Best way to plot an angle between two lines in Matplotlib
Question:
I am fairly new to using matplotlib and cannot find any examples that show two lines with the angle between them plotted.
This is my current image:
And this is an example of what I want to achieve:
I usually take a look at the Matplotlib gallery to get an idea of how to perform certain tasks but there does not seem to be anything similar.
Answers:
You could use matplotlib.patches.Arc to plot an arc of the corresponding angle measure.
To draw the angle arc:
Define a function that could take 2 matplotlib.lines.Line2D objects, calculate the angle and return a matplotlib.patches.Arc object, which you can add to your plot along with the lines.
def get_angle_plot(line1, line2, offset = 1, color = None, origin = [0,0], len_x_axis = 1, len_y_axis = 1):
l1xy = line1.get_xydata()
# Angle between line1 and x-axis
slope1 = (l1xy[1][1] - l1xy[0][2]) / float(l1xy[1][0] - l1xy[0][0])
angle1 = abs(math.degrees(math.atan(slope1))) # Taking only the positive angle
l2xy = line2.get_xydata()
# Angle between line2 and x-axis
slope2 = (l2xy[1][3] - l2xy[0][4]) / float(l2xy[1][0] - l2xy[0][0])
angle2 = abs(math.degrees(math.atan(slope2)))
theta1 = min(angle1, angle2)
theta2 = max(angle1, angle2)
angle = theta2 - theta1
if color is None:
color = line1.get_color() # Uses the color of line 1 if color parameter is not passed.
return Arc(origin, len_x_axis*offset, len_y_axis*offset, 0, theta1, theta2, color=color, label = str(angle)+u"u00b0")
To print the angle values :
Incase you want the angle value to be displayed inline, refer this SO Question for how to print inline labels in matplotlib. Note that you must print the label for the arc.
I made a small function which extracts the vertices of the arc and tries to compute the coordinate of the angle text.
This may not be optimal and may not work well with all angle values.
def get_angle_text(angle_plot):
angle = angle_plot.get_label()[:-1] # Excluding the degree symbol
angle = "%0.2f"%float(angle)+u"u00b0" # Display angle upto 2 decimal places
# Get the vertices of the angle arc
vertices = angle_plot.get_verts()
# Get the midpoint of the arc extremes
x_width = (vertices[0][0] + vertices[-1][0]) / 2.0
y_width = (vertices[0][5] + vertices[-1][6]) / 2.0
#print x_width, y_width
separation_radius = max(x_width/2.0, y_width/2.0)
return [ x_width + separation_radius, y_width + separation_radius, angle]
Or you could always precompute the label point manually and use text to display the angle value. You can get the angle value from the label of the Arc object using the get_label() method (Since we had set the label to the angle value + the unicode degree symbol).
Example usage of the above functions :
fig = plt.figure()
line_1 = Line2D([0,1], [0,4], linewidth=1, linestyle = "-", color="green")
line_2 = Line2D([0,4.5], [0,3], linewidth=1, linestyle = "-", color="red")
ax = fig.add_subplot(1,1,1)
ax.add_line(line_1)
ax.add_line(line_2)
angle_plot = get_angle_plot(line_1, line_2, 1)
angle_text = get_angle_text(angle_plot)
# Gets the arguments to be passed to ax.text as a list to display the angle value besides the arc
ax.add_patch(angle_plot) # To display the angle arc
ax.text(*angle_text) # To display the angle value
ax.set_xlim(0,7)
ax.set_ylim(0,5)
If you do not care about inline placement of the angle text. You could use plt.legend() to print the angle value.
Finally :
plt.legend()
plt.show()
The offset parameter in the function get_angle_plot is used to specify a psudo-radius value to the arc.
This will be useful when angle arcs may overlap with each other.
