I made a Fourier Series/Transform Tkinter app, and so far everything works as I want it to, except that I am having issues with the circles misaligning.
Here is an image explaining my issue (the green and pink were added after the fact to better explain the issue):
I have narrowed down the problem to the start of the lines, as it seems that they end in the correct place, and the circles are in their correct places.
The distance between the correct positions and the position where the lines start seems to grow, but is actually proportional to the speed of the circle rotating, as the circle rotates by larger amounts, thus going faster.
Here is the code:
from tkinter import *
import time
import math
import random
root = Tk()
myCanvas = Canvas(root, width=1300, height=750)
myCanvas.pack()
myCanvas.configure(bg="#0A2239")
global x,y, lines, xList, yList
NumOfCircles = 4
rList = [200]
n=3
for i in range(0, NumOfCircles):
rList.append(rList[0]/n)
n=n+2
print(rList)
num = 250/sum(rList)
for i in range(0, NumOfCircles):
rList[i] = rList[i]*num
x=0
y=0
lines = []
circles = []
centerXList = [300]
for i in range(0,NumOfCircles):
centerXList.append(0)
centerYList = [300]
for i in range(0,NumOfCircles):
centerYList.append(0)
xList = [0]*NumOfCircles
yList = [0]*NumOfCircles
waveLines = []
wavePoints = []
con=0
endCoord = []
for i in range(0, NumOfCircles):
endCoord.append([0,0])
lastX = 0
lastY = 0
count = 0
randlist = []
n=1
for i in range(0, NumOfCircles):
randlist.append(200/n)
n=n+2
def createCircle(x, y, r, canvasName):
x0 = x - r
y0 = y - r
x1 = x + r
y1 = y + r
return canvasName.create_oval(x0, y0, x1, y1, width=r/50, outline="#094F9A")
def updateCircle(i):
newX = endCoord[i-1][0]
newY = endCoord[i-1][1]
centerXList[i] = newX
centerYList[i] = newY
x0 = newX - rList[i]
y0 = newY - rList[i]
x1 = newX + rList[i]
y1 = newY + rList[i]
myCanvas.coords(circles[i], x0, y0, x1, y1)
def circleWithLine(i):
global line, lines
circle = createCircle(centerXList[i], centerYList[i], rList[i], myCanvas)
circles.append(circle)
line = myCanvas.create_line(centerXList[i], centerYList[i], centerXList[i], centerYList[i], width=2, fill="#1581B7")
lines.append(line)
def update(i, x, y):
endCoord[i][0] = x+(rList[i]*math.cos(xList[i]))
endCoord[i][1] = y+(rList[i]*math.sin(yList[i]))
myCanvas.coords(lines[i], x, y, endCoord[i][0], endCoord[i][1])
xList[i] += (math.pi/randlist[i])
yList[i] += (math.pi/randlist[i])
def lineBetweenTwoPoints(x, y, x2, y2):
line = myCanvas.create_line(x, y, x2, y2, fill="white")
return line
def lineForWave(y1, y2, y3, y4, con):
l = myCanvas.create_line(700+con, y1, 702+con, y2, 704+con, y3, 706+con, y4, smooth=1, fill="white")
waveLines.append(l)
for i in range(0,NumOfCircles):
circleWithLine(i)
myCanvas.create_line(700, 20, 700, 620, fill="black", width = 3)
myCanvas.create_line(700, 300, 1250, 300, fill="red")
myCanvas.create_line(0, 300, 600, 300, fill="red", width = 0.5)
myCanvas.create_line(300, 0, 300, 600, fill="red", width = 0.5)
while True:
for i in range(0, len(lines)):
update(i, centerXList[i], centerYList[i])
for i in range(1, len(lines)):
updateCircle(i)
if count >= 8:
lineBetweenTwoPoints(lastX, lastY, endCoord[i][0], endCoord[i][1])
if count % 6 == 0 and con<550:
lineForWave(wavePoints[-7],wavePoints[-5],wavePoints[-3],wavePoints[-1], con)
con += 6
wavePoints.append(endCoord[i][1])
myCanvas.update()
lastX = endCoord[i][0]
lastY = endCoord[i][1]
if count != 108:
count += 1
else:
count = 8
time.sleep(0.01)
root.mainloop()
I am aware that this is not the best way to achieve what I am trying to achieve, as using classes would be much better. I plan to do that in case nobody can find a solution, and hope that when it is re-written, this issue does not persist.
