Machine Generation of Art Patterns in Vector Fields

Question

I am trying to rewrite this article:We draw, programming. Machine-generated generation of artistic patterns in vector fields (Russian language) from pseudo-code in Python. I am new to ML, hence the following question arises: How to build a grid of angles and output it through PyCharm? I am at this stage:

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

width = 100
height = 100

left_x = int(width * -0.5)
right_x = int(width * 1.5)
top_y = int(height * -0.5)
bottom_y = int(height * 1.5)

resolution = int(width * 0.01)

num_columns = int((right_x - left_x) / resolution)
num_rows = int((bottom_y - top_y) / resolution)

grid=np.ndarray((num_columns, num_rows))
grid[:,:]=math.pi * 0.25

In this code, I create a grid array in which 200 rows and 200 columns, into which the angle 'default_angle' is inserted. Please tell me whether I’m moving in the right direction and how to "draw" a grid, as in an attached link. So far I think I need to use matplotlib.

Kresten · Answer 1 · 2020-02-12T09:01:28.177

I believe you need to take a look at meshgrid from numpy

from the meshgrid documentation examples:

x = np.arange(-5, 5, 0.1)
y = np.arange(-5, 5, 0.1)
xx, yy = np.meshgrid(x, y, sparse=True)
z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
h = plt.contourf(x,y,z)

Edit. After seeing you r link a better resource is the matplotlib quiver demo

import matplotlib.pyplot as plt
import numpy as np

X = np.arange(-10, 10, 1)
Y = np.arange(-10, 10, 1)
U, V = np.meshgrid(X, Y)

fig, ax = plt.subplots()
q = ax.quiver(X, Y, U, V)
ax.quiverkey(q, X=0.3, Y=1.1, U=10,
             label='Quiver key, length = 10', labelpos='E')

plt.show()

score 0 · Accepted Answer · answered Feb 12 '20 at 11:11

You need to make several steps to recreate this:

create vector field based on some function or equation
normalize arrows for proper display
draw line 3.1. set starting parameters 3.2. set while out condition 3.3. calculate new position based on angle from starting point 3.4. get new position index --> net new angle 3.5. update starting positions
draw vector field and line

import numpy as np import matplotlib.pyplot as plt

size = 50
X = np.arange(1, size, 1)
Y = np.arange(1, size, 1)
U, V = np.meshgrid(X, Y)

# Normalize the arrows:
U = U / np.sqrt(U**2 + V**2)
V = V / np.sqrt(U**2 + V**2)

# create angles field
data = []
for i in np.linspace(0, 180, Y.shape[0]):
    data.append([i]*X.shape[0])

angle = np.array(data)

# set starting parameters
x_start_position = 2
y_start_position = 2
step_length = 1.0
point_angle = angle[x_start_position, y_start_position]
line_coordinates = [[x_start_position, y_start_position]]

# collect line points for each step
while x_start_position >= 2:

    # calculate tep based on angle
    x_step = step_length * np.cos(point_angle*np.pi/180)
    y_step = step_length * np.sin(point_angle*np.pi/180)

    # calculate new position
    x_new_position = x_start_position + x_step
    y_new_position = y_start_position + y_step

    # get array index of new position
    x_new_index = int(x_new_position)
    y_new_index = int(y_new_position)

    # get new angle
    point_angle = angle[y_new_index, x_new_index]

    # update start position
    x_start_position = x_new_position
    y_start_position = y_new_position

    # collect results
    line_coordinates.append([x_new_position, y_new_position])

# set line coordinates
line_data = np.array(line_coordinates)
x_line = line_data[:,0]
y_line = line_data[:,1]

# plot field
plt.quiver(X, Y, U, V, color='black', angles=angle, width=0.005)
# plot line
plt.plot(x_line, y_line, '-', color='red')
plt.show()

Output:

Machine Generation of Art Patterns in Vector Fields

2 Answers2