from __future__ import print_function
import sys
import numpypy # if using stock python, use plain numpy

'''
Todo:
- fixmes
- Make a System class
- Provision to draw successive steps iteratively
- Check physics (esp. mass)
- Find reasonable timestep tradeoff
- Colors
- Different metrics
'''

W = 1000
H = 500

img = numpypy.zeros((H, W, 3), dtype=numpypy.uint8)

def clip(d, o, b):
	return min(max(d, o), b)

def pk(c):
	chan = (1.0/c)*255
	chan = clip(0, c, 255)
	chan = int(chan)
	return [chan, chan, chan]

class Body(object):
	def __init__(self, m, x, v):
		self.m = m # mass
		self.x = x # position
		self.v = v # velocity
		self.a = 0+0j # acceleration
		self.lasta = self.a # acceleration at the last step
	
	def force_from(self, other):
		difference = other.x - self.x		
		strength = other.m * (1.0/(abs(difference)**2))
		force = complex(difference.real * strength, difference.imag * strength)
		return force

	def xstep(self):
		self.x += self.v + (self.a/2.0)
	
	def astep(self, s):
		self.lasta = self.a
		self.a = 0+0j
		for other in s:
			if other.x == self.x: continue # fixme
			self.a += self.force_from(other)
		self.v += (self.a + self.lasta)/2.0

for x in range(W):
	for y in range(H):
		system = []
		system.append(Body(0.0, complex((x-W/2.0)/10.0, (y-H/2.0)/10.0), 0-0j))
		system.append(Body(2.5, 20+0j, 0-2j))
		system.append(Body(5.0, -20+0j, 0+1j))
	
		for step in range(int(sys.argv[1])):
			for body in system: body.xstep()
			for body in system: body.astep(system)
		
		d = abs(system[0].x)
		#print d
		if d == 0:
			d = 1/1e300 # fixme
		setting = pk(d)
		#print setting
		img[y, x] = setting

def array_to_p6(a):
	#print a
	w = a.shape[1]
	h = a.shape[0]
	header = "P6\n%i %i\n%i\n" % (w, h, 255)
	print(header, end='')
	for x in range(h):
		for y in range(w):
			c = a[x][y]
			#print ec
			o = "%s%s%s" % (chr(c[0]), chr(c[1]), chr(c[2]))
			print(o, end='')

array_to_p6(img)