我正在尝试在球体上进行以下操作。
到目前为止我有以下内容
使用代码
\documentclass[12pt,a4paper,oneside]{book}
\textwidth 16cm
\textheight 23cm
\oddsidemargin 0.8cm
\addtolength{\voffset}{-2.4cm}
\addtolength{\hoffset}{-0.5cm}
\usepackage{tikz, tkz-base, tkz-fct, tkz-euclide}
\usepackage[american]{circuitikz}
\usepackage{siunitx}
\usepackage{pgfplots}
\usetikzlibrary{mindmap}% mapas mentales
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{60}{110}
\pgfplotsset{compat=newest}
\usepackage{amsfonts,amssymb,amsmath}
\usepackage{enumerate}
\usepackage{verbatim}
\usepackage[english]{babel}
\usepackage{tikz}
\usepackage{makecell}
\usepackage{subfigure}
\usepackage{hyperref}
\usepackage{pgfplots}
\usepackage{yfonts}
\usepackage{graphicx}
\usepackage{tocbibind}
\usepackage{multirow}%%para combinar filas en tablas.
\usepackage{array}%%para tablas
\usepackage{tabularx}
\usepackage{float}
\begin{document}
\begin{figure}[h!]
\begin{center}
\subfigure []{ \begin{tikzpicture}[tdplot_main_coords, scale = 3.0]
% Create a point (P)
\coordinate (Px) at (1/1.4, {1/sqrt(2)},0);
\coordinate (P1x) at (- 1/1.4 , {1/sqrt(2)}, 0);
\coordinate (P2x) at ( 1/1.4,-{1/sqrt(2)},0);
\coordinate (P3x) at (-1/1.4 , -{1/sqrt(2)},0);
\coordinate (P4x) at (0, {1/sqrt(2)},0);
\coordinate (P5x) at (0, -{1/sqrt(2)}, 0);
Draw shaded circle
\shade[ball color = lightgray,
opacity = 0.5
] (0,0,0) circle (1cm);
%draw the equator
%red
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{180}{180}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
%blue
\tdplotsetrotatedcoords{45}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{270}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{225}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
%Draw the near curve to equator
%red
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{325}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{325}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:40:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:40:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:39:1);
%blue
\tdplotsetrotatedcoords{48}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:39:1);
\tdplotsetrotatedcoords{48}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{270}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:39:1);
\tdplotsetrotatedcoords{232}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:39:1);
\tdplotsetrotatedcoords{270}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{232}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
%Great circle in blue
\tdplotsetrotatedcoords{90}{90}{180};
\draw[
tdplot_rotated_coords,
blue
] (1,0,0) arc (0:160:1);
\tdplotsetrotatedcoords{90}{90}{340};
\draw[dashed,
tdplot_rotated_coords,
blue
] (1,0,0) arc (0:200:1);
%Great circle in red
\tdplotsetrotatedcoords{180}{90}{100};
\draw[
tdplot_rotated_coords,
red
] (1,0,0) arc (0:170:1);
\tdplotsetrotatedcoords{180}{90}{270};
\draw[dashed,
tdplot_rotated_coords,
red
] (1,0,0) arc (0:190:1);
% Axes in 3 d coordinate system
\draw[-stealth] (0,0,0) -- (2.2,0,0)node[right]{$x$};
\draw[-stealth] (0,0,0) -- (0,1.70,0)node[right]{$y$};
\draw[-stealth] (0,0,0) -- (0,0,1.70)node[right]{$z$};
\draw[dashed, gray, -stealth] (0,0,0) -- (-2.2,0,0);
\draw[dashed, gray, -stealth] (0,0,0) -- (0,-1.70,0);
% Add small circle at (P)
\draw[fill = green] (Px) circle (0.7pt);
\draw[fill = green] (P1x) circle (0.7pt);
\draw[fill = green] (P2x) circle (0.7pt);
\draw[fill = green] (P3x) circle (0.7pt);
\end{tikzpicture}}
\end{center}
\end{figure}
\end{document}
我现在的问题是我无法像椭圆体上的曲线那样绘制连接赤道上方和下方线条的平滑曲线。
我改进了我的代码并得到以下结果
使用以下代码，（前言与上面的相同）
\documentclass[12pt,a4paper,oneside]{book}
\textwidth 16cm
\textheight 23cm
\oddsidemargin 0.8cm
\addtolength{\voffset}{-2.4cm}
\addtolength{\hoffset}{-0.5cm}
\usepackage{tikz, tkz-base, tkz-fct, tkz-euclide}
\usepackage[american]{circuitikz}
\usepackage{siunitx}
\usepackage{pgfplots}
\usetikzlibrary{mindmap}% mapas mentales
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{60}{110}
\pgfplotsset{compat=newest}
\usepackage{amsfonts,amssymb,amsmath}
\usepackage{enumerate}
\usepackage{verbatim}
\usepackage[english]{babel}
\usepackage{tikz}
\usepackage{makecell}
\usepackage{subfigure}
\usepackage{hyperref}
\usepackage{pgfplots}
\usepackage{yfonts}
\usepackage{graphicx}
\usepackage{tocbibind}
\usepackage{multirow}%%para combinar filas en tablas.
