How to draw graph stick with rotated rectangle properly in matplotlib?

Question

I am trying to figure out how to draw the following properly.

Lets say I have two nodes, i.e. 2 points in R^2, namely src=(x1,y1) and dst=(x2,y2).

I want to draw an edge/line between them, but starting with a box.

This is an example I created with Tikz:

src and dest are the centers of these nodes. Note that they can also be on different heights. The problem is when I try to build the box (using patches.Rectangle), I have to rotate it and then it changes its size.

Thanks in advance

ImportanceOfBeingErnest · Accepted Answer · 2017-07-06T08:11:16.087

If you're happy to use a filled rectange for the graph with a rotated rectangle as stick, this can be emulated by a simple line, which is as thick as a scatter point at the graph edges.

import matplotlib.pyplot as plt
import numpy as np

def plot_spec_line(src, dst, length=0.3, srctext="v", dsttext="w", 
                   ax=None, color="k", textcolor="k"):
    if not ax: ax=plt.gca()
    lend=src+(dst-src)*length
    ax.plot([src[0],lend[0]], [src[1],lend[1]], lw=24,solid_capstyle="butt", zorder=1, color=color )
    ax.plot([src[0],dst[0]], [src[1],dst[1]], lw=2,solid_capstyle="butt", zorder=0, color=color)
    ax.scatter([src[0],dst[0]], [src[1],dst[1]], s=24**2, marker="o", lw=2, edgecolors=color, c="w", zorder=2)
    ax.text(src[0],src[1], srctext, fontsize=12, ha="center", va="center", zorder=3, color=textcolor)
    ax.text(dst[0],dst[1], dsttext, fontsize=12, ha="center", va="center", zorder=3, color=textcolor)

s = np.array([1,1])
d = np.array([3,2])    
plot_spec_line(s, d, length=0.3, srctext="v", dsttext="w")

s = np.array([1.5,0.9])
d = np.array([2.8,1.2])    
plot_spec_line(s, d, length=0.2, srctext="a", dsttext="b", color="gray")

s = np.array([1,2])
d = np.array([2,1.9])    
plot_spec_line(s, d, length=0.7, srctext="X", dsttext="Y", textcolor="limegreen", color="limegreen")

plt.margins(0.2)
plt.show()

To obtain a rectangle, which can be filled or not and more imporatantly, has an edge, you can use a Rectangle. You can rotate a rectangle by setting an appropriate transform. It then makes sense to use a plot of equal aspect ratio, such that the Rectangle and circles are not skewed.

import matplotlib.pyplot as plt
import matplotlib.transforms
import numpy as np

def plot_spec_line(src, dst, length=0.3, radius=0.1, srctext="v", dsttext="w", 
                   ax=None, color="k", textcolor="k", reccolor="w", lw=1 ):
    if not ax: ax=plt.gca()
    lend=np.sqrt(np.sum(((dst-src)*length)**2))
    s = dst-src
    angle = np.rad2deg(np.arctan2(s[1],s[0]))
    delta = np.array([0,radius])
    tr = matplotlib.transforms.Affine2D().rotate_deg_around(src[0],src[1], angle)
    t = tr + ax.transData
    rec = plt.Rectangle(src-delta, width=lend, height=radius*2, ec=color,facecolor=reccolor, transform=t, linewidth=lw)
    ax.add_patch(rec)
    ax.plot([src[0],dst[0]], [src[1],dst[1]], lw=lw,solid_capstyle="butt", zorder=0, color=color)
    circ1= plt.Circle(src, radius=radius, fill=True, facecolor="w", edgecolor=color, lw=lw)
    circ2= plt.Circle(dst, radius=radius, fill=True, facecolor="w", edgecolor=color, lw=lw)
    ax.add_patch(circ1)
    ax.add_patch(circ2)
    ax.text(src[0],src[1], srctext, fontsize=12, ha="center", va="center", zorder=3, color=textcolor)
    ax.text(dst[0],dst[1], dsttext, fontsize=12, ha="center", va="center", zorder=3, color=textcolor)

s = np.array([1,1])
d = np.array([3,2])    
plot_spec_line(s, d, length=0.3, srctext="v", dsttext="w", radius=0.06,
               reccolor="plum", )

s = np.array([1.5,0.9])
d = np.array([2.8,1.2])    
plot_spec_line(s, d, length=0.2, srctext="a", dsttext="b", color="gray", lw=2.5)

s = np.array([1,2])
d = np.array([2,1.9])    
plot_spec_line(s, d, length=0.7, srctext="X", dsttext="Y", textcolor="limegreen",
               reccolor="palegreen", color="limegreen")

plt.margins(0.2)
plt.gca().set_aspect("equal")
plt.show()

Though it would be nice to know how to draw the same without being filled. What could be an approach? — Doc, Jul 05 '17 at 10:34
Here the trick is to use a line, which is per definition "filled". If you want an unfilled rectangle, two options are to (a) use a `Rectangle` and rotate it or (b) to use a `PathPatch`. In the first case the challenge is to find the point of rotation, in the second case you need to calculate the coordinates of the corner points. I could help you with one of the solutions, but I first wanted to make sure, the the above (filled) solution isn't already what you want. — ImportanceOfBeingErnest, Jul 05 '17 at 10:40
It would be great if you could help me with one of the solutions. The status quo is good, but it would be even better if I could have them not filled (I plan to fill them later with different colors). The thing is, as described above, rotating rectangles changes their size for some reason. If you want me to, I can upload an example. Thanks a lot for your help! — Doc, Jul 05 '17 at 12:35
I updated the answer. You should of course have added an example from the beginning on (this is not a question of if I want it, but rather if you want to help others help you). — ImportanceOfBeingErnest, Jul 05 '17 at 15:41
Thanks a lot. In your first example you scattered the circles with size s=24^2 and the linewidth of the "rectangle" was 24. I still scatter these circles and do not use the Circle class. How do i choose the variable radius properly if s=24^2? 24^2 = radius^2 * pi does not seem to be the right formula. — Doc, Jul 05 '17 at 16:54
Linewidth is given in units of points (which is the unit of fontsize), which is independent on the data coordinates (a line is always x points, no matter on which scale). Scatter point size is given in points^2. So in the first example linewith=x implies to use `s=x**2` as scattersize. The Rectangle from the second solution is given in data coordinates. So you would need to transform data coordinates into points. This is possible, see e.g. [this answer](https://stackoverflow.com/a/42972469/4124317) and then square this to get the scatter size. But I would acutally recommend to use the circle. — ImportanceOfBeingErnest, Jul 05 '17 at 17:07

How to draw graph stick with rotated rectangle properly in matplotlib?

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