( In this figure, like I said, my get_angle_text function is not very optimal in placing the text value, but should give you an idea on how to compute the point )
Adding a third line :
line_3 = Line2D([0,7], [0,1], linewidth=1, linestyle = "-", color="brown")
ax.add_line(line_3)
angle_plot = get_angle_plot(line_1, line_3, 2, color="red") # Second angle arc will be red in color
angle_text = get_angle_text(angle_plot)
ax.add_patch(angle_plot) # To display the 2nd angle arc
ax.text(*angle_text) # To display the 2nd angle value
Taking idea from @user3197452 here is what I use. This version combines text and also takes care of in-proportional axis ratios.
def add_corner_arc(ax, line, radius=.7, color=None, text=None, text_radius=.5, text_rotatation=0, **kwargs):
''' display an arc for p0p1p2 angle
Inputs:
ax - axis to add arc to
line - MATPLOTLIB line consisting of 3 points of the corner
radius - radius to add arc
color - color of the arc
text - text to show on corner
text_radius - radius to add text
text_rotatation - extra rotation for text
kwargs - other arguments to pass to Arc
'''
lxy = line.get_xydata()
if len(lxy) < 3:
raise ValueError('at least 3 points in line must be available')
p0 = lxy[0]
p1 = lxy[1]
p2 = lxy[2]
width = np.ptp([p0[0], p1[0], p2[0]])
height = np.ptp([p0[1], p1[1], p2[1]])
n = np.array([width, height]) * 1.0
p0_ = (p0 - p1) / n
p1_ = (p1 - p1)
p2_ = (p2 - p1) / n
theta0 = -get_angle(p0_, p1_)
theta1 = -get_angle(p2_, p1_)
if color is None:
# Uses the color line if color parameter is not passed.
color = line.get_color()
arc = ax.add_patch(Arc(p1, width * radius, height * radius, 0, theta0, theta1, color=color, **kwargs))
if text:
v = p2_ / np.linalg.norm(p2_)
if theta0 < 0:
theta0 = theta0 + 360
if theta1 < 0:
theta1 = theta1 + 360
theta = (theta0 - theta1) / 2 + text_rotatation
pt = np.dot(rotation_transform(theta), v[:,None]).T * n * text_radius
pt = pt + p1
pt = pt.squeeze()
ax.text(pt[0], pt[1], text,
horizontalalignment='left',
verticalalignment='top',)
return arc
get_angle function is what I have posted here, but copied again for completeness.
def get_angle(p0, p1=np.array([0,0]), p2=None):
''' compute angle (in degrees) for p0p1p2 corner
Inputs:
p0,p1,p2 - points in the form of [x,y]
'''
if p2 is None:
p2 = p1 + np.array([1, 0])
v0 = np.array(p0) - np.array(p1)
v1 = np.array(p2) - np.array(p1)
angle = np.math.atan2(np.linalg.det([v0,v1]),np.dot(v0,v1))
return np.degrees(angle)
def rotation_transform(theta):
''' rotation matrix given theta
Inputs:
theta - theta (in degrees)
'''
theta = np.radians(theta)
A = [[np.math.cos(theta), -np.math.sin(theta)],
[np.math.sin(theta), np.math.cos(theta)]]
return np.array(A)
To use it one can do this:
ax = gca()
line, = ax.plot([0, 0, 2], [-1, 0, 0], 'ro-', lw=2)
add_corner_arc(ax, line, text=u'%du00b0' % 90)
I’ve written a function to create a matplotlib Arc object that takes several helpful arguments. It also works on lines that do not intersect at the origin. For a given set of two lines, there are many possible arcs that the user may want to draw. This function lets one specify which one using the arguments. The text is drawn at the midpoint between the arc and the origin. Improvements are more than welcome in the comments, or on the gist containing this function.
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
Arc = matplotlib.patches.Arc
def halfangle(a, b):
"Gets the middle angle between a and b, when increasing from a to b"
if b < a:
b += 360
return (a + b)/2 % 360
def get_arc_patch(lines, radius=None, flip=False, obtuse=False, reverse=False, dec=0, fontsize=8):
"""For two sets of two points, create a matplotlib Arc patch drawing
an arc between the two lines.
lines: list of lines, of shape [[(x0, y0), (x1, y1)], [(x0, y0), (x1, y1)]]
radius: None, float or tuple of floats. If None, is set to half the length
of the shortest line
orgio: If True, draws the arc around the point (0,0). If False, estimates
the intersection of the lines and uses that point.
flip: If True, flips the arc to the opposite side by 180 degrees
obtuse: If True, uses the other set of angles. Often used with reverse=True.
