如何用 tikz 绘制三叶曲线

Question

我需要用 tikz 绘制以下形状的封闭曲线，

这有点像三叶结被压缩到一个平面，但也被旋转了。我想知道是否有任何帮助或建议？提前谢谢。

Answer 1

\documentclass{standalone}
\usepackage{tikz}

\begin{document}

 \begin{tikzpicture}[scale=0.7]
\draw[line width=0.3mm, -stealth] (0,-4)--(0,4);
\draw[line width=0.3mm, -stealth] (-4,0)--(4,0);
\draw[-stealth, domain=0:540, variable=\t,samples=200, line width=0.7mm]
plot ({-cos(\t)+2*cos(2*\t)}, {sin(\t)+2*sin(2*\t)});
\draw[fill=white, line width=0.5mm] (0,0) circle[radius=0.25 em];
\draw[fill=white, line width=0.5mm] (2,0) circle[radius=0.25 em];
\draw(-0.3,-0.1) node[below]{$0$};
\draw(2,0.1) node[above]{$1$};
\end{tikzpicture}
\end{document}

Answer 2

\documentclass{standalone} 
\usepackage{tkz-fct}

\begin{document} 
 \begin{tikzpicture}
   \tkzInit[xmin=-4,xmax=4,ymin=-4,ymax=4,xstep=.2,ystep=.2]
   \tkzFctPar[samples=400,domain=-pi:pi]{-cos(t)+2*cos(2*t)}{sin(t)+2*sin(2*t)}
 \end{tikzpicture}
\end{document}

Answer 3

这是我做的两种方法，但我认为第二种方法更接近您想要的。

\documentclass{standalone}
\usepackage{tikz}
\usepackage{xcolor}
\definecolor{sidecolor}{HTML}{E7E7E7}

\begin{document}

\begin{tikzpicture}[very thick]
\draw[gray!30] (-2,-2) grid (2,2);

\draw (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)}] (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);
\draw[rotate=120] (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)},rotate=240] (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);
\draw[rotate=240] (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)},rotate=120] (1.3,0) .. controls (1,0.8) and (0,0.5) .. (-0.5,0);

\end{tikzpicture}

\begin{tikzpicture}[very thick]
\draw[gray!30] (-2,-2) grid (2,2);

\draw (1.3,0) to[out=90,in=60] (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)}] (1.3,0) to[out=90,in=60] (-0.5,0);
\draw[rotate=120] (1.3,0) to[out=90,in=60] (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)},rotate=240] (1.3,0) to[out=90,in=60] (-0.5,0);
\draw[rotate=240] (1.3,0) to[out=90,in=60] (-0.5,0);
\draw[cm={1,0,0,-1,(0,0)},rotate=120] (1.3,0) to[out=90,in=60] (-0.5,0);

\end{tikzpicture}

\end{document}

Answer 4

一个 SkiaSharp 解决方案，只是为了好玩！我们可以编译以下内容，\immediate\write18使其与 TeX 更相关。

using CSharpMath.SkiaSharp;
using SkiaSharp;
using System.Diagnostics;
using static System.MathF;

class Diagram
{
    const float scale = SKDocument.DefaultRasterDpi / 2.54f; // dots per cm

    static float PtToCm(float pt) => pt / scale;

    static readonly SKPaint strokeBlack = new SKPaint
    {
        Style = SKPaintStyle.Stroke,
        StrokeWidth = PtToCm(0.8f),
        Color = SKColors.Black,
        StrokeCap = SKStrokeCap.Round,
        IsAntialias = true
    };

    static readonly SKPaint strokeRed = new SKPaint
    {
        Style = SKPaintStyle.Stroke,
        StrokeWidth = PtToCm(0.8f),
        Color = SKColors.Red,
        StrokeCap = SKStrokeCap.Round,
        IsAntialias = true
    };


    static readonly SKPaint fillGreen = new SKPaint
    {
        Style = SKPaintStyle.Fill,
        StrokeWidth = PtToCm(0.8f),
        Color = SKColors.Green,
        StrokeCap = SKStrokeCap.Round,
        IsAntialias = true
    };

    static readonly SKRect domain = new SKRect(-5f, 5f, 5f, -5f);

    static readonly float width = domain.Width * scale;
    static readonly float height = -domain.Height * scale;


    public static void Generate(string filename)
    {
        using (var stream = new SKFileWStream($"{filename}.pdf"))
        using (var document = SKDocument.CreatePdf(stream))
        using (var canvas = document.BeginPage(width, height))
        {
            canvas.Scale(scale, -scale);
            canvas.Translate(-domain.Left, -domain.Top);

            canvas.DrawLine(domain.Left + 0.5f, 0, domain.Right - 0.5f, 0, strokeBlack);
            canvas.DrawLine(0, domain.Bottom + 0.5f, 0, domain.Top - 0.5f, strokeBlack);

            int N = 100;
            int start = 0; // degrees
            int stop = 360; // degrees
            float d = (stop - start) * PI / (180 * N);

            SKPoint[] pts = Enumerable
                                .Range(0, N)
                                .Select(i => new SKPoint
                                {
                                    X = -Cos(i * d) + 2 * Cos(2 * i * d),
                                    Y = Sin(i * d) + 2 * Sin(2 * i * d)
                                })
                                .ToArray();

            for (int i = 0; i < N; ++i)
                canvas.DrawLine(pts[i], pts[(i + 1) % N], strokeRed);

            canvas.DrawCircle(1, 0, PtToCm(2), fillGreen);

            MathPainterExtension.Painter.FontSize = PtToCm(12);
            canvas.Draw("1", 1.3f, PtToCm(10));

            MathPainterExtension.Painter.FontSize = PtToCm(8);
            canvas.Draw(@"\begin{cases} x(t) = -\cos t + 2 \cos (2t) \\ y(t) = \sin t + 2 \sin (2t) \end{cases}", 2.5f, 4);
            document.EndPage();
        }
    }