The main problem that you are facing is that you receive floating point numbers from your calculations but you can only use integers for pixels. In the following I will show you where you fail and the quickest way to solve the issue.
First your goal is to have connected lines and you calculate the points here:
def update(i, x, y):
endCoord[i][0] = x+(rList[i]*math.cos(xList[i]))
endCoord[i][1] = y+(rList[i]*math.sin(yList[i]))
myCanvas.coords(lines[i], x, y, endCoord[i][0], endCoord[i][1])
xList[i] += (math.pi/randlist[i])
yList[i] += (math.pi/randlist[i])
when you add the following code into this function you see that it fails there.
if i != 0:
print(i,x,y)
print(i,endCoord[i-1][0], endCoord[i-1][1])
Because x and y should always match with the last point (end of the previous line) that will be endCoord[i-1][0] and endCoord[i-1][1].
to solve your problem I simply skipt the match for the sarting point of the follow up lines and took the coordinates of the previous line with the following alternated function:
def update(i, x, y):
endCoord[i][0] = x+(rList[i]*math.cos(xList[i]))
endCoord[i][1] = y+(rList[i]*math.sin(yList[i]))
if i == 0:
points = x, y, endCoord[i][0], endCoord[i][1]
else:
points = endCoord[i-1][0], endCoord[i-1][1], endCoord[i][0], endCoord[i][1]
myCanvas.coords(lines[i], *points)
xList[i] += (math.pi/randlist[i])
yList[i] += (math.pi/randlist[i])
Additional proposals are:
don't use wildcard imports
import just what you really use in the code random isnt used in your example
the use of global in the global namespace is useless
create functions to avoid repetitive code
def listinpt_times_circles(inpt):
return [inpt]*CIRCLES
x_list = listinpt_times_circles(0)
y_list = listinpt_times_circles(0)
center_x_list = listinpt_times_circles(0)
center_x_list.insert(0,300)
center_y_list = listinpt_times_circles(0)
center_y_list.insert(0,300)
use .after(ms,func,*args) instead of a interrupting while loop and blocking call time.sleep
def animate():
global count,con,lastX,lastY
for i in range(0, len(lines)):
update(i, centerXList[i], centerYList[i])
for i in range(1, len(lines)):
updateCircle(i)
if count >= 8:
lineBetweenTwoPoints(lastX, lastY, endCoord[i][0], endCoord[i][1])
if count % 6 == 0 and con<550:
lineForWave(wavePoints[-7],wavePoints[-5],wavePoints[-3],wavePoints[-1], con)
con += 6
wavePoints.append(endCoord[i][1])
myCanvas.update_idletasks()
lastX = endCoord[i][0]
lastY = endCoord[i][1]
if count != 108:
count += 1
else:
count = 8
root.after(10,animate)
animate()
root.mainloop()
read the PEP 8 -- Style Guide for Python
use intuitive variable names to make your code easier to read for others and yourself in the future
list_of_radii = [200] #instead of rList
as said pixels will be expressed with integers not with floating point numbers
myCanvas.create_line(0, 300, 600, 300, fill="red", width = 1) #0.5 has no effect compare 0.1 to 1
using classes and a canvas for each animation will become handy if you want to show more cycles
dont use tkinters update method
As #Thingamabobs said, the main reason for the misalignment is that pixel coordinates work with integer values. I got excited about your project and decided to make an example using matplotlib, this way I do not have to work with integer values for the coordinates. The example was made to work with any function, I implemented samples with sine, square and sawtooth functions.
I also tried to follow some good practices for naming, type annotations and so on, I hope this helps you
from numbers import Complex
from typing import Callable, Iterable, List
import matplotlib.pyplot as plt
import numpy as np
def fourier_series_coeff_numpy(f: Callable, T: float, N: int) -> List[Complex]:
"""Get the coefficients of the Fourier series of a function.
Args:
f (Callable): function to get the Fourier series coefficients of.
T (float): period of the function.
N (int): number of coefficients to get.
Returns:
List[Complex]: list of coefficients of the Fourier series.
"""
f_sample = 2 * N
t, dt = np.linspace(0, T, f_sample + 2, endpoint=False, retstep=True)
y = np.fft.fft(f(t)) / t.size
return y
def evaluate_fourier_series(coeffs: List[Complex], ang: float, period: float) -> List[Complex]:
"""Evaluate a Fourier series at a given angle.
