Cómo dibujar la curva del trébol con tikz.

Question

Necesito dibujar con tikz una curva cerrada de la siguiente forma,

que es algo así como un nudo trébol suprimido en un plano, pero también girado. Me preguntaba si podría haber alguna ayuda o sugerencia al respecto. Gracias de antemano.

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

Aquí hay dos formas en que lo hice, pero creo que la segunda se acerca más a lo que estás buscando.

\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

¡Una solución SkiaSharp solo por diversión! Podemos compilar lo siguiente para \immediate\write18hacerlo más relacionado con TeX.

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();
        }
    }