\usepackage{array}%%para tablas
\usepackage{tabularx}
\usepackage{float}
\begin{document}
\begin{figure}[h!]
\begin{center}
\rotatebox{0}{ \subfigure []{ \begin{tikzpicture}[tdplot_main_coords, scale = 3.0]
% Create a point (P)
\coordinate (Px) at (1/1.4, {1/sqrt(2)},0);
\coordinate (P1x) at (- 1/1.4 , {1/sqrt(2)}, 0);
\coordinate (P2x) at ( 1/1.4,-{1/sqrt(2)},0);
\coordinate (P3x) at (-1/1.4 , -{1/sqrt(2)},0);
\coordinate (P4x) at (0, {1/sqrt(2)},0);
\coordinate (P5x) at (0, -{1/sqrt(2)}, 0);
Draw shaded circle
\shade[ball color = lightgray,
opacity = 0.5
] (0,0,0) circle (1cm);
%draw the equator
%red
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{180}{180}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,0) arc (0:45:1);
%blue
%left
\tdplotsetrotatedcoords{45}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{270}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
\tdplotsetrotatedcoords{225}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,0) arc (0:45:1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Draw the curve near the equator
%red
%front red 1
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:42:1);
\tdplotsetrotatedcoords{318}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:42:1);
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:41.3:1);
\tdplotsetrotatedcoords{319}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:41:1);
%front red 2
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (0.968,0,1/4) arc (0:40:1);
\tdplotsetrotatedcoords{318}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (0.968,0,1/4) arc (0:40:1);
\tdplotsetrotatedcoords{0}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (0.968,0,-1/4) arc (0:39.3:1);
\tdplotsetrotatedcoords{319}{0}{0};
\draw[ tdplot_rotated_coords,
red
] (0.968,0,-1/4) arc (0:39:1);
%back red 1
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:40:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (1,0,1/8) arc (0:39:1);
%back red 2
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (0.968,0,1/4) arc (0:38:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (0.968,0,-1/4) arc (0:38:1);
\tdplotsetrotatedcoords{180}{0}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (0.968,0,-1/4) arc (0:37:1);
\tdplotsetrotatedcoords{0}{180}{0};
\draw[dashed, tdplot_rotated_coords,
red
] (0.968,0,1/4) arc (0:37:1);
%blue
%right blue 1
\tdplotsetrotatedcoords{44.9}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:42:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:39:1);
\tdplotsetrotatedcoords{45}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:41:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
%right blue 2
\tdplotsetrotatedcoords{46.5}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (0.968,0,1/4) arc (0:40:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (0.968,0,1/4) arc (0:37:1);