Args:
coeffs (List[Complex]): list of coefficients of the Fourier series.
ang (float): angle to evaluate the Fourier series at.
period (float): period of the Fourier series.
Returns:
List[Complex]: list of complex numbers representing the Fourier series.
"""
N = np.fft.fftfreq(len(coeffs), d=1/len(coeffs))
N = filter(lambda x: x >= 0, N)
y = 0
radius = []
for n, c in zip(N, coeffs):
r = 2 * c * np.exp(1j * n * ang / period)
y += r
radius.append(r)
return radius
def square_function_factory(period: float):
"""Builds a square function with given period.
Args:
period (float): period of the square function.
"""
def f(t):
if isinstance(t, Iterable):
return [1.0 if x % period < period / 2 else -1.0 for x in t]
elif isinstance(t, float):
return 1.0 if t % period < period / 2 else -1.0
return f
def saw_tooth_function_factory(period: float):
"""Builds a saw-tooth function with given period.
Args:
period (float): period of the saw-tooth function.
"""
def f(t):
if isinstance(t, Iterable):
return [1.0 - 2 * (x % period / period) for x in t]
elif isinstance(t, float):
return 1.0 - 2 * (t % period / period)
return f
def main():
PERIOD = 1
GRAPH_RANGE = 3.0
N_COEFFS = 30
f = square_function_factory(PERIOD)
# f = lambda t: np.sin(2 * np.pi * t / PERIOD)
# f = saw_tooth_function_factory(PERIOD)
coeffs = fourier_series_coeff_numpy(f, 1, N_COEFFS)
radius = evaluate_fourier_series(coeffs, 0, 1)
fig, axs = plt.subplots(nrows=1, ncols=2, sharey=True, figsize=(10, 5))
ang_cum = []
amp_cum = []
for ang in np.linspace(0, 2*np.pi * PERIOD * 3, 200):
radius = evaluate_fourier_series(coeffs, ang, 1)
x = np.cumsum([x.imag for x in radius])
y = np.cumsum([x.real for x in radius])
x = np.insert(x, 0, 0)
y = np.insert(y, 0, 0)
axs[0].plot(x, y)
axs[0].set_ylim(-GRAPH_RANGE, GRAPH_RANGE)
axs[0].set_xlim(-GRAPH_RANGE, GRAPH_RANGE)
ang_cum.append(ang)
amp_cum.append(y[-1])
axs[1].plot(ang_cum, amp_cum)
axs[0].axhline(y=y[-1],
xmin=x[-1] / (2 * GRAPH_RANGE) + 0.5,
xmax=1.2,
c="black",
linewidth=1,
zorder=0,
clip_on=False)
min_x, max_x = axs[1].get_xlim()
line_end_x = (ang - min_x) / (max_x - min_x)
axs[1].axhline(y=y[-1],
xmin=-0.2,
xmax=line_end_x,
c="black",
linewidth=1,
zorder=0,
clip_on=False)
plt.pause(0.01)
axs[0].clear()
axs[1].clear()
if __name__ == '__main__':
main()
How can I find the indices of ALL the elements in all the eight directions (left, right, up, down, left-upper, right-upper, left-lower, right-lower) of a given 2D Matrix/Array?
For example in the given matrix below, I'm looking to extract the elements marked X for the input 0 and so on...:
X**X**X
*X*X*X*
**XXX**
XXX0XXX
**XXX**
X0XXXXX
XXX****
*X*X***
*X**X**
*X***X*
I used this lambda function to get the list of all the adjacent elements in all eight directions.
X = len(grid)
Y = len(grid[0])
neighbors = lambda x, y : [(x2, y2) for x2 in range(x-1, x+2)
for y2 in range(y-1, y+2)
if (-1 < x < X and
-1 < y < Y and
(x != x2 or y != y2) and
(0 <= x2 < X) and
(0 <= y2 < Y))]
**XXX**
**X0X**
**XXX**
*******
I want to be able to expand the above to get the above.
