3D 中的路径裁剪仅在三个平面中的两个平面中有效？

Question

在下面的代码中，我尝试在三个正交平面上绘制三个剪裁圆。我使用这方法来裁剪圆的适当部分。这在 xy 和 yz 平面上效果很好，但在 xz 平面上效果不佳，如输出所示。

根据输出，我似乎犯了一个简单的错误，但我就是找不到它。我尝试检查示波器中 xz 平面（红色圆圈）的坐标，它们似乎是正确的。我附上了三张图，显示了每个示波器的剪切路径。（绘制的剪切路径显示了一些小错误，但这些与问题无关。）任何帮助查找错误的帮助都将不胜感激。

一些可能使代码更清晰的数学属性：

• 盒子的中心是点 (1,1,1)
• 绘制的轴交于 (1,1,1)，而不是原点，因此图形本质上移动了 [1,1,1]
• 所有圆都以中心点 (1,1,1) 为同心圆
• 圆的半径是 2

---

\documentclass[11pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz,tikz-3dplot}
    \usetikzlibrary{arrows}

\begin{document}

\definecolor{darkgreen}{rgb}{0.1,0.7,0.1}
\tdplotsetmaincoords{60}{125}

\begin{tikzpicture}[tdplot_main_coords,>=latex]

    \pgfsetlinewidth{0.8}

    \tdplotsetcoord{P}{3.4641}{54.74}{45}

    % box
    \draw[fill=black!10] (Px) -- (Pxy) -- (Py) -- (Pyz) -- (Pz) -- (Pxz) -- cycle;
    \draw (Pxy)  --  (P);
    \draw (Pxz)  --  (P);
    \draw (Pyz)  --  (P);

    \pgfsetlinewidth{1.4}

    \begin{scope} % blue circle, xy plane
        \color{blue}
        \tikzstyle{reverseclip}=[insert path={(3.1,3.1,1) -- (-1.1,3.1,1) -- (-1,-1.1,1) -- (3.1,-1.1,1) -- (3.1,3.1,1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (1.3,-1.1,1) -- (-1.1,-1.1,1) -- (-1.1,2,1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{2}{0}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % green circle, yz plane
        \color{darkgreen}
        \tikzstyle{reverseclip}=[insert path={(1,3.1,3.1) -- (1,3.1,-1.1) -- (1,-1.1,-1.1) -- (1,-1.1,3.1) -- (1,3.1,3.1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (1,-1.1,1.8) -- (1,-1.1,-1.1) -- (1,1.7,-1.1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{0}{2}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % red circle, xz plane
        \color{red}
        \tikzstyle{reverseclip}=[insert path={(3.1,1,3.1) -- (-1.1,1,3.1) -- (-1.1,1,-1.1) -- (3.1,1,-1.1) -- (3.1,1,3.1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (-1.1,1,2) -- (-1.1,1,-1.1) -- (1.5,1,-1.1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    % axes
    \draw[line width=0.8pt,->]  (2,1,1)  --  (4,1,1)  node[anchor=north  east]{\textbf{x}};
    \draw[line width=0.8pt,->]  (1,2,1)  --  (1,4,1)  node[anchor=north  west]{\textbf{y}};
    \draw[line width=0.8pt,->]  (1,1,2)  --  (1,1,4)  node[anchor=south]{\textbf{z}};

\end{tikzpicture}

\end{document}

---

Answer 1

使用

\path[clip] (1.5,1,-1.1) -- (-1.1,1,-1.1) -- (-1.1,1,2) -- (1,1,1) -- cycle [reverseclip];

在最后一种情况下，反转剪切路径的方向。

\documentclass[11pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz,tikz-3dplot}
    \usetikzlibrary{arrows}

\begin{document}

\definecolor{darkgreen}{rgb}{0.1,0.7,0.1}
\tdplotsetmaincoords{60}{125}

\begin{tikzpicture}[tdplot_main_coords,>=latex]

    \pgfsetlinewidth{0.8}

    \tdplotsetcoord{P}{3.4641}{54.74}{45}

    % box
    \draw[fill=black!10] (Px) -- (Pxy) -- (Py) -- (Pyz) -- (Pz) -- (Pxz) -- cycle;
    \draw (Pxy)  --  (P);
    \draw (Pxz)  --  (P);
    \draw (Pyz)  --  (P);

    \pgfsetlinewidth{1.4}

    \begin{scope} % blue circle, xy plane
        \color{blue}
        \tikzstyle{reverseclip}=[insert path={(3.1,3.1,1) -- (-1.1,3.1,1) -- (-1,-1.1,1) -- (3.1,-1.1,1) -- (3.1,3.1,1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (1.3,-1.1,1) -- (-1.1,-1.1,1) -- (-1.1,2,1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{2}{0}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % green circle, yz plane
        \color{darkgreen}
        \tikzstyle{reverseclip}=[insert path={(1,3.1,3.1) -- (1,3.1,-1.1) -- (1,-1.1,-1.1) -- (1,-1.1,3.1) -- (1,3.1,3.1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (1,-1.1,1.8) -- (1,-1.1,-1.1) -- (1,1.7,-1.1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{0}{2}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % red circle, xz plane
        \color{red}
        \tikzstyle{reverseclip}=[insert path={(3.1,1,3.1) -- (-1.1,1,3.1) -- (-1.1,1,-1.1) -- (3.1,1,-1.1) -- (3.1,1,3.1)}]
        \begin{pgfinterruptboundingbox}
             \path[clip] (1.5,1,-1.1) -- (-1.1,1,-1.1) -- (-1.1,1,2) -- (1,1,1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    % axes
    \draw[line width=0.8pt,->]  (2,1,1)  --  (4,1,1)  node[anchor=north  east]{\textbf{x}};
    \draw[line width=0.8pt,->]  (1,2,1)  --  (1,4,1)  node[anchor=north  west]{\textbf{y}};
    \draw[line width=0.8pt,->]  (1,1,2)  --  (1,1,4)  node[anchor=south]{\textbf{z}};