reverse: If True, reverses the two angles so that the arc is drawn
"the opposite way around the circle"
dec: The number of decimals to round to
fontsize: fontsize of the angle label
"""
import numpy as np
from matplotlib.patches import Arc
linedata = [np.array(line.T) for line in lines]
scales = [np.diff(line).T[0] for line in linedata]
scales = [s[1] / s[0] for s in scales]
# Get angle to horizontal
angles = np.array([np.rad2deg(np.arctan(s/1)) for s in scales])
if obtuse:
angles[1] = angles[1] + 180
if flip:
angles += 180
if reverse:
angles = angles[::-1]
angle = abs(angles[1]-angles[0])
if radius is None:
lengths = np.linalg.norm(lines, axis=(0,1))
radius = min(lengths)/2
# Solve the point of intersection between the lines:
t, s = np.linalg.solve(np.array([line1[1]-line1[0], line2[0]-line2[1]]).T, line2[0]-line1[0])
intersection = np.array((1-t)*line1[0] + t*line1[1])
# Check if radius is a single value or a tuple
try:
r1, r2 = radius
except:
r1 = r2 = radius
arc = Arc(intersection, 2*r1, 2*r2, theta1=angles[1], theta2=angles[0])
half = halfangle(*angles[::-1])
sin = np.sin(np.deg2rad(half))
cos = np.cos(np.deg2rad(half))
r = r1*r2/(r1**2*sin**2+r2**2*cos**2)**0.5
xy = np.array((r*cos, r*sin))
xy = intersection + xy/2
textangle = half if half > 270 or half < 90 else 180 + half
textkwargs = {
'x':xy[0],
'y':xy[1],
's':str(round(angle, dec)) + "°",
'ha':'center',
'va':'center',
'fontsize':fontsize,
'rotation':textangle
}
return arc, textkwargs
It creates arcs like in the following image, using the attached script:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Arc
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
lines = [line1, line2]
fig, AX = plt.subplots(nrows=2, ncols=2)
for ax in AX.flatten():
for line in lines:
x,y = line.T
ax.plot(x,y)
ax.axis('equal')
ax1, ax2, ax3, ax4 = AX.flatten()
arc, angle_text = get_arc_patch(lines)
ax1.add_artist(arc)
ax1.set(title='Default')
ax1.text(**angle_text)
arc, angle_text = get_arc_patch(lines, flip=True)
ax2.add_artist(arc)
ax2.set(title='flip=True')
ax2.text(**angle_text)
arc, angle_text = get_arc_patch(lines, obtuse=True, reverse=True)
ax3.add_artist(arc)
ax3.set(title='obtuse=True, reverse=True')
ax3.text(**angle_text)
arc, angle_text = get_arc_patch(lines, radius=(2,1))
ax4.add_artist(arc)
ax4.set(title='radius=(2,1)')
ax4.text(**angle_text)
plt.tight_layout()
plt.show()
I was looking for more of an all in one solution and found the AngleAnnotation class. I highly recommend it.
It is often useful to mark angles between lines or inside shapes with a circular arc. While Matplotlib provides an Arc, an inherent problem when directly using it for such purposes is that an arc being circular in data space is not necessarily circular in display space. Also, the arc’s radius is often best defined in a coordinate system which is independent of the actual data coordinates – at least if you want to be able to freely zoom into your plot without the annotation growing to infinity.
You can find it here https://matplotlib.org/stable/gallery/text_labels_and_annotations/angle_annotation.html
I save it as AngleAnnotation.py (of course you can name it differently) in my working directory and import it in my code with
from AngleAnnotation import AngleAnnotation
here is a snippet of how I use it:
...
#intersection of the two lines
center = (0.0,0.0)
#any point (other than center) on one line
p1 = (6,2)
# any point (other than center) on the other line
p2 = (6,0)
# you may need to switch around p1 and p2 if the arc is drawn enclosing the lines instead
# of between
# ax0 is the axes in which your lines exist
# size sets how large the arc will be
# text sets the label for your angle while textposition lets you rougly set where the label is, here "inside"
# you can pass kwargs to the textlabel using text_kw=dict(...)
# especially useful is the xytext argument which lets you customize the relative position of your label more precisely
am1 = AngleAnnotation(center, p1, p2, ax=ax0, size=130, text="some_label", textposition = "inside", text_kw=dict(fontsize=20, xytext = (10,-5)))
You can find many more details in the link above. It’s working for me on matplotlib 3.4.2 right now.
I find TomNorway’s approach better, it has more flexibility in other cases than the accepted answer. I tested the code and made some quick fixes for even more applicability by creating a class.
