Can I enlarge lines in TikZ?

Question

I'm currently creating lecture notes for "Geometry and Topology". As we now arrived at part about euclidean geometry, I quite often have the situation that I need to visualize lines (not line segments, but lines).

For example, I have the following image (the code is at the end)

enter image description here

But PQ should be a line, so I need to "enlarge" the line segment PQ. Usually, I would calculate the equation of PQ like this

m = (P.y - Q.y)/(P.x - Q.x) -- mind the special case of P.x = Q.x
P.y = m * P.x + t
<=> t = P.y - m*P.x

Then I would add two helping points A and B:

(enlarge by 0.5)
A.x := P.x - 0.5 
B.x := Q.x + 0.5
A.y = m*A.x + t
B.y = m*B.x + t

And finally I would draw the line A - P - Q - B which is my "enlarged line 'PQ'".

But this seems to be quite complicated to me for a task that could be done automatically. So is there a way in TikZ to enlarge lines?

\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
    \node (P)[point,label={[label distance=0cm]-90:$P$}] at (0,0) {};
    \node (Q)[point,label={[label distance=0cm]-90:$Q$}] at (5,1) {};
    \node (A)[point,label={[label distance=0cm]180:$\varphi_1(R)$}] at (2,2) {};
    \node (B)[point,label={[label distance=0cm]190:$\varphi_2(R)$}] at (1,3) {};

    \draw[very thick, enlarge] (P) edge node  {} (Q);
    \draw[very thick, red] (P) edge node {} (A);
    \draw[very thick, red] (P) edge node {} (B);
    \draw[very thick, green] (Q) edge node {} (A);
    \draw[very thick, green] (Q) edge node {} (B);
\end{tikzpicture}
\end{document}

Related TikZ: how to find the intersection of two extended lines? and How to draw a line passing through a point and perpendicular to another?. — Jake, Jan 14 '14 at 12:35
You might also want to look at the tkz-euclide package for drawings like this. The syntax takes a bit of getting used to, but once you've got the hang of it, it makes drawing diagrams like this much easier. — Jake, Jan 14 '14 at 12:36
@Jake: thanks, it works with \draw ($(P)!-1cm!(Q)$) -- ($(Q)!-1cm!(P)$); :-) — Martin Thoma, Jan 14 '14 at 12:49
Ok. But although I currenlty use the solution I have found with your help I would like to accept your answer acknowledge your help (and I think your answer might be cleaner ... although I don't completely understand it at the moment. For example, how does tikz decide how long the line PQ should be?) — Martin Thoma, Jan 14 '14 at 12:59
The line drawn by \tkzDrawLine extends over the points by 20 % of the distance between the two points. You can adjust that amount using \tkzDrawLine[add=0.1 and 0.4](P,Q) to make the line extend by 10 % and 40 % of the distance, for example. — Jake, Jan 14 '14 at 13:04
Oh, I've just seen that tkz-euclide is documented in French only. I did not think that I would need French after school. — Martin Thoma, Jan 14 '14 at 13:11
Hehe, yeah, it was the same for me. It's not too difficult to figure out, though. — Jake, Jan 14 '14 at 13:12

score 14 · Accepted Answer · answered Jan 14 '14 at 12:45

14

When using tkz-euclide to construct the drawing, you can indicate a line passing through two points using \tkzDrawLine(P,Q), while the line segment would be drawn using \tkzDrawSegment(P,Q):

\documentclass{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}
\tkzDefPoints{0/0/P, 5/1/Q, 2/2/Phi1, 1/3/Phi2}

\tkzDrawSegments[red](P,Phi1 P,Phi2)
\tkzDrawSegments[blue](Q,Phi1 Q,Phi2)

\tkzDrawLine(P,Q)

\tkzDrawPoints(P,Q,Phi1,Phi2)
\tkzLabelPoints[below](P,Q)
\tkzLabelPoint[above left](Phi1){$\varphi_1(R)$}
\tkzLabelPoint[above left](Phi2){$\varphi_2(R)$}
\end{tikzpicture}
\end{document}

answered Jan 14 '14 at 12:45

Jake

232,450

1

This solution looks very much the same as my solution when you use \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black]. – Martin Thoma Jan 14 '14 at 13:14
What does \usetkzobj{all} do? Removing it seems to have no effect. – Martin Thoma Jan 14 '14 at 13:27
1

@moose: That command loads tools for drawing polygons, arcs and circles. It's actually not necessary for this code. – Jake Jan 14 '14 at 13:28
1