\tdplotsetrotatedcoords{46.7}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (0.968,0,-1/4) arc (0:39:1);
\tdplotsetrotatedcoords{90}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (0.968,0,-1/4) arc (0:37:1);
%left blue 1
\tdplotsetrotatedcoords{277}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:40:1);
\tdplotsetrotatedcoords{226}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,1/8) arc (0:39:1);
\tdplotsetrotatedcoords{276}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:39:1);
\tdplotsetrotatedcoords{225}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (1,0,-1/8) arc (0:45:1);
%left blue 2
\tdplotsetrotatedcoords{277}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (0.968,0,1/4) arc (0:38:1);
\tdplotsetrotatedcoords{226}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (0.968,0,1/4) arc (0:37:1);
\tdplotsetrotatedcoords{276}{0}{0};
\draw[ tdplot_rotated_coords,
blue
] (0.968,0,-1/4) arc (0:37:1);
\tdplotsetrotatedcoords{225}{0}{0};
\draw[dashed, tdplot_rotated_coords,
blue
] (0.968,0,-1/4) arc (0:43:1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55
%Great circle in blue
\tdplotsetrotatedcoords{90}{90}{180};
\draw[
tdplot_rotated_coords,
blue
] (1,0,0) arc (0:160:1);
\tdplotsetrotatedcoords{90}{90}{340};
\draw[dashed,
tdplot_rotated_coords,
blue
] (1,0,0) arc (0:200:1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Great circle in red
\tdplotsetrotatedcoords{180}{90}{100};
\draw[
tdplot_rotated_coords,
red
] (1,0,0) arc (0:170:1);
\tdplotsetrotatedcoords{180}{90}{270};
\draw[dashed,
tdplot_rotated_coords,
red
] (1,0,0) arc (0:190:1);
% Axes in 3 d coordinate system
\draw[-stealth] (0,0,0) -- (2.2,0,0)node[right]{$x$};
\draw[-stealth] (0,0,0) -- (0,1.70,0)node[right]{$y$};
\draw[-stealth] (0,0,0) -- (0,0,1.70)node[right]{$z$};
\draw[dashed, gray, -stealth] (0,0,0) -- (-2.2,0,0);
\draw[dashed, gray, -stealth] (0,0,0) -- (0,-1.70,0);
% Add small circle at (P)
\draw[fill = green] (Px) circle (0.7pt);
\draw[fill = green] (P1x) circle (0.7pt);
\draw[fill = green] (P2x) circle (0.7pt);
\draw[fill = green] (P3x) circle (0.7pt);
%\draw[fill = red] (0.661, {1/sqrt(2)},1/4) circle (0.3pt);
%\draw[fill = red] (0.654, {1/sqrt(2.6)},0.1875) circle (0.3pt);
%\draw[fill = red] (0.735, {1/sqrt(3)},1/8) circle (0.3pt);
%\draw[fill = red] (0.834, {1/sqrt(3.3)},0) circle (0.3pt);
%\draw[fill = red] (0.806, {1/sqrt(3)},-1/8) circle (0.3pt);
%\draw[fill = red] (0.761, {1/sqrt(2.6)},-0.1875) circle (0.3pt);
%\draw[fill = red] (0.661, {1/sqrt(2)},-1/4) circle (0.3pt);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% completing of D1, point on the first quadrant
%blue front 1