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Arc
class LinesAngles:
def __init__(self, line1, line2, radius=None, flip=False, obtuse=False, reverse=False, dec=0, fontsize=8, title=""):
"""
line1: list of two points, of shape [[x0, y0], [x1, y1]]
line2: list of two points, of shape [[x0, y0], [x1, y1]]
radius: None, float or tuple of floats. If None, is set to half the length
of the shortest line orgio: If True, draws the arc around the point (0,0). If False, estimates
the intersection of the lines and uses that point.
flip: If True, flips the arc to the opposite side by 180 degrees
obtuse: If True, uses the other set of angles. Often used with reverse=True.
reverse: If True, reverses the two angles so that the arc is drawn "the opposite way around the circle"
dec: The number of decimals to round to
fontsize: fontsize of the angle label
title: Title of the plot
"""
self.line1 = line1
self.line2 = line2
self.lines = [line1, line2]
self.radius = radius
self.flip = flip
self.obtuse = obtuse
self.reverse = reverse
self.dec = dec
self.fontsize = fontsize
self.title = title
def halfangle(self,a, b) -> float:
"""
Gets the middle angle between a and b, when increasing from a to b
a: float, angle in degrees
b: float, angle in degrees
returns: float, angle in degrees
"""
if b < a:
b += 360
return (a + b)/2 % 360
def get_arc_patch(self, lines: list):
"""
For two sets of two points, create a matplotlib Arc patch drawing
an arc between the two lines.
lines: list of lines, of shape [[(x0, y0), (x1, y1)], [(x0, y0), (x1, y1)]]
returns: Arc patch, and text for the angle label
"""
linedata = [np.array(line.T) for line in lines]
scales = [np.diff(line).T[0] for line in linedata]
scales = [s[1] / s[0] for s in scales]
# Get angle to horizontal
angles = np.array([np.rad2deg(np.arctan(s/1)) for s in scales])
if self.obtuse:
angles[1] = angles[1] + 180
if self.flip:
angles += 180
if self.reverse:
angles = angles[::-1]
angle = abs(angles[1]-angles[0])
if self.radius is None:
lengths = np.linalg.norm(lines, axis=(0,1))
self.radius = min(lengths)/2
# Solve the point of intersection between the lines:
t, s = np.linalg.solve(np.array([line1[1]-line1[0], line2[0]-line2[1]]).T, line2[0]-line1[0])
intersection = np.array((1-t)*line1[0] + t*line1[1])
# Check if radius is a single value or a tuple
try:
r1, r2 = self.radius
except:
r1 = r2 = self.radius
arc = Arc(intersection, 2*r1, 2*r2, theta1=angles[1], theta2=angles[0])
half = self.halfangle(*angles[::-1])
sin = np.sin(np.deg2rad(half))
cos = np.cos(np.deg2rad(half))
r = r1*r2/(r1**2*sin**2+r2**2*cos**2)**0.5
xy = np.array((r*cos, r*sin))
xy = intersection + xy/2
textangle = half if half > 270 or half < 90 else 180 + half
textkwargs = {
'x':xy[0],
'y':xy[1],
's':str(round(angle, self.dec)) + "°",
'ha':'center',
'va':'center',
'fontsize':self.fontsize,
'rotation':textangle
}
return arc, textkwargs
def plot(self) -> None:
"""!
Plot the lines and the arc
"""
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
for line in self.lines:
x,y = line.T
ax.plot(x,y)
ax.axis('equal')
arc, angle_text = self.get_arc_patch(self.lines)
ax.add_artist(arc)
ax.set(title=self.title)
ax.text(**angle_text)
plt.show()
For using it you just create the instance and the plot function.
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
default = LinesAngles(line1, line2, title="Default")
#Plot single pair of lines
default.plot()
If you still want to plot multiple cases, I created a function that accepts the instances and plots automatically to the subplots you need.
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
default = LinesAngles(line1, line2, title="Default")
flip = LinesAngles(line1, line2, title='flip=True', flip=True)
obtuse = LinesAngles(line1, line2, title='obtuse=True, reverse=True', obtuse=True, reverse=True)
radius = LinesAngles(line1, line2, title='radius=(2,1)', radius=(2,1))
#Plot single pair of lines
default.plot()
#Plot multiple line pairs
multiple_plot(default, flip, obtuse, radius, num_subplots=4)
Thanks to TomNorway for his answer, all credit to him I only made some modifications.
