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尝试绘制 y^2 = x^3 + 5 (tikz)

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尝试绘制 y^2 = x^3 + 5 (tikz)

我正在尝试绘制一条椭圆曲线，但它留下了一个奇怪的“间隙”。我尝试了不同的域值，但间隙仍然存在。

    \begin{tikzpicture}
        \begin{axis}[
            xmin=-2.5,
            xmax=3,
            ymin=-5,
            ymax=5,
            xlabel={$x$},
            ylabel={$y$},
            scale only axis,
            axis lines=middle,
            domain=-1.71:3,
            samples=200,
            smooth,
            % to avoid that the "plot node" is clipped (partially)
            clip=false,
            % use same unit vectors on the axis
            axis equal image=true,
        ]
            \addplot [red] {sqrt(x^3+5)};
            \addplot [red] {-sqrt(x^3+5)};

            
        \end{axis}
        
    \end{tikzpicture}

图片

答案1

你得到

NOTE: coordinate (2Y1.71e0],3Y0.0e0]) has been dropped because it is unbounded
(in y). (see also unbounded coords=jump).
NOTE: coordinate (2Y1.71e0],3Y0.0e0]) has been dropped because it is unbounded
(in y). (see also unbounded coords=jump).

计算 5 的立方根，例如 Ti钾Z 会的。

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{compat=1.18}

\begin{document}

\begin{tikzpicture}
  \pgfmathsetmacro{\cuberootoffive}{exp(ln(5)/3)}
  \begin{axis}[
    xmin=-2.5,
    xmax=3,
    ymin=-5,
    ymax=5,
    xlabel={$x$},
    ylabel={$y$},
    scale only axis,
    axis lines=middle,
    domain=-\cuberootoffive:3,
    samples=200,
    smooth,
    % to avoid that the "plot node" is clipped (partially)
    clip=false,
    % use same unit vectors on the axis
    axis equal image=true,
  ]
    \addplot [red] {sqrt(x^3+5)};
    \addplot [red] {-sqrt(x^3+5)};
  \end{axis}
\end{tikzpicture}

\end{document}

在此处输入图片描述

但仍然存在微小的差距：

在此处输入图片描述

没有间隙xfp并且该图确实是正确的。

\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfmath-xfp,xfp}

\pgfplotsset{compat=1.18}

\begin{document}

\begin{tikzpicture}
  \edef\cuberootoffive{\fpeval{exp(ln(5)/3)}}
  \pgfmxfpdeclarefunction{cubic}{1}{sqrt((#1)^3+5)}
  \begin{axis}[
    xmin=-2.5,
    xmax=3,
    ymin=-5,
    ymax=5,
    xlabel={$x$},
    ylabel={$y$},
    scale only axis,
    axis lines=middle,
    domain=-\cuberootoffive:3,
    samples=200,
    smooth,
    % to avoid that the "plot node" is clipped (partially)
    clip=false,
    % use same unit vectors on the axis
    axis equal image=true,
  ]
    \addplot [red] {cubic(x)};
    \addplot [red] {-cubic(x)};
  \end{axis}
\end{tikzpicture}

\end{document}

在此处输入图片描述

在此处输入图片描述

答案2

你可以用 pstricks 包绘制隐函数曲线pst-func。代码如下：

    \documentclass[svgnames, pstricks, border=10pt]{standalone}
    \usepackage{pst-plot,pst-func }

    \begin{document}

    \begin{pspicture*}(-3,-5)(3,5)
    \psset{plotpoints=4000, showorigin=false, arrowinset=0.12, linejoin=1}
    \psaxes[labelFontSize=\scriptstyle,ticksize=0 4pt, Dx=2, Dy=2]{->}(0,0)(-3,-5)(3,5)[$x$,-120][$y$,210]
    \psplotImp[algebraic, linecolor=Tomato, linewidth=1.2pt](-4,-6)(4,6){x^3-y^2 + 5}
    \end{pspicture*}

    \end{document}

在此处输入图片描述

答案3

这是一个渐近线绘制该隐函数。另请参阅这个答案。

在此处输入图片描述

// Run on http://asymptote.ualberta.ca/
unitsize(1cm);
import contour;
import graph;
real f(real x, real y) { return y^2-x^3; }
pair A=(-2.5,-5), B=(3,5);
limits(A,B);
guide[][] g = contour(f,A,B, new real[] {5});
draw(g[0],blue+1pt);

real[] x={-2,2};
real[] y={-4,-2,2,4};
xaxis(Label("$x$",EndPoint,align=N),Ticks(x,1mm,red));
yaxis(Label("$y$",EndPoint,align=E),Ticks(y,1mm,red));

shipout(bbox(5mm,invisible));

答案4

因为 pgfplots 不能（据我所知？）绘制隐式曲线，你必须手动对其进行参数化（或切换到另一个包，如另一个答案中所述），如果您想要好的曲线，您必须找到好的参数化。

这种情况下，让参数为变量 y 效果会更好：

%! TEX program = lualatex
\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    xmin=-2.5,
    xmax=3,
    ymin=-5,
    ymax=5,
    xlabel={$x$},
    ylabel={$y$},
    scale only axis,
    axis lines=middle,
    smooth,
    % to avoid that the "plot node" is clipped (partially)
    clip=false,
    % use same unit vectors on the axis
    axis equal image=true
    ]
\addplot [variable=t, domain=-5:5, samples=50, red] ({abs(t^2-5)^0.333333333333*sign(t^2-5)}, {t});
\end{axis}
\end{tikzpicture}
\end{document}

参考：https://tex.stackexchange.com/a/582731/250119（手动参数化示例）如何使用 pgfplots 绘制隐式方程？（如何计算立方根）使用 pgfplots 创建二维参数化参数图（如何绘制参数化图表）

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