\draw[line width=0.5pt, blue] (1/1.4, {1/sqrt(2)},1/8) .. controls (0.731, {1/sqrt(2.2)},1/10) and (0.747, {1/sqrt(2.3)},1/12) .. (0.763, {1/sqrt(2.4)},0) .. controls (0.747, {1/sqrt(2.3)},-1/12) and (0.731, {1/sqrt(2.3)},-1/10) .. (1/1.4, {1/sqrt(2)},-1/8);
\draw[line width=0.5pt, blue] (1/1.4, -{1/sqrt(2)},1/8) .. controls (0.731, -{1/sqrt(2.2)},1/10) and (0.747, -{1/sqrt(2.3)},1/12) .. (0.763, -{1/sqrt(2.4)},0) .. controls (0.747, -{1/sqrt(2.3)},-1/12) and (0.731, -{1/sqrt(2.3)},-1/10) .. (1/1.4, -{1/sqrt(2)},-1/8);
%blue front 2
\draw[line width=0.5pt, blue] (0.661, {1/sqrt(2)},1/4) .. controls (0.654, {1/sqrt(2.6)},0.1875) and (0.735, {1/sqrt(3)},1/8) .. (0.816, {1/sqrt(3)},0) .. controls (0.806, {1/sqrt(3)},-1/8) and (0.761, {1/sqrt(2.6)},-0.1875) .. (0.661, {1/sqrt(2)},-1/4);
\draw[line width=0.5pt, blue] (0.661, -{1/sqrt(2)},1/4) .. controls (0.654, -{1/sqrt(2.6)},0.1875) and (0.735, -{1/sqrt(3)},1/8) .. (0.829, -{1/sqrt(3.2)},0) .. controls (0.806, -{1/sqrt(3)},-1/8) and (0.761, -{1/sqrt(2.6)},-0.1875) .. (0.661, -{1/sqrt(2)},-1/4);
%blue back 1
\draw[line width=0.5pt, blue, dashed] (-1/1.4, -{1/sqrt(2)},1/8) .. controls (-0.731, -{1/sqrt(2.2)},1/10) and (-0.747, -{1/sqrt(2.3)},1/12) .. (-0.763, -{1/sqrt(2.4)},0) .. controls (-0.747, -{1/sqrt(2.3)},-1/12) and (-0.731, -{1/sqrt(2.3)},-1/10) .. (-1/1.4, -{1/sqrt(2)},-1/8);
\draw[line width=0.5pt, blue, dashed] (-1/1.4, {1/sqrt(2)},1/8) .. controls (-0.731, {1/sqrt(2.2)},1/10) and (-0.747, {1/sqrt(2.3)},1/12) .. (-0.763, {1/sqrt(2.4)},0) .. controls (-0.747, {1/sqrt(2.3)},-1/12) and (-0.731, {1/sqrt(2.3)},-1/10) .. (-1/1.4, {1/sqrt(2)},-1/8);
%blue back 2
\draw[line width=0.5pt, blue, dashed] (-0.661, -{1/sqrt(2)},1/4) .. controls (-0.779, -{1/sqrt(2.8)},0.1875) and (-0.735, -{1/sqrt(3)},1/8) .. (-0.829, -{1/sqrt(3.2)},0) .. controls (-0.806, -{1/sqrt(3)},-1/8) and (-0.779, -{1/sqrt(2.8)},-0.1875) .. (-0.661, -{1/sqrt(2)},-1/4);
\draw[line width=0.5pt, blue, dashed] (-0.661, {1/sqrt(2)},1/4) .. controls (-0.779, {1/sqrt(2.8)},0.1875) and (-0.735,{1/sqrt(3)},1/8) .. (-0.829, {1/sqrt(3.2)},0) .. controls (-0.806, {1/sqrt(3)},-1/8) and (-0.779, {1/sqrt(2.8)},-0.1875) .. (-0.661, {1/sqrt(2)},-1/4);
%\draw[fill = red] (0.743, {1/sqrt(2.6)},1/4) circle (0.3pt);
%\draw[fill = red] (0.598, {1/sqrt(2.2)},0.1875) circle (0.3pt);
%\draw[fill = red] (0.535, {1/sqrt(1.7)},1/8) circle (0.3pt);
%\draw[fill = red] (0.557, {1/sqrt(1.45)},0) circle (0.3pt);
%\draw[fill = red] (0.599, -{1/sqrt(1.6)}, -1/8) circle (0.3pt);
%\draw[fill = red] (0.676, -{1/sqrt(2.2)}, -1/4) circle (0.3pt);
%\draw[fill = red] (0.743, -{1/sqrt(2.6)},-1/4) circle (0.3pt);
%front red 1
\draw[line width=0.5pt, red] (0.741, {1/sqrt(2.3)},1/8) .. controls (0.654, {1/sqrt(1.8)},1/10) and (0.638, {1/sqrt(1.7)},1/16) .. (0.633, {1/sqrt(1.67)},0) .. controls (0.638, {1/sqrt(1.7)},-1/16) and (0.654, {1/sqrt(1.8)},-1/10) .. (0.741, {1/sqrt(2.3)},-1/8);
