获得了 (yz) 平面中的投影。以下是我的 tikz 源代码，您可以轻松地在等距投影和斜投影之间切换：

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{}

\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{2mm}

\tikzstyle{cavaliere} = [x={(-0.866cm,-0.5cm)},y={(1cm,0cm)},z={(0cm,1cm)}]
\tikzstyle{isometrique} = [x={(-0.866cm,-0.5cm)},y={(0.866cm,-0.5cm)},z={(0cm,1cm)}]
\tikzstyle{mesh} = [color=gray, opacity=0.4]

\begin{document}

%
% norm selection :
%
%   if(isometrique)
%
\begin{tikzpicture}[isometrique]
       \def\scal{1.}

%   else if(cavaliere)
%
%\begin{tikzpicture}[cavaliere]
%       \def\scal{0.3}
%

    \coordinate (O) at (0,0,0);
    \draw[->] (O) -- ({\scal * 3},0,0) node[below] {x};
    \draw[->] (O) -- (0,3,0) node[below] {y};
    \draw[->] (O) -- (0,0,3) node[right] {z};

    \def\r{2.}

    % meridiens
    % \rho joue le role de theta    
    \foreach \phi in {0,10,...,170} {
        \draw[mesh] ({\scal * \r * cos(\phi)}, {\r * sin(\phi)}, 0)
            \foreach \rho in {5,10,...,360} {
                --({\scal * \r * cos(\phi) * cos(\rho)}, {\r * sin(\phi) * cos(\rho)}, {\r * sin(\rho)})
        } -- cycle;
    }

    % parallels
    \foreach \rho in {-60, -40, -19.57, 0, 19.57, 40, 60} {
        \draw[mesh] ({\scal * \r * cos(\rho)}, 0, {\r * sin(\rho)}) 
            \foreach \phi in {5,10,...,360} {
                -- ({\scal * \r * cos(\rho) * cos(\phi)}, {\r * cos(\rho) * sin(\phi)}, {\r * sin(\rho)})
            } -- cycle;
    }
\end{tikzpicture}

\end{document}

你知道如何在斜投影中绘制正确的球体吗？我更喜欢那个，因为我放入球体中的视图比等距投影更好。

谢谢

编辑：轴 z 垂直

\begin{tikzpicture}[x={(-0.385cm,-0.385cm)},y={(1cm,0cm)},z={(0cm,1cm)},scale=4]

\coordinate (O) at (0,0,0);
\draw[->] (O) -- (2,0,0) node[below] {x};
\draw[->] (O) -- (0,2,0) node[below] {y};
\draw[->] (O) -- (0,0,2) node[right] {z};

\foreach \z in {-0.98,-0.96,...,0.98}  {%
 \begin{scope}[canvas is xy plane at z=\z]
    \draw[gray] (0,0) circle ({sqrt(1-\z*\z)});
  \end{scope}} 

\begin{scope}[canvas is zy plane at x=0]
   \draw (0,0) circle (1cm);
   \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}

\begin{scope}[canvas is zx plane at y=0]
   \draw (0,0) circle (1cm);
   \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}

\begin{scope}[canvas is xy plane at z=0]
   \draw (0,0) circle (1cm);
   \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}       

\end{tikzpicture}

因此我得到了

在此处输入图片描述

答案1

简单的代码，最好使用arc和来确定可见部分。

我认为结果是这样的：

  \documentclass{article} 
  \usepackage{tikz} 
  \usetikzlibrary{3D} 

  \pagestyle{empty} 

  \begin{document}  
   \begin{tikzpicture}[scale=4]

  \foreach \z in {-0.98,-0.96,...,0.98}  {%
     \begin{scope}[canvas is xy plane at z=\z]
        \draw[gray] (0,0) circle ({sqrt(1-\z*\z)});
      \end{scope}}     

  \begin{scope}[canvas is zy plane at x=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}

  \begin{scope}[canvas is zx plane at y=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}

  \begin{scope}[canvas is xy plane at z=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}       

   \end{tikzpicture}  
  \end{document}

在此处输入图片描述

如何改变轴

如果面向观察者的平面是 yz ，后退轴是 x ，那么一个点的投影如下：

 y'= y + 1/2  cos(a) x 
 z'= z + 1/2  sin(a) x

如果您想要 k=0.5 和 a=45°，则需要像这样更改系统：

                   x = { ({-0.5*cos(45)},{-0.5*sin(45)})},
                   y = { (1cm,0cm)},
                   z = { (0cm,1cm)}

所以 x =(-0.35355,-0.35355)。我不知道为什么在 pgf 中 z =(-0.385,-0.385)。

可以尝试 a=30 度或 a=60 度。

  \documentclass{article} 
  \usepackage{tikz} 
  \usetikzlibrary{3D} 

  \pagestyle{empty} 

  \begin{document}  
   \begin{tikzpicture}[x = { ({-0.5*cos(45)},{-0.5*sin(45)})},
                       y = { (1cm,0cm)},
                       z = { (0cm,1cm)},
                       scale = 4]

  \foreach \x in {-0.98,-0.96,...,0.98}  {%
     \begin{scope}[canvas is zy plane at x=\x]
        \draw[gray] (0,0) circle ({sqrt(1-\x*\x)});
      \end{scope}}     

  \begin{scope}[canvas is zy plane at x=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}

  \begin{scope}[canvas is zx plane at y=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}

  \begin{scope}[canvas is xy plane at z=0]
     \draw (0,0) circle (1cm);
     \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
  \end{scope}       

   \end{tikzpicture}

  \end{document}

在此处输入图片描述

答案2

这是我从 altermundus 中改编的代码：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{3d}
\begin{document}
\begin{tikzpicture}[x={({cos(135)},{-sin(45)})},y={(1cm,0cm)},z={(0cm,1cm)},scale=4]

\coordinate (O) at (0,0,0);
\draw[->] (O) -- (2,0,0) node[below] {x};
\draw[->] (O) -- (0,2,0) node[below] {y};
\draw[->] (O) -- (0,0,2) node[right] {z};

\foreach \z in {-0.98,-0.96,...,0.98}  {%
 \begin{scope}[canvas is xy plane at z=\z]
    \draw[gray] (0,0) circle ({sqrt(1-\z*\z)});
  \end{scope}} 

\begin{scope}[canvas is zy plane at x=0]
   \draw (0,0) circle (1cm);
   \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}

\begin{scope}[canvas is zx plane at y=0]
  \draw (0,0) circle (1cm);
  \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope} 

\begin{scope}[canvas is xy plane at z=0]
  \draw (0,0) circle (1cm);
  \draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}       

\end{tikzpicture}  
\end{document}

我尝试将 z 垂直放置在页面上的 y 上，将 x 垂直放置在页面上，但看起来不太好，如下所示：

在此处输入图片描述

这很奇怪，因为在 altermundus 图上，z 轴似乎与垂直方向成 45° 角。

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