[Tex/LaTex] TikZ: Drawing an ellipse through two points

intersectionstikz-pgf

I am trying to construct a portion of an ellipse that connects point P1 and P2 but I don't know anything about the ellipse besides that F is one of the foci. All I know is that an elliptic arc connects the two points. I tried using \draw let ... and then specifying the start and end angle but I don't what the x radius and y radius would be nor the orientation of the ellipse. Any ideas on how to construct this? I have a similar question which never received a definitive answer since it was more restrictive. That post can be found here ellipse intersecting a circle but I was just winging it there.

  \documentclass{article}
  \usepackage{tikz, intersections}
  \begin{document}
  \begin{tikzpicture}[
    every label/.append style = {font = \small},
    dot/.style = {outer sep = +0pt, inner sep = +0pt,
      shape = circle, draw = black, label = {#1}},
    dot/.default =,
    small dot/.style = {minimum size = 2pt, dot = {#1}},
    small dot/.default =,
    big dot/.style = {minimum size = 4pt, dot = {#1}},
    big dot/.default =,
    line join = round, line cap = round, >=triangle 45
    ]

    \node[scale = .75, fill = black, big dot = {below: \(F\)}] (F)
    at (0, 0) {};
    \node[scale = .75, fill = black, big dot = {below: \(P_1\)}] (P1)
    at (2, 0) {};
    \node[scale = .75, fill = black, big dot = {above, right = .25cm: \(P2\)}]
    (P2) at (-2, 2) {};
    \draw[-latex] (F) -- (P1) node[scale = .75, fill = white, inner sep = 0cm,
    shape = circle, pos = .5] {\(\mathbf{r}_1\)};
    \draw[-latex] (F) -- (P2) node[scale = .75, fill = white, inner sep = 0cm,
    shape = circle, pos = .5] {\(\mathbf{r}_2\)};
    \draw (-1, 0) -- (F);
    \draw let
      \p0 = (F),
      \p1 = (P1),
      \p2 = (P2),
      \n1 = {atan2(\x1 - \x0, \y1 - \y0)},
      \n2 = {atan2(\x2 - \x0, \y2 - \y0)},
      \n3 = {.4cm}
    in (F) +(\n1:\n3) arc [radius = \n3, start angle = \n1, end angle = \n2]
    node[scale = .75, pos = .5, above = .4cm] {\(\Delta\nu\)};
    \draw (P1) -- (P2) node[scale = .75, fill = white, inner sep = 0cm,
    shape = circle, pos = .5] {\(c\)};
  \end{tikzpicture}
  \end{document}

enter image description here

Best Answer

Well, as Jake commented you have an underdefined problem so the best approach is the manually placed arc and be done with it. Because to automate it, you have to supply more info. A possibility is to make a quarter arc directly

  \documentclass[tikz]{standalone}
  \usetikzlibrary{arrows,calc}

  \begin{document}

  \begin{tikzpicture}[
    dot/.style = {outer sep = +0pt, inner sep = +0pt, shape = circle, draw = black, label = {#1}},
    small dot/.style = {minimum size = 1pt, dot = {#1}},
    big dot/.style = {minimum size = 2pt, dot = {#1}},
    line join = round, line cap = round, >=triangle 45
    ]
    \node[ fill = black, big dot = {below: \(F\)}] (F) at (0, 0) {};
    \node[ fill = black, big dot = {below: \(P_1\)}] (P1)  at (2, 0) {};
    \node[ fill = black, big dot = {above right=.25cm:\(P_2\)}] (P2) at (-2, 2) {};

    \draw let
      \p0 = ($(P2)-(F)$),
      \p1 = ($(P1)-(P2)$)
    in  (P2|-P1) ++(\x1,0) arc (0:270:\x1 and \y0);