\draw[line width=0.5pt, red] (0.741, -{1/sqrt(2.3)},1/8) .. controls (0.654, -{1/sqrt(1.8)},1/10) and (0.638, -{1/sqrt(1.7)},1/16) .. (0.633, -{1/sqrt(1.67)},0) .. controls (0.638, -{1/sqrt(1.7)},-1/16) and (0.654, -{1/sqrt(1.8)},-1/10) .. (0.741, -{1/sqrt(2.3)},-1/8);
%front red 2
\draw[line width=0.5pt, red] (0.743, {1/sqrt(2.6)},1/4) .. controls (0.598, {1/sqrt(2.2)},0.1875) and (0.535, {1/sqrt(1.7)},1/8) .. (0.577, {1/sqrt(1.5)},0) .. controls (0.599, {1/sqrt(1.6)}, -1/8) and (0.395, {1/sqrt(2.2)}, -1/3) .. (0.743, {1/sqrt(2.6)},-1/4);
\draw[line width=0.5pt, red] (0.743, -{1/sqrt(2.6)},1/4) .. controls (0.598, -{1/sqrt(2.2)},0.1875) and (0.535, -{1/sqrt(1.7)},1/8) .. (0.577, -{1/sqrt(1.5)},0) .. controls (0.599, -{1/sqrt(1.6)}, -1/8) and (0.676, -{1/sqrt(2.2)}, -1/4) .. (0.743, -{1/sqrt(2.6)}, -1/4);
%back red 1
\draw[line width=0.5pt, red, dashed] (-0.741, -{1/sqrt(2.3)},1/8) .. controls (-0.654, -{1/sqrt(1.8)},1/10) and (-0.638, -{1/sqrt(1.7)},1/16) .. (-0.633, -{1/sqrt(1.67)},0) .. controls (-0.638, -{1/sqrt(1.7)},-1/16) and (-0.654, -{1/sqrt(1.8)},-1/10) .. (-0.741, -{1/sqrt(2.3)},-1/8);
\draw[line width=0.5pt, red, dashed] (-0.741, {1/sqrt(2.3)},1/8) .. controls (-0.654, {1/sqrt(1.8)},1/10) and (-0.638, {1/sqrt(1.7)},1/16) .. (-0.633, {1/sqrt(1.67)},0) .. controls (-0.638, {1/sqrt(1.7)},-1/16) and (-0.654, {1/sqrt(1.8)},-1/10) .. (-0.741, {1/sqrt(2.3)},-1/8);
%back red 2
\draw[line width=0.5pt, red, dashed] (-0.743, -{1/sqrt(2.6)},1/4) .. controls (-0.579, -{1/sqrt(1.57)},1/6) and (-0.612, -{1/sqrt(1.6)},1/8) .. (-0.577, -{1/sqrt(1.5)},0) .. controls (-0.612, -{1/sqrt(1.6)},-1/8) and (-0.579, -{1/sqrt(1.57)},-1/6) .. (-0.743, -{1/sqrt(2.6)},-1/4);
%\draw[fill = red] (-0.743, -{1/sqrt(2.6)},1/4) circle (0.3pt);
%\draw[fill = red] (-0.645, -{1/sqrt(1.8)},1/6) circle (0.3pt);
%\draw[fill = red] (-0.612, -{1/sqrt(1.6)},1/8) circle (0.3pt);
%\draw[fill = red] (-0.534, -{1/sqrt(1.4)},0) circle (0.3pt);
%\draw[fill = red] (-0.612, -{1/sqrt(1.6)},-1/8) circle (0.3pt);
%\draw[fill = red] (-0.645, -{1/sqrt(1.8)},-1/6) circle (0.3pt);
%\draw[fill = red] (-0.743, -{1/sqrt(2.6)},-1/4) circle (0.3pt);
%\draw[blue,rotate=160] (Px) ellipse (0.3 and 0.12);
%\draw[blue, rotate=4] (1/1.4, {1/sqrt(2)},-1/8) arc(270:90: 0.2cm and 0.09cm);
%\draw [green] plot [smooth ] coordinates {(1/1.4, {1/sqrt(2)},1/8) (0.749, {1/sqrt(2.3)},1/16) (0.784, {1/sqrt(2.6)},0) (0.749, {1/sqrt(2.3)},-1/16) (1/1.4, {1/sqrt(2)},-1/8)};
%\tdplotsetrotatedcoords{0}{180}{180};
%\draw[ tdplot_rotated_coords,
%red
%] (-1/1.4, {1/sqrt(2)},1/8) arc (0:180:1/4);
\end{tikzpicture}}}
\end{center}
\end{figure}
\end{document}
但我的曲线仍然显得不平滑，特别是左侧部分。如何改善？