Gdtyjr

Inspired by a recent question on stackoverflow about how to draw maps of transportation networks, I'm wondering how to draw paths that consists of vertical, horizontal and diagonal segments.

Just like one can use |- to compose the path of vertical and horizontal segments, I'd like to have a method to automatically replace all square corners with diagonal lines (it is not important if the diagonal segment is at the start, end or in the middle of the path, all would be fine -- bonus points if the inclination if the diagonal segments remains constant)

For illustration: I'd like to automatically draw the red path in the following image without manually adding the break points

Points that have a larger vertical than horizontal distance could be connected like this:

MWE:

documentclassstandalone

usepackagetikz

begindocument

begintikzpicture

coordinate (Marmot) at (0,1);
coordinate (Duck) at (2,0);

draw (Marmot) -- (Duck);
draw (Marmot) |- (Duck);

draw[red] (Marmot) -- (0.5,1) -- (1.5,0) -- (Duck);

node[rotate=45,anchor=west] at (Marmot) Marmot Burrow;
draw (Marmot) circle (0.05);

node[rotate=45,anchor=west] at (Duck) Duck Pond;
draw (Duck) circle (0.05);

endtikzpicture

enddocument

I felt like I want to slightly adapt this code to the somewhat more general requirements. This answer comes with a modified connect with angle style which can be used like this:

draw[blue] (Marmot) to[connect with angle=-60] (Duck);

It does all the cases automatically, and is arguably more TikZy than writing a macro. This is also because you can combine such paths as in

draw[orange] (Duck) to[connect with angle=125] (Marmot)
to[connect with angle=115] (Koala);

These paths can then define contours of something you want to fill, shade or clip against, or compute intersections with.

Here is the MWE.

documentclass[border=3.14mm,tikz]standalone
usepackagetikzducks,tikzlings
usetikzlibrarycalc
tikzsetconnect with angle/.style=to path=%
let p1=(tikztostart),p2=(tikztotarget),n1=sin(#1-atan2(y2-y1,x2-x1)) in 
ifdimn1>0pt
-- ++(0,((y2-y1)-(x2-x1)*tan(#1))/2) 
-- ++((x2-x1),(x2-x1)*tan(#1))
-- (tikztotarget)
else
-- ++(((x2-x1)-(y2-y1)*cot(#1))/2,0) 
-- ++((y2-y1)*cot(#1),y2-y1)
-- (tikztotarget)
fi
newsaveboxDuck
newsaveboxKoala
newsaveboxMarmot
sboxDucktikzduck
sboxKoalatikzkoala
sboxMarmottikzmarmot
begindocument
 begintikzpicture
 coordinate[label=below:marmot] (Marmot) at (0,1);
 coordinate[label=below:duck] (Duck) at (2,0);
 coordinate[label=below:koala] (Koala) at (-2,3);
 draw (Marmot) -- (Duck);
 draw (Marmot) |- (Duck);
 node[rotate=-10,anchor=south] at (Marmot) useboxMarmot;
 draw (Marmot) circle (0.05);
 node[rotate=-45,anchor=south] at (Duck) useboxDuck;
 draw (Duck) circle (0.05);
 node[rotate=10,anchor=south] at (Koala) useboxKoala;
 draw (Koala) circle (0.05);
 draw[red] (Duck) to[connect with angle=135] (Marmot);
 draw[blue] (Marmot) to[connect with angle=-60] (Duck);
 draw[red] (Marmot) to[connect with angle=120] (Koala);
 draw[blue] (Koala) to[connect with angle=-80] (Marmot);
 draw[orange,fill=red,fill opacity=0.2] (Duck) to[connect with angle=125] (Marmot)
 to[connect with angle=115] (Koala) |-cycle;
 endtikzpicture
enddocument

Edit:

With 45 degrees angle (but if their angle is already 45,135,225 or 315 it will give a straight line)

I used the command of @AlanMatthes from here

documentclassstandalone

usepackagetikz
usetikzlibrarycalc

newcommandtikzAngleOfLinetikz@AngleOfLine
 deftikz@AngleOfLine(#1)(#2)#3%
 pgfmathanglebetweenpoints%
 pgfpointanchor#1center%
 pgfpointanchor#2center
 pgfmathsetmacro#3pgfmathresult%
 


%Command diagconnect
% #1 is the arguments of draw command like, red, thick etc
% #2 is the optional argument of the fraction of the horizontal distance for the break according to the horizontal distance of the points
% #3 and #4 are the points to be connected
newcommanddiagconnect[3][-,red,thick]
tikzAngleOfLine(#2)(#3)Angle
xdefPerfectAngle0
foreach x in 45,135,225,315 ifdimdimexpr Angle ptrelax=dimexprx ptrelaxxdefPerfectAngle1fi
ifnumPerfectAngle=0
ifdimdimexprAngle pt relax< dimexpr90 ptrelaxrelax
draw[#1] letp1=(#2),p2=(#3) in (#2)-- ($(#2)+((x2-x1)-abs(x2-x1)/(x2-x1)*abs(y2-y1))/2,0)$)--($(#3)-((x2-x1)-abs(x2-x1)/(x2-x1)*abs(y2-y1))/2,0)$)--(#3);
else 
draw[#1] letp1=(#2),p2=(#3) in (#2)-- ($(#2)+(0,(x2-x1)-abs(x2-x1)/(x2-x1)*abs(y2-y1))/2)$)--($(#3)-(0,(x2-x1)-abs(x2-x1)/(x2-x1)*abs(y2-y1))/2)$)--(#3);
fi
else
draw[#1] (#2)--(#3);
fi

