Sunday, October 5, 2014

Kurva Parametrik #1

Dalam matematika, persamaan parametrik dari suatu kurva menyatakan koordinat titik-titik pada kurva itu sebagai fungsi dari suatu variabel, yang disebut parameter. Sebagai contoh, 
\begin{align}
x &= \cos t \\
y &= \sin t
\end{align}
adalah persamaan parametrik untuk lingkaran satuan, di mana $t$ adalah parameter. Secara bersama-sama, kedua persamaan itu disebut representasi parametrik dari kurva tersebut. (wikipedia)

Nah, berikut ini saya tampilkan tiga contoh kurva parametrik. Semuanya saya susun (compile) dalam jaringan melalui Online LaTeX Editor ShareLaTeX.
Demikian semoga bermanfaat.

Adjie Gumarang Pujakelana 2014 




Contoh 1

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.text}
\usetikzlibrary{arrows,intersections,decorations.markings}
\tikzset{
    arrow inside/.style = {
        postaction = {
            decorate,
            decoration={
                markings,
                mark=at position 0.5 with {\arrow{>}}
            }
        }
    }
}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[scale=1.25]
    
\fill [draw=MidnightBlue,fill=none,very thick,
         postaction={decorate,
                     decoration={raise=4pt,
                                 text along path,text color=DarkSlateGray,
text={}
                                }}]
                     plot[thick,domain=-8:8,samples=500]({7*cos(\x r)^3},{7*sin(\x r)^3});
\draw node [Maroon] at (0,0) {\fontsize{.75cm}{1.95cm}\selectfont$\left(7\cos x^3,\ 7\sin x^3\right)$};
\end{tikzpicture}

\end{document}



Contoh 2

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.text}
\usetikzlibrary{arrows,intersections,decorations.markings}
\tikzset{
    arrow inside/.style = {
        postaction = {
            decorate,
            decoration={
                markings,
                mark=at position 0.5 with {\arrow{>}}
            }
        }
    }
}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[scale=1]
    
\fill [draw=MidnightBlue,fill=none,very thick,
         postaction={decorate,
                     decoration={raise=4pt,
                                 text along path,text color=DarkSlateGray,
text={}
                                }}]
                     plot[domain=-2.5:2.5,samples=500]({(\x)^3-3*\x},{3*(\x)^2-16});
\draw node [Maroon] at (0,-1) {\fontsize{.75cm}{1.95cm}\selectfont$\left(x^3-3x,\ 3x^2-16\right)$};
\end{tikzpicture}

\end{document}



Contoh 3

\documentclass[a4paper,10pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{concmath,gentium}
\usepackage[svgnames]{xcolor}
\setlength{\parindent}{0pt}
\usepackage{fix-cm}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{xpicture}
\usepackage[T1]{fontenc}
\usepackage{xcolor}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
    \usepgfplotslibrary{polar}
    \usepgfplotslibrary{units}
\pgfplotsset{every axis/.append style={
                    axis x line=middle,    % put the x axis in the middle
                    axis y line=middle,    % put the y axis in the middle
                    axis line style={<->,color=blue}, % arrows on the axis
                    xlabel={$x$},          % default put x on x-axis
                    ylabel={$y$},          % default put y on y-axis
            }}

\begin{document}

\color{MidnightBlue}
\centering
\begin{tikzpicture}[scale=2.25]
        \begin{polaraxis}
[axis lines*=none,ytick=\empty,xlabel=\empty,ylabel=\empty,hide y axis,
axis line style = {draw=White,line width=0.0001pt},]
            \def\FREQUENCY{3}
            \addplot[IndianRed,domain=0:360,samples=360,smooth,thick] (x,{30-25*sin(\FREQUENCY*x)});
            \addplot[dashed,domain=0:2*pi,samples=360] (deg(x),30);
\addplot[mark=*,only marks] coordinates {(0,0)};
        \end{polaraxis}
    \end{tikzpicture}

\end{document}



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