tikz를 사용하여 세잎 곡선을 그리는 방법

Question

tikz를 사용하여 다음 모양의 닫힌 곡선을 그려야 합니다.

이는 개미자리 매듭이 하나의 평면으로 억제되지만 회전되는 것과 비슷합니다. 이에 대한 도움이나 제안이 있는지 궁금합니다. 미리 감사드립니다.

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

제가 한 두 가지 방법이 있지만 두 번째 방법이 여러분이 찾고 있는 방법에 더 가깝다고 생각합니다.

\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

재미를 위한 SkiaSharp 솔루션! \immediate\write18TeX와 더 관련되게 만들기 위해 다음을 컴파일할 수 있습니다 .

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();
        }
    }