from itertools import permutations as nPp
import math
from math import pi as pi
from math import atan as invT
from math import sqrt as SR
import matplotlib
import matplotlib.pyplot as plt
import moviepy.video.io.ImageSequenceClip
import os
import pandas as pd
def createDF(m) :
#(x,y), distance, and angle with x-axis
data = pd.DataFrame(columns=['X', 'Y', 'D', 'A'])
for x in range(1, m+1) :
for y in range(1, m+1) :
#Angle with x-axis.
a = 180*invT(y/x)/pi
#If the angle does not exist, add it to the df.
if not data['A'].isin([a]).any() :
data.loc[len(data)] = [x, y, SR(x**2 + y**2), a]
#See only up to m units.
data = data[(data['D'] <= m)].sort_values(by = 'A')
#Get the difference.
data['dA'] = data['A'].diff()
data.sort_values(by = 'A', inplace = True)
data.reset_index(inplace = True, drop = True)
return(data)
#Clear axes.
def clearAx(ax):
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["bottom"].set_visible(False)
ax.spines["left"].set_visible(False)
ax.set_xticks([])
ax.set_yticks([])
return(ax)
def plotForest(ax, m) :
df = createDF(m)
for i in range(len(df)) :
ax.plot([0, df.at[i, 'X']], [0, df.at[i, 'Y']], lw = 0.5, c = 'r')
X = []
Y = []
for x in range(0, m+1) :
for y in range(0, m+1) :
if SR(x**2 + y**2) <= m :
X.append(x)
Y.append(y)
ax.scatter(X, Y, lw = 2, c = 'k', zorder = 2)
def animateForest(m) :
fig = plt.figure(figsize = (8, 8))
ax = fig.add_subplot(xlim = (-0.1, m+0.1),
ylim = (-0.1, m+0.1))
fig.subplots_adjust(left = 0.02, bottom = 0.02, right = 0.98, top = 0.98)
#Remove axes and ticks.
ax = clearAx(ax)
plotForest(ax, m)
data = createDF(7)
data[data['A'] <= 45].sort_values('dA').tail(4)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 3 | 3.0 | 1.0 | 3.162278 | 18.434949 | 4.398705 |
| 5 | 2.0 | 1.0 | 2.236068 | 26.565051 | 4.763642 |
| 10 | 1.0 | 1.0 | 1.414214 | 45.000000 | 6.340192 |
| 0 | 6.0 | 1.0 | 6.082763 | 9.462322 | NaN |
data = createDF(8)
data[data['A'] <= 45].sort_values('dA').tail(6)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 11 | 4.0 | 3.0 | 5.000000 | 36.869898 | 3.179830 |
| 6 | 5.0 | 2.0 | 5.385165 | 21.801409 | 3.366461 |
| 8 | 2.0 | 1.0 | 2.236068 | 26.565051 | 3.366461 |
| 9 | 5.0 | 3.0 | 5.830952 | 30.963757 | 4.398705 |
| 14 | 1.0 | 1.0 | 1.414214 | 45.000000 | 5.194429 |
| 0 | 7.0 | 1.0 | 7.071068 | 8.130102 | NaN |
data = createDF(20)
data[data['A'] <= 45].sort_values('dA').tail(6)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 71 | 3.0 | 2.0 | 3.605551 | 33.690068 | 0.954841 |
| 40 | 17.0 | 6.0 | 18.027756 | 19.440035 | 1.005086 |
| 57 | 17.0 | 9.0 | 19.235384 | 27.897271 | 1.332220 |
| 56 | 2.0 | 1.0 | 2.236068 | 26.565051 | 1.363928 |
| 95 | 1.0 | 1.0 | 1.414214 | 45.000000 | 2.121096 |
| 0 | 19.0 | 1.0 | 19.026298 | 3.012788 | NaN |
data = createDF(21)
data[data['A'] <= 45].sort_values('dA').tail(8)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 30 | 4.0 | 1.0 | 4.123106 | 14.036243 | 0.795724 |
