3b1b-manim/moser/moser_helpers.py
2015-04-14 17:55:25 -07:00

34 lines
1 KiB
Python

import numpy as np
import operator as op
import itertools as it
def choose(n, r):
if n < r: return 0
if r == 0: return 1
denom = reduce(op.mul, xrange(1, r+1), 1)
numer = reduce(op.mul, xrange(n, n-r, -1), 1)
return numer//denom
def moser_function(n):
return choose(n, 4) + choose(n, 2) + 1
def intersection(line1, line2):
"""
A "line" should come in the form [(x0, y0), (x1, y1)] for two
points it runs through
"""
p0, p1, p2, p3 = map(
lambda tup : np.array(tup[:2]),
[line1[0], line1[1], line2[0], line2[1]]
)
p1, p2, p3 = map(lambda x : x - p0, [p1, p2, p3])
transform = np.zeros((2, 2))
transform[:,0], transform[:,1] = p1, p2
if np.linalg.det(transform) == 0: return
inv = np.linalg.inv(transform)
new_p3 = np.dot(inv, p3.reshape((2, 1)))
#Where does line connecting (0, 1) to new_p3 hit x axis
x_intercept = new_p3[0] / (1 - new_p3[1])
result = np.dot(transform, [[x_intercept], [0]])
result = result.reshape((2,)) + p0
return result