\end{tikzpicture}

\end{document}

这给了我一个想法：

\documentclass[11pt,crop=false,preview=false]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz,tikz-3dplot}
    \usetikzlibrary{arrows}

\begin{document}

\definecolor{darkgreen}{rgb}{0.1,0.7,0.1}
\tdplotsetmaincoords{60}{125}

\begin{tikzpicture}[tdplot_main_coords,>=latex]

    \pgfsetlinewidth{0.8}

    \tdplotsetcoord{P}{3.4641}{54.74}{45}

    % box
    \draw[fill=black!10] (Px) -- (Pxy) -- (Py) -- (Pyz) -- (Pz) -- (Pxz) -- cycle;
    \draw (Pxy)  --  (P);
    \draw (Pxz)  --  (P);
    \draw (Pyz)  --  (P);

    \pgfsetlinewidth{1.4}

    \begin{scope} % blue circle, xy plane
        \color{blue}
        \tikzstyle{reverseclip}=[insert path={(3.1,3.1,1) -- (-1.1,3.1,1) -- (-1,-1.1,1) -- (3.1,-1.1,1) -- (3.1,3.1,1)}]
        \begin{pgfinterruptboundingbox}
            \path[clip] (1,1,1) -- (1.3,-1.1,1) -- (-1.1,-1.1,1) -- (-1.1,2,1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{2}{0}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % green circle, yz plane
        \color{darkgreen}
        \tikzstyle{reverseclip}=[insert path={(1,3.1,3.1) -- (1,3.1,-1.1) -- (1,-1.1,-1.1) -- (1,-1.1,3.1) -- (1,3.1,3.1)}]
        \begin{pgfinterruptboundingbox}
           \draw[purple,->] (1,1,1) -- (1,-1.1,1.8) -- (1,-1.1,-1.1) -- (1,1.7,-1.1);
           \path[clip] (1,1,1) -- (1,-1.1,1.8) -- (1,-1.1,-1.1) -- (1,1.7,-1.1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{0}{2}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    \begin{scope} % red circle, xz plane
        \color{red}
        \tikzstyle{reverseclip}=[insert path={(3.1,1,3.1) -- (-1.1,1,3.1) -- (-1.1,1,-1.1) -- (3.1,1,-1.1) -- (3.1,1,3.1)}]
        \begin{pgfinterruptboundingbox}
            \draw[orange,->] (1,1,1) -- (-1.1,1,2) -- (-1.1,1,-1.1) -- (1.5,1,-1.1);
            \path[clip] (1,1,1) -- (-1.1,1,2) -- (-1.1,1,-1.1) -- (1.5,1,-1.1) -- cycle [reverseclip];
        \end{pgfinterruptboundingbox}
        \pgfpathellipse{\pgfpointxyz{1}{1}{1}}{\pgfpointxyz{2}{0}{0}}{\pgfpointxyz{0}{0}{2}}
        \pgfusepath{draw}
    \end{scope}

    % axes
    \draw[line width=0.8pt,->]  (2,1,1)  --  (4,1,1)  node[anchor=north  east]{\textbf{x}};
    \draw[line width=0.8pt,->]  (1,2,1)  --  (1,4,1)  node[anchor=north  west]{\textbf{y}};
    \draw[line width=0.8pt,->]  (1,1,2)  --  (1,1,4)  node[anchor=south]{\textbf{z}};

\end{tikzpicture}

\end{document}

Answer 2

在这种情况下，也许您可​​以使用弧线和rotate around围绕指定轴向量旋转坐标系的键，如下所示（注意，shift要使此功能正常工作，需要将 a 置于框的中心）。但是，它确实需要最新版本的PGF。我对原始代码进行了一些改动。

\documentclass[tikz,border=5]{standalone}
\usepackage{tikz-3dplot}
\begin{document}

\definecolor{dark green}{rgb}{0.1,0.7,0.1}
\tdplotsetmaincoords{60}{125}

\begin{tikzpicture}[tdplot_main_coords,>=latex, thick, line cap=round, line join=round]

\tdplotsetcoord{P}{3.4641}{54.74}{45}
\coordinate (O) at (1,1,1);
% box
\draw[fill=black!10] (Px) -- (Pxy) -- (Py) -- (Pyz) -- (Pz) -- (Pxz) -- cycle;
\draw (Pxy) --  (P) (Pxz) --  (P) (Pyz) --  (P);

\tikzset{shift={(O)}, ultra thick}

\draw  [blue, rotate around z=-90] 
  (15:2) arc (15:245:2);
\draw  [dark green, rotate around z=-90, rotate around x=90] 
  (15:2) arc (15:245:2);
\draw  [red, rotate around z=-90, rotate around y=90] 
  (15:2) arc (15:245:2);

\tikzset{thick}
% axes
\draw [->] (1,0,0) -- (3,0,0) node[below left]  {\textbf{x}};
\draw [->] (0,1,0) -- (0,3,0) node[below right] {\textbf{y}};
\draw [->] (0,0,1) -- (0,0,3) node[above]       {\textbf{z}};

\end{tikzpicture}

\end{document}