| 77 | 16.0 | 11.0 | 19.416488 | 34.508523 | 0.818455 |
| 41 | 3.0 | 1.0 | 3.162278 | 18.434949 | 0.909380 |
| 42 | 17.0 | 6.0 | 18.027756 | 19.440035 | 1.005086 |
| 61 | 17.0 | 9.0 | 19.235384 | 27.897271 | 1.332220 |
| 60 | 2.0 | 1.0 | 2.236068 | 26.565051 | 1.363928 |
| 103 | 1.0 | 1.0 | 1.414214 | 45.000000 | 1.974934 |
| 0 | 20.0 | 1.0 | 20.024984 | 2.862405 | NaN |
data = createDF(22)
data[data['A'] <= 45].sort_values('dA').tail(12)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 55 | 17.0 | 7.0 | 18.384776 | 22.380135 | 0.578726 |
| 94 | 4.0 | 3.0 | 5.000000 | 36.869898 | 0.616060 |
| 34 | 4.0 | 1.0 | 4.123106 | 14.036243 | 0.643746 |
| 35 | 19.0 | 5.0 | 19.646883 | 14.743563 | 0.707319 |
| 86 | 3.0 | 2.0 | 3.605551 | 33.690068 | 0.784825 |
| 87 | 16.0 | 11.0 | 19.416488 | 34.508523 | 0.818455 |
| 46 | 20.0 | 7.0 | 21.189620 | 19.290046 | 0.855097 |
| 45 | 3.0 | 1.0 | 3.162278 | 18.434949 | 0.909380 |
| 68 | 19.0 | 10.0 | 21.470911 | 27.758541 | 1.193489 |
| 67 | 2.0 | 1.0 | 2.236068 | 26.565051 | 1.218875 |
| 115 | 1.0 | 1.0 | 1.414214 | 45.000000 | 1.847610 |
| 0 | 21.0 | 1.0 | 21.023796 | 2.726311 | NaN |
data = createDF(194)
data[data['A'] <= 45].sort_values('dA').tail(12)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 2254 | 5.0 | 1.0 | 5.099020 | 11.309932 | 0.059251 |
| 7361 | 153.0 | 115.0 | 191.400104 | 36.929768 | 0.059870 |
| 2798 | 187.0 | 47.0 | 192.815974 | 14.108314 | 0.072070 |
| 2797 | 4.0 | 1.0 | 4.123106 | 14.036243 | 0.072895 |
| 6723 | 3.0 | 2.0 | 3.605551 | 33.690068 | 0.082203 |
| 6724 | 160.0 | 107.0 | 192.481168 | 33.772626 | 0.082559 |
| 3677 | 3.0 | 1.0 | 3.162278 | 18.434949 | 0.093468 |
| 3678 | 182.0 | 61.0 | 191.950514 | 18.529340 | 0.094392 |
| 5303 | 173.0 | 87.0 | 193.644003 | 26.697374 | 0.132323 |
| 5302 | 2.0 | 1.0 | 2.236068 | 26.565051 | 0.132629 |
| 8983 | 1.0 | 1.0 | 1.414214 | 45.000000 | 0.209874 |
| 0 | 193.0 | 1.0 | 193.002591 | 0.296867 | NaN |
data = createDF(195)
data[data['A'] <= 45].sort_values('dA').tail(14)
| X | Y | D | A | dA | |
|---|---|---|---|---|---|
| 2279 | 5.0 | 1.0 | 5.099020 | 11.309932 | 0.057700 |
| 2280 | 189.0 | 38.0 | 192.782261 | 11.368219 | 0.058287 |
| 7434 | 4.0 | 3.0 | 5.000000 | 36.869898 | 0.059190 |
| 7435 | 153.0 | 115.0 | 191.400104 | 36.929768 | 0.059870 |
| 2828 | 4.0 | 1.0 | 4.123106 | 14.036243 | 0.071352 |
| 2829 | 187.0 | 47.0 | 192.815974 | 14.108314 | 0.072070 |
| 6790 | 3.0 | 2.0 | 3.605551 | 33.690068 | 0.082203 |
| 6791 | 160.0 | 107.0 | 192.481168 | 33.772626 | 0.082559 |
| 3715 | 3.0 | 1.0 | 3.162278 | 18.434949 | 0.093468 |
| 3716 | 182.0 | 61.0 | 191.950514 | 18.529340 | 0.094392 |
| 5356 | 173.0 | 87.0 | 193.644003 | 26.697374 | 0.132323 |
| 5355 | 2.0 | 1.0 | 2.236068 | 26.565051 | 0.132629 |
| 9072 | 1.0 | 1.0 | 1.414214 | 45.000000 | 0.208347 |
| 0 | 194.0 | 1.0 | 194.002577 | 0.295336 | NaN |