  \end{tikzpicture}
  \end{document}

enter image description here

A possible visual solution is to add

  \documentclass[tikz]{standalone}
  \usetikzlibrary{arrows,calc}

  \begin{document}

  \begin{tikzpicture}[
    dot/.style = {outer sep = +0pt, inner sep = +0pt, shape = circle, draw = black, label = {#1}},
    small dot/.style = {minimum size = 1pt, dot = {#1}},
    big dot/.style = {minimum size = 2pt, dot = {#1}},
    line join = round, line cap = round, >=triangle 45
    ]
    \node[ fill = black, big dot = {below: \(F\)}] (F) at (0, 0) {};
    \node[ fill = black, big dot = {below: \(P_1\)}] (P1)  at (2, 0) {};
    \node[ fill = black, big dot = {above right=.25cm:\(P_2\)}] (P2) at (-2, 2) {};    

    \begin{scope}[decoration={%
        markings,%
        mark=at position .5 with {\arrow[line width=0.4pt]{triangle 45}}%
        },
    ]
    \pgfpathmoveto{\pgfpointanchor{P1}{center}}
    \pgfpatharcto{2.55cm}{4cm}{0}{0}{1}{\pgfpointanchor{P2}{center}}
    \pgfgetpath\temppath
    \pgfusepath{draw}
    \pgfsetpath\temppath
    \pgfdecoratecurrentpath{markings}
    \end{scope}

  \end{tikzpicture}
  \end{document}

enter image description here

1. Draw Straight Line:

\draw  (G) -- (R)

produces the straight olive line from (G) to (R).

2. Curved Line:

\draw    (R) to[out=-20,in=-70] (B)

produces the red line with curvature. Instead of using --, we use the to syntax, and the options out= specifies the angle at the start point, and the in= specifies the angle at the end point.

Using distance=3cm with the same in=, and out= we get the red dotted line.

3. Shortened Line:

Withe either of the straight or curved lines, one can use shorten <= to shorten the start point or shorten >= to shorten the end point. A shorten of 0.25cm is applied to both ends of the violet line.

Code:

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[ultra thick]
\coordinate (G) at (2.3,6.1);
\coordinate (R) at (6.4,3.9);
\coordinate (B) at (2.1,1.7);

\node [fill=green,circle] at (G) {}; 
\node [fill=red,  circle] at (R) {};
\node [fill=blue, circle] at (B) {};

\draw [olive, -] (G) -- (R);
\draw [red]   (R) to[out=-20,in=-70] (B);
\draw [red,dotted]   (R) to[out=-20,in=-70, distance=3cm ] (B);
\draw [violet, ->, shorten <= 0.25cm, shorten >= 0.25cm] (B) to[out=120,in=150] (G);
\end{tikzpicture}
\end{document}

[Tex/LaTex] Increase the thickness of node border in TikZ

The node’s border is a path, you can use the same options for a \path, e.g. ultra thin, thick, very thick, and so on:

\node[circle, draw=blue!80, thick, inner sep=0pt, minimum size=12pt] (1) at (0,0) {1};

The line width key works as well:

\node[circle,draw=blue!80, line width=1mm, inner sep=0pt,minimum size=12pt] (1) at(0,0) {1};

All predefined line widths are

\tikzset{
    ultra thin/.style= {line width=0.1pt},
    very thin/.style=  {line width=0.2pt},
    thin/.style=       {line width=0.4pt},% thin is the default
    semithick/.style=  {line width=0.6pt},
    thick/.style=      {line width=0.8pt},
    very thick/.style= {line width=1.2pt},
    ultra thick/.style={line width=1.6pt}
}

Code

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
   every node/.append style={circle, draw=blue!80, inner sep=0pt, minimum size=12pt}]
\node                 (1) at (0,0) {1};
\node[thick]          (2) at (1,0) {2};
\node[line width=1mm] (3) at (2,0) {3};
\end{tikzpicture}
\end{document}

Output

enter image description here

Best Answer

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1. Draw Straight Line:

2. Curved Line:

3. Shortened Line:

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[Tex/LaTex] Increase the thickness of node border in TikZ

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