You cad just write \tkzDrawLineadd=0.1 and 0.2 and play with 0.1 and 0.2. Thee are the percentages of the segment PQ this segment will be extended beyond the points. The first number (0.1) is for the extension beyond the first point, the second number (0.2) is for the extension beyond the second point – Sergey Belyaev Nov 10 '16 at 14:14

score 10 · Answer 2 · answered Jan 14 '14 at 13:05

Solution

\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}
    \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
    \node (P)[point,label={[label distance=0cm]-90:$P$}] at (0,0) {};
    \node (Q)[point,label={[label distance=0cm]-90:$Q$}] at (5,1) {};
    \node (A)[point,label={[label distance=0cm]180:$\varphi_1(R)$}] at (2,2) {};
    \node (B)[point,label={[label distance=0cm]190:$\varphi_2(R)$}] at (1,3) {};

    \draw[very thick] (P) edge node  {} (Q);
    \draw[very thick, red] (P) edge node {} (A);
    \draw[very thick, red] (P) edge node {} (B);
    \draw[very thick, blue] (Q) edge node {} (A);
    \draw[very thick, blue] (Q) edge node {} (B);

    \draw[very thick] ($(P)!-1cm!(Q)$) -- ($(Q)!-1cm!(P)$);
\end{tikzpicture}
\end{document}

Explanation

The key line is

\draw[very thick] ($(P)!-1cm!(Q)$) -- ($(Q)!-1cm!(P)$);

$(P)!-1cm!(Q)$ defines a point that is 1cm more in direction P when you look at the line PQ. The same for ($(Q)!-1cm!(P)$). This way, you have "enlarged" the line PQ by 1cm in both directions.

Image

enter image description here

score 10 · Answer 3 · answered Jan 14 '14 at 13:10

Another solution would be to just use shorten > and shorten <:

\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
    \node (P)[point,label={[label distance=0cm]-90:$P$}] at (0,0) {};
    \node (Q)[point,label={[label distance=0cm]-90:$Q$}] at (5,1) {};
    \node (A)[point,label={[label distance=0cm]180:$\varphi_1(R)$}] at (2,2) {};
    \node (B)[point,label={[label distance=0cm]190:$\varphi_2(R)$}] at (1,3) {};

    \draw[very thick, shorten >=-1cm, shorten <=-1cm] (P) edge node  {} (Q);
    \draw[very thick, red] (P) edge node {} (A);
    \draw[very thick, red] (P) edge node {} (B);
    \draw[very thick, green] (Q) edge node {} (A);
    \draw[very thick, green] (Q) edge node {} (B);

    \path[use as bounding box] (-1,1) rectangle (6, 3.3);
\end{tikzpicture}
\end{document}

Note, however, that TikZ will not extend the bounding box automatically, which is why I had to add \path[use as bounding box] ...;

score 4 · Answer 4 · answered Jan 14 '14 at 15:09

4

With PSTricks.

\documentclass[pstricks,border=12pt,12pt]{standalone}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}[linejoin=1,linecap=1](8,6)
    \pstGeonode
    [
        PointName={\varphi_2(R),\varphi_1(R),default},
        PosAngle={180,180,-90},
        PointNameSep={24pt,24pt,12pt},
    ](3,5.5){T}(4,3){B}(1,1){P}(7,2){Q}
    \psline[linecolor=red](B)(P)(T)
    \psline[linecolor=blue](B)(Q)(T)
    \pcline[nodesep=-1](P)(Q)
\end{pspicture}
\end{document}

enter image description here

answered Jan 14 '14 at 15:09

kiss my armpit

36,086

Can the lines be drawn behind the circles? – Jake Jan 14 '14 at 15:13
@Jake: Yes. Redraw the circles after drawing the lines. The circles given above are automatically provided by \pstGeonode as a useful bonus as long as linecolor=black. – kiss my armpit Jan 14 '14 at 15:17
Thank you for answering. It is sad that redrawing the circles is the only solution, since it is not best practice and unnecessarily takes up space in the resulting file. – Jake Jan 14 '14 at 15:24
@Jake: Then prevent \pstGeonode from providing bonus circles when constructing nodes via PointSymbol=none. So we draw (rather than redraw) the circles manually after constructing the lines. It will save the data storage which in turn reduce the carbon emission. – kiss my armpit Jan 14 '14 at 15:27
That's a much better idea, thank you. +1 – Jake Jan 14 '14 at 15:29
@Jake: Thank you for upvoting. :-) – kiss my armpit Jan 14 '14 at 15:30

Can I enlarge lines in TikZ?

4 Answers4

Solution

Explanation

Image