The following will provide the indexes in all eight directions:
from itertools import product
def valid_indexes(lst, row, col):
return row in range(len(lst)) and col in range(len(lst[0]))
# Queen's view since it's the same as what a queen in chess can 'view'
def queens_view(lst, row, col, dr=0, dc=0):
if dr or dc:
yield (row, col)
if valid_indexes(lst, row+dr, col+dc):
yield from queens_view(lst, row+dr, col+dc, dr, dc)
else:
for dr, dc in product([-1, 0, 1], [-1, 0, 1]):
if dr or dc and valid_indexes(lst, row+dr, col+dc):
yield from queens_view(lst, row+dr, col+dc, dr, dc)
start_row, start_col = 3, 4 # Index of the '0' in your list
for row, col in queens_view(lst, start_row, start_col):
print(row, col)
# Do what you like with the index
You can make a functions that 'shoots' in every direction from the desired point until the end of the grid is reached. Returning all the points found:
def direction_points(g_len_x, g_len_y, point_x, point_y):
result = []
directions = [
[0, -1], # up
[1, -1], # up right
[1, 0], # right
[1, 1], # down right
[0, 1], # down
[-1, 1], # down left
[-1, 0], # left
[-1, -1], # left up
]
for direction in directions:
x = point_x
y = point_y
end_reached = False
while not end_reached:
x = x + direction[0]
y = y + direction[1]
if (0 <= x < g_len_x) and not end_reached:
if (0 <= y < g_len_y) and not end_reached:
result.append([x, y])
else:
end_reached = True
else:
end_reached = True
return result
With that you can create the lines or grid:
grid_len_x = 10
grid_len_y = 12
mid_point_x = 4
mid_point_y = 6
points = direction_points(grid_len_x, grid_len_y, mid_point_x, mid_point_y)
lines = []
for y in range(grid_len_y):
line = ''
for x in range(grid_len_x):
if [x, y] in points:
line += 'X'
else:
if x == mid_point_x and y == mid_point_y:
line += '0'
else:
line += '*'
lines.append(line)
for line in lines:
print(line)
Result
****X*****
****X****X
X***X***X*
*X**X**X**
**X*X*X***
***XXX****
XXXX0XXXXX
***XXX****
**X*X*X***
*X**X**X**
X***X***X*
****X****X
I have a clicking applicaiton on a phone.
I want to sample last N points so it won't click the same "place" over and over again.
I guess it should be kind of this:
This I want to avoid.
I guess the circlue center should be the center of all points ?
How to determind the radius ?
I think calculation of the last N dots can be used to calculte the "new" N dots once a new click is done, to reduce performance.
Any suggestions ?
Thanks
def clicking_loop_protection(self, x, y, methods):
'''
:param x:
:param y:
:param method: 'xpath'/'point' it can be both
:return:
'''
def centroid(points):
_len = len(points)
x_coords = [p[0] for p in points]
y_coords = [p[1] for p in points]
centroid_x = sum(x_coords) / _len
centroid_y = sum(y_coords) / _len
return centroid_x, centroid_y
def calculate_points_distance(x1, y1, x2, y2):
dist = math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
return dist
point_res = True
if 'point' in methods:
# add current point
_point = (x, y)
try:
self.points_history[self.points_history_index] = _point
except IndexError:
self.points_history.append(_point)
if len(self.points_history) == self.points_history_length:
centroid_point_x, centroid_point_y = centroid(self.points_history)
radius = self.displayWidth/10
for point in self.points_history:
# distance from centroid should be less than radius (to fail the test)
distance = calculate_points_distance(centroid_point_x, centroid_point_y, point[0], point[1])
if distance > radius:
point_res = True # pass test !
break
else:
point_res = False
self.points_history_index += 1
self.points_history_index %= self.points_history_length
return xpath_res and point_res
This is an exercise 6.1 in the book "Think Python". The question is to find the print result.
This is what I can get so far.
x = 1, y = 2
bring to a(x, y), return 4
b(z), return z**2 + z
I couldn't find the valve z from c(x, y, z) function.
def b(z):
prod = a(z, z)
print(z, prod)
return prod
def a(x, y):
x = x + 1
return x * y
def c(x, y, z):
total = x + y + z
square = b(total)**2
return square
x = 1
y = x + 1
print(c(x, y+3, x+y))
The x and y in def a(x, y): are not the same x and y defined elsewhere in the script. It might as well say def a(j, k):. When you see prod = a(z, z), you need to know what the value of z is, and then go to the definition of def a(j, k): and think j = z and k = z.
If we just tell you what the output is, then you wouldn't learn to "Think Python"