I am fairly new to using matplotlib and cannot find any examples that show two lines with the angle between them plotted.
This is my current image:
And this is an example of what I want to achieve:
I usually take a look at the Matplotlib gallery to get an idea of how to perform certain tasks but there does not seem to be anything similar.
You could use matplotlib.patches.Arc to plot an arc of the corresponding angle measure.
To draw the angle arc:
Define a function that could take 2 matplotlib.lines.Line2D objects, calculate the angle and return a matplotlib.patches.Arc object, which you can add to your plot along with the lines.
def get_angle_plot(line1, line2, offset = 1, color = None, origin = [0,0], len_x_axis = 1, len_y_axis = 1):
l1xy = line1.get_xydata()
# Angle between line1 and x-axis
slope1 = (l1xy[1][1] - l1xy[0][2]) / float(l1xy[1][0] - l1xy[0][0])
angle1 = abs(math.degrees(math.atan(slope1))) # Taking only the positive angle
l2xy = line2.get_xydata()
# Angle between line2 and x-axis
slope2 = (l2xy[1][3] - l2xy[0][4]) / float(l2xy[1][0] - l2xy[0][0])
angle2 = abs(math.degrees(math.atan(slope2)))
theta1 = min(angle1, angle2)
theta2 = max(angle1, angle2)
angle = theta2 - theta1
if color is None:
color = line1.get_color() # Uses the color of line 1 if color parameter is not passed.
return Arc(origin, len_x_axis*offset, len_y_axis*offset, 0, theta1, theta2, color=color, label = str(angle)+u"u00b0")
To print the angle values :
Incase you want the angle value to be displayed inline, refer this SO Question for how to print inline labels in matplotlib. Note that you must print the label for the arc.
I made a small function which extracts the vertices of the arc and tries to compute the coordinate of the angle text.
This may not be optimal and may not work well with all angle values.
def get_angle_text(angle_plot):
angle = angle_plot.get_label()[:-1] # Excluding the degree symbol
angle = "%0.2f"%float(angle)+u"u00b0" # Display angle upto 2 decimal places
# Get the vertices of the angle arc
vertices = angle_plot.get_verts()
# Get the midpoint of the arc extremes
x_width = (vertices[0][0] + vertices[-1][0]) / 2.0
y_width = (vertices[0][5] + vertices[-1][6]) / 2.0
#print x_width, y_width
separation_radius = max(x_width/2.0, y_width/2.0)
return [ x_width + separation_radius, y_width + separation_radius, angle]
Or you could always precompute the label point manually and use text to display the angle value. You can get the angle value from the label of the Arc object using the get_label() method (Since we had set the label to the angle value + the unicode degree symbol).
Example usage of the above functions :
fig = plt.figure()
line_1 = Line2D([0,1], [0,4], linewidth=1, linestyle = "-", color="green")
line_2 = Line2D([0,4.5], [0,3], linewidth=1, linestyle = "-", color="red")
ax = fig.add_subplot(1,1,1)
ax.add_line(line_1)
ax.add_line(line_2)
angle_plot = get_angle_plot(line_1, line_2, 1)
angle_text = get_angle_text(angle_plot)
# Gets the arguments to be passed to ax.text as a list to display the angle value besides the arc
ax.add_patch(angle_plot) # To display the angle arc
ax.text(*angle_text) # To display the angle value
ax.set_xlim(0,7)
ax.set_ylim(0,5)
If you do not care about inline placement of the angle text. You could use plt.legend() to print the angle value.
Finally :
plt.legend()
plt.show()
The offset parameter in the function get_angle_plot is used to specify a psudo-radius value to the arc.
This will be useful when angle arcs may overlap with each other.
( In this figure, like I said, my get_angle_text function is not very optimal in placing the text value, but should give you an idea on how to compute the point )
Adding a third line :
line_3 = Line2D([0,7], [0,1], linewidth=1, linestyle = "-", color="brown")
ax.add_line(line_3)
angle_plot = get_angle_plot(line_1, line_3, 2, color="red") # Second angle arc will be red in color
angle_text = get_angle_text(angle_plot)
ax.add_patch(angle_plot) # To display the 2nd angle arc
ax.text(*angle_text) # To display the 2nd angle value
Taking idea from @user3197452 here is what I use. This version combines text and also takes care of in-proportional axis ratios.
def add_corner_arc(ax, line, radius=.7, color=None, text=None, text_radius=.5, text_rotatation=0, **kwargs):
''' display an arc for p0p1p2 angle
Inputs:
ax - axis to add arc to
line - MATPLOTLIB line consisting of 3 points of the corner
radius - radius to add arc
color - color of the arc
text - text to show on corner
text_radius - radius to add text
text_rotatation - extra rotation for text
kwargs - other arguments to pass to Arc
'''
lxy = line.get_xydata()
if len(lxy) < 3:
raise ValueError('at least 3 points in line must be available')
p0 = lxy[0]
p1 = lxy[1]
p2 = lxy[2]
width = np.ptp([p0[0], p1[0], p2[0]])
height = np.ptp([p0[1], p1[1], p2[1]])
n = np.array([width, height]) * 1.0
p0_ = (p0 - p1) / n
p1_ = (p1 - p1)
p2_ = (p2 - p1) / n
theta0 = -get_angle(p0_, p1_)
theta1 = -get_angle(p2_, p1_)
if color is None:
# Uses the color line if color parameter is not passed.
color = line.get_color()
arc = ax.add_patch(Arc(p1, width * radius, height * radius, 0, theta0, theta1, color=color, **kwargs))
if text:
v = p2_ / np.linalg.norm(p2_)
if theta0 < 0:
theta0 = theta0 + 360
if theta1 < 0:
theta1 = theta1 + 360
theta = (theta0 - theta1) / 2 + text_rotatation
pt = np.dot(rotation_transform(theta), v[:,None]).T * n * text_radius
pt = pt + p1
pt = pt.squeeze()
ax.text(pt[0], pt[1], text,
horizontalalignment='left',
verticalalignment='top',)
return arc
get_angle function is what I have posted here, but copied again for completeness.
def get_angle(p0, p1=np.array([0,0]), p2=None):
''' compute angle (in degrees) for p0p1p2 corner
Inputs:
p0,p1,p2 - points in the form of [x,y]
'''
if p2 is None:
p2 = p1 + np.array([1, 0])
v0 = np.array(p0) - np.array(p1)
v1 = np.array(p2) - np.array(p1)
angle = np.math.atan2(np.linalg.det([v0,v1]),np.dot(v0,v1))
return np.degrees(angle)
def rotation_transform(theta):
''' rotation matrix given theta
Inputs:
theta - theta (in degrees)
'''
theta = np.radians(theta)
A = [[np.math.cos(theta), -np.math.sin(theta)],
[np.math.sin(theta), np.math.cos(theta)]]
return np.array(A)
To use it one can do this:
ax = gca()
line, = ax.plot([0, 0, 2], [-1, 0, 0], 'ro-', lw=2)
add_corner_arc(ax, line, text=u'%du00b0' % 90)
I’ve written a function to create a matplotlib Arc object that takes several helpful arguments. It also works on lines that do not intersect at the origin. For a given set of two lines, there are many possible arcs that the user may want to draw. This function lets one specify which one using the arguments. The text is drawn at the midpoint between the arc and the origin. Improvements are more than welcome in the comments, or on the gist containing this function.
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
Arc = matplotlib.patches.Arc
def halfangle(a, b):
"Gets the middle angle between a and b, when increasing from a to b"
if b < a:
b += 360
return (a + b)/2 % 360
def get_arc_patch(lines, radius=None, flip=False, obtuse=False, reverse=False, dec=0, fontsize=8):
"""For two sets of two points, create a matplotlib Arc patch drawing
an arc between the two lines.
lines: list of lines, of shape [[(x0, y0), (x1, y1)], [(x0, y0), (x1, y1)]]
radius: None, float or tuple of floats. If None, is set to half the length
of the shortest line
orgio: If True, draws the arc around the point (0,0). If False, estimates
the intersection of the lines and uses that point.
flip: If True, flips the arc to the opposite side by 180 degrees
obtuse: If True, uses the other set of angles. Often used with reverse=True.
reverse: If True, reverses the two angles so that the arc is drawn
"the opposite way around the circle"
dec: The number of decimals to round to
fontsize: fontsize of the angle label
"""
import numpy as np
from matplotlib.patches import Arc
linedata = [np.array(line.T) for line in lines]
scales = [np.diff(line).T[0] for line in linedata]
scales = [s[1] / s[0] for s in scales]
# Get angle to horizontal
angles = np.array([np.rad2deg(np.arctan(s/1)) for s in scales])
if obtuse:
angles[1] = angles[1] + 180
if flip:
angles += 180
if reverse:
angles = angles[::-1]
angle = abs(angles[1]-angles[0])
if radius is None:
lengths = np.linalg.norm(lines, axis=(0,1))
radius = min(lengths)/2
# Solve the point of intersection between the lines:
t, s = np.linalg.solve(np.array([line1[1]-line1[0], line2[0]-line2[1]]).T, line2[0]-line1[0])
intersection = np.array((1-t)*line1[0] + t*line1[1])
# Check if radius is a single value or a tuple
try:
r1, r2 = radius
except:
r1 = r2 = radius
arc = Arc(intersection, 2*r1, 2*r2, theta1=angles[1], theta2=angles[0])
half = halfangle(*angles[::-1])
sin = np.sin(np.deg2rad(half))
cos = np.cos(np.deg2rad(half))
r = r1*r2/(r1**2*sin**2+r2**2*cos**2)**0.5
xy = np.array((r*cos, r*sin))
xy = intersection + xy/2
textangle = half if half > 270 or half < 90 else 180 + half
textkwargs = {
'x':xy[0],
'y':xy[1],
's':str(round(angle, dec)) + "°",
'ha':'center',
'va':'center',
'fontsize':fontsize,
'rotation':textangle
}
return arc, textkwargs
It creates arcs like in the following image, using the attached script:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Arc
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
lines = [line1, line2]
fig, AX = plt.subplots(nrows=2, ncols=2)
for ax in AX.flatten():
for line in lines:
x,y = line.T
ax.plot(x,y)
ax.axis('equal')
ax1, ax2, ax3, ax4 = AX.flatten()
arc, angle_text = get_arc_patch(lines)
ax1.add_artist(arc)
ax1.set(title='Default')
ax1.text(**angle_text)
arc, angle_text = get_arc_patch(lines, flip=True)
ax2.add_artist(arc)
ax2.set(title='flip=True')
ax2.text(**angle_text)
arc, angle_text = get_arc_patch(lines, obtuse=True, reverse=True)
ax3.add_artist(arc)
ax3.set(title='obtuse=True, reverse=True')
ax3.text(**angle_text)
arc, angle_text = get_arc_patch(lines, radius=(2,1))
ax4.add_artist(arc)
ax4.set(title='radius=(2,1)')
ax4.text(**angle_text)
plt.tight_layout()
plt.show()
I was looking for more of an all in one solution and found the AngleAnnotation class. I highly recommend it.
It is often useful to mark angles between lines or inside shapes with a circular arc. While Matplotlib provides an Arc, an inherent problem when directly using it for such purposes is that an arc being circular in data space is not necessarily circular in display space. Also, the arc’s radius is often best defined in a coordinate system which is independent of the actual data coordinates – at least if you want to be able to freely zoom into your plot without the annotation growing to infinity.
You can find it here https://matplotlib.org/stable/gallery/text_labels_and_annotations/angle_annotation.html
I save it as AngleAnnotation.py (of course you can name it differently) in my working directory and import it in my code with
from AngleAnnotation import AngleAnnotation
here is a snippet of how I use it:
...
#intersection of the two lines
center = (0.0,0.0)
#any point (other than center) on one line
p1 = (6,2)
# any point (other than center) on the other line
p2 = (6,0)
# you may need to switch around p1 and p2 if the arc is drawn enclosing the lines instead
# of between
# ax0 is the axes in which your lines exist
# size sets how large the arc will be
# text sets the label for your angle while textposition lets you rougly set where the label is, here "inside"
# you can pass kwargs to the textlabel using text_kw=dict(...)
# especially useful is the xytext argument which lets you customize the relative position of your label more precisely
am1 = AngleAnnotation(center, p1, p2, ax=ax0, size=130, text="some_label", textposition = "inside", text_kw=dict(fontsize=20, xytext = (10,-5)))
You can find many more details in the link above. It’s working for me on matplotlib 3.4.2 right now.
I find TomNorway’s approach better, it has more flexibility in other cases than the accepted answer. I tested the code and made some quick fixes for even more applicability by creating a class.
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Arc
class LinesAngles:
def __init__(self, line1, line2, radius=None, flip=False, obtuse=False, reverse=False, dec=0, fontsize=8, title=""):
"""
line1: list of two points, of shape [[x0, y0], [x1, y1]]
line2: list of two points, of shape [[x0, y0], [x1, y1]]
radius: None, float or tuple of floats. If None, is set to half the length
of the shortest line orgio: If True, draws the arc around the point (0,0). If False, estimates
the intersection of the lines and uses that point.
flip: If True, flips the arc to the opposite side by 180 degrees
obtuse: If True, uses the other set of angles. Often used with reverse=True.
reverse: If True, reverses the two angles so that the arc is drawn "the opposite way around the circle"
dec: The number of decimals to round to
fontsize: fontsize of the angle label
title: Title of the plot
"""
self.line1 = line1
self.line2 = line2
self.lines = [line1, line2]
self.radius = radius
self.flip = flip
self.obtuse = obtuse
self.reverse = reverse
self.dec = dec
self.fontsize = fontsize
self.title = title
def halfangle(self,a, b) -> float:
"""
Gets the middle angle between a and b, when increasing from a to b
a: float, angle in degrees
b: float, angle in degrees
returns: float, angle in degrees
"""
if b < a:
b += 360
return (a + b)/2 % 360
def get_arc_patch(self, lines: list):
"""
For two sets of two points, create a matplotlib Arc patch drawing
an arc between the two lines.
lines: list of lines, of shape [[(x0, y0), (x1, y1)], [(x0, y0), (x1, y1)]]
returns: Arc patch, and text for the angle label
"""
linedata = [np.array(line.T) for line in lines]
scales = [np.diff(line).T[0] for line in linedata]
scales = [s[1] / s[0] for s in scales]
# Get angle to horizontal
angles = np.array([np.rad2deg(np.arctan(s/1)) for s in scales])
if self.obtuse:
angles[1] = angles[1] + 180
if self.flip:
angles += 180
if self.reverse:
angles = angles[::-1]
angle = abs(angles[1]-angles[0])
if self.radius is None:
lengths = np.linalg.norm(lines, axis=(0,1))
self.radius = min(lengths)/2
# Solve the point of intersection between the lines:
t, s = np.linalg.solve(np.array([line1[1]-line1[0], line2[0]-line2[1]]).T, line2[0]-line1[0])
intersection = np.array((1-t)*line1[0] + t*line1[1])
# Check if radius is a single value or a tuple
try:
r1, r2 = self.radius
except:
r1 = r2 = self.radius
arc = Arc(intersection, 2*r1, 2*r2, theta1=angles[1], theta2=angles[0])
half = self.halfangle(*angles[::-1])
sin = np.sin(np.deg2rad(half))
cos = np.cos(np.deg2rad(half))
r = r1*r2/(r1**2*sin**2+r2**2*cos**2)**0.5
xy = np.array((r*cos, r*sin))
xy = intersection + xy/2
textangle = half if half > 270 or half < 90 else 180 + half
textkwargs = {
'x':xy[0],
'y':xy[1],
's':str(round(angle, self.dec)) + "°",
'ha':'center',
'va':'center',
'fontsize':self.fontsize,
'rotation':textangle
}
return arc, textkwargs
def plot(self) -> None:
"""!
Plot the lines and the arc
"""
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
for line in self.lines:
x,y = line.T
ax.plot(x,y)
ax.axis('equal')
arc, angle_text = self.get_arc_patch(self.lines)
ax.add_artist(arc)
ax.set(title=self.title)
ax.text(**angle_text)
plt.show()
For using it you just create the instance and the plot function.
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
default = LinesAngles(line1, line2, title="Default")
#Plot single pair of lines
default.plot()
If you still want to plot multiple cases, I created a function that accepts the instances and plots automatically to the subplots you need.
# lines are formatted like this: [(x0, y0), (x1, y1)]
line1 = np.array([(1,-2), (3,2)])
line2 = np.array([(2,2), (2,-2)])
default = LinesAngles(line1, line2, title="Default")
flip = LinesAngles(line1, line2, title='flip=True', flip=True)
obtuse = LinesAngles(line1, line2, title='obtuse=True, reverse=True', obtuse=True, reverse=True)
radius = LinesAngles(line1, line2, title='radius=(2,1)', radius=(2,1))
#Plot single pair of lines
default.plot()
#Plot multiple line pairs
multiple_plot(default, flip, obtuse, radius, num_subplots=4)
Thanks to TomNorway for his answer, all credit to him I only made some modifications.