绘制对角网格线，相交线的角度可变

Question

I am trying to plot some diagonal grid lines on a plot of random data for now. I am currently able to produce 90 degree intersecting lines, but I am unsure how to produce anything other than that angle. Here is the code:

import numpy as np
import matplotlib.pyplot as plt
f, ax = plt.subplots(figsize=(6, 6))
mean, cov = [0, 0], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 100).T
y += x + 1

ax.scatter(x, y, c=".3")

ax.plot([0, 1], [0, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.1, 1], [0, 0.9], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.2, 1], [0, 0.8], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.3, 1], [0, 0.7], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.4, 1], [0, 0.6], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.5, 1], [0, 0.5], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.6, 1], [0, 0.4], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.7, 1], [0, 0.3], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.8, 1], [0, 0.2], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([0.9, 1], [0, 0.1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.1, 1], [0, 1.1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.2, 1], [0, 1.2], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.3, 1], [0, 1.3], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.4, 1], [0, 1.4], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.5, 1], [0, 1.5], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.6, 1], [0, 1.6], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.7, 1], [0, 1.7], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.8, 1], [0, 1.8], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-0.9, 1], [0, 1.9], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([-1, 1], [0, 2], transform=ax.transAxes, color='black', linewidth=0.5)


ax.plot([1, 0], [0, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.9], [0.9, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.8], [0.8, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.7], [0.7, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.6], [0.6, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.5], [0.5, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.4], [0.4, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.3], [0.3, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.2], [0.2, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, 0.1], [0.1, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.9], [-0.9, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.8], [-0.8, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.7], [-0.7, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.6], [-0.6, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.5], [-0.5, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.4], [-0.4, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.3], [-0.3, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.2], [-0.2, 1], transform=ax.transAxes, color='black', linewidth=0.5)
ax.plot([1, -0.1], [-0.1, 1], transform=ax.transAxes, color='black', linewidth=0.5)

plt.show()

plot to show 90 degree intersecting grid lines, want to make that angle a variable one, say 25 degree or 60

Ideally, I would like to incorporate this into a function that I can specify the intersecting degree and the number of lines in the plot.

Answer 1

You have a lot of repeating lines of code, which suggests that a loop can be a sensible approach. The coordinates also follow a strict geometrical pattern, so can be calculated mathematically.

In my answer below I used a loop and some trigonometry to generate the coordinates automatically. Your definition of "intersecting degree" of angle is ambiguous - is it top/bottom angle or the left/right angle? I assumed it is the former in my solution.

If you are keen to understand the geometrical reasoning, sketch a right-angled triangle, such as here . On that sketch side b is 1 and side a is tan(A) . That should help you.

This might be possible using matplotlib built-ins, but I am not sure. I just adapted your approach and automated it.

import numpy as np
import matplotlib.pyplot as plt
f, ax = plt.subplots(figsize=(6, 6))
mean, cov = [0, 0], [(1, .6), (.6, 1)]
x, y = np.random.multivariate_normal(mean, cov, 100).T
y += x + 1

ax.scatter(x, y, c=".3")

intersecting_angle = 30  # the top/bottom angle of intersection of the lines
horizontal_angle = (180-intersecting_angle)/2  # calculated angle from horizontal

num_of_lines = 20  # number of lines to be visible on the screen in each direction.
gap = (1+ np.tan(np.deg2rad(horizontal_angle)))/num_of_lines  # calculated gap between lines

for i in range(num_of_lines):  # we know how many lines we want to repeat this for
    for direction in [-1, 1]:  # some of the lines go above the x axis, some will go below to draw in that empty area on the right.
        startx = 0  # all lines start at the leftmost part of the screen
        starty = 0 + gap*i*direction  # lines are spaced by the same gap vertically

        endx = 1  # all lines end at the rightmost part of the screen
        endy = np.tan(np.deg2rad(horizontal_angle)) + gap*i*direction  # trig used to calculate the end y-coordinate for the given angle

        # a line is drawn from left to right upwards
        ax.plot([startx, endx], [starty, endy], transform=ax.transAxes, color='black', linewidth=0.5)
        # a line is drawn from left to right downwards
        ax.plot([startx, endx], [endy, starty], transform=ax.transAxes, color='black', linewidth=0.5)


plt.show()

EDIT: A modification to the line-drawing to ensure that the lines cross on the left side of the screen. Looks nicer and would make it easier to make it align with specific axis ticks if necessary:

### LIBRARY AND SETUP STUFF ###
for i in range(num_of_lines):
    for direction in [-1, 1]:
        startx = 0
        starty = 0 + gap*i*direction

        endx = 1
        endy = np.tan(np.deg2rad(horizontal_angle)) + gap*i*direction
        endy_flip = -np.tan(np.deg2rad(horizontal_angle)) + gap*i*direction

        ax.plot([startx, endx], [starty, endy], transform=ax.transAxes, color='black', linewidth=0.5)
        ax.plot([startx, endx], [starty, endy_flip], transform=ax.transAxes, color='black', linewidth=0.5)