begindocument

begintikzpicture

node[rotate=45,anchor=west] (Point1) at (0,0)Point 1;
node[rotate=45,anchor=west] (Point2) at (1,3) Point 2;

node[rotate=45,anchor=west] (Point3) at (4,0)Point 3;
node[rotate=45,anchor=west] (Point4) at (7,1) Point 4;

diagconnectPoint1Point2;

diagconnectPoint3Point4

node[rotate=45,anchor=west] (Point5) at (0,-4)Point 5;
node[rotate=45,anchor=west] (Point6) at (2,-6) Point 6;

node[rotate=45,anchor=west] (Point7) at (4,-4)Point 7;
node[rotate=45,anchor=west] (Point8) at (5,-7) Point 8;

diagconnectPoint5Point6;

diagconnectPoint7Point8

node[rotate=45,anchor=west] (Point9) at (9,0)Point 9;
node[rotate=45,anchor=west] (Point10) at (9,2) Point 10;

node[rotate=45,anchor=west] (Point11) at (7,-4)Point 11;
node[rotate=45,anchor=west] (Point12) at (9,-4) Point 12;

diagconnectPoint9Point10;

diagconnectPoint11Point12
endtikzpicture

enddocument

Old answer (but useful in other cases):

You can define a newcommand with an extra argument (except the draw options that is optional and the two points that are required) that will be the fraction of the horizontal distance of the points that you want this "break".

documentclassstandalone

usepackagetikz
usetikzlibrarycalc
%Command diagconnect
% #1 is the arguments of draw command like, red, thick etc
% #2 is the optional argument of the fraction of the horizontal distance for the break according to the horizontal distance of the points
% #3 and #4 are the points to be connected
newcommanddiagconnect[4][]draw[#1] letp1=(#3),p2=(#4) in (#3)-- ($(#3)+(abs(x2-x1)/(x2-x1)*abs(x2-x1)*#2,0)$)--($(#4)-(abs(x2-x1)/(x2-x1)*abs(x2-x1)*#2,0)$)--(#4);
begindocument

begintikzpicture

coordinate (Marmot) at (0,1);
coordinate (Duck) ate (2,0);

draw (Marmot) -- (Duck);
draw (Marmot) |- (Duck);

%draw[red] (Marmot) -- (0.5,1) -- (1.5,0) -- (Duck);
diagconnect[thick,red]0.3MarmotDuck
node[rotate=45,anchor=west] at (Marmot) Marmot Burrow;
draw (Marmot) circle (0.05);

node[rotate=45,anchor=west] at (Duck) Duck Pond;
draw (Duck) circle (0.05);

endtikzpicture

enddocument

Output:

Based on @koleygr 's answer I changed the code a bit to always draw a 45° connection and adapt to which point is more left/right in the picture (or higher/lower). Unfortunately I couldn't come up with a way to do it horizontally and vertically in an automated fashion, but I provided the two codes for hconnect and vconnect. Maybe someone more experienced with macros and conditional statements can figure out a way to do it even better :)

documentclassstandalone
usepackagetikz
usetikzlibrarycalc
newcommandvconnect[3][]
 draw[#1] letp1=(#2),p2=(#3) in (#2)-- ($(#2)+(0,((y2-y1)/abs(y2-y1))*(abs(y2-y1)-abs(x2-x1))*0.5)$)--($(#3)-(0,((y2-y1)/abs(y2-y1))*(abs(y2-y1)-abs(x2-x1))*0.5)$)--(#3);

newcommandhconnect[3][]
 draw[#1] letp1=(#2),p2=(#3) in (#2)-- ($(#2)+(((x2-x1)/abs(x2-x1))*(abs(x2-x1)-abs(y2-y1))*0.5,0)$)--($(#3)-(((x2-x1)/abs(x2-x1))*(abs(x2-x1)-abs(y2-y1))*0.5,0)$)--(#3);


begindocument

 begintikzpicture

 coordinate (Marmot) at (0,2);
 coordinate (Duck) at (1,0);
 coordinate (Deer) at (2,3);

% draw (Marmot) -- (Duck);
% draw (Marmot) |- (Duck);

 %draw[red] (Marmot) -- (0.5,1) -- (1.5,0) -- (Duck);
 vconnect[thick,red]MarmotDuck
 hconnect[thick,red]MarmotDeer


 node[rotate=45,anchor=west] at (Marmot) Marmot Burrow;
 draw (Marmot) circle (0.05);

 node[rotate=45,anchor=west] at (Deer) Deer Lake;
 draw (Deer) circle (0.05);

 node[rotate=45,anchor=west] at (Duck) Duck Pond;
 draw (Duck) circle (0.05);

 endtikzpicture

enddocument

Produces: