# ===-- vec3.py -----------------------------------------------------------===##
# 
#                      The KLEE Symbolic Virtual Machine
# 
#  This file is distributed under the University of Illinois Open Source
#  License. See LICENSE.TXT for details.
# 
# ===----------------------------------------------------------------------===##

from __future__ import division
from math import ceil,floor,sqrt
from random import random as _random
_min,_max= min,max

def random():
	return (_random()*2-1,_random()*2-1,_random()*2-1)

def inv(a):	return (-a[0],-a[1],-a[2])

def add(a,b):	return (a[0]+b[0], a[1]+b[1], a[2]+b[2])
def sub(a,b):	return (a[0]-b[0], a[1]-b[1], a[2]-b[2])
def mul(a,b):	return (a[0]*b[0], a[1]*b[1], a[2]*b[2])
def div(a,b):	return (a[0]/b[0], a[1]/b[1], a[2]/b[2])
def mod(a,b):	return (a[0]%b[0], a[1]%b[1], a[2]%b[2])
def dot(a,b):	return (a[0]*b[0]+ a[1]*b[1]+ a[2]*b[2])

def addN(a,n):	return (a[0]+n, a[1]+n, a[2]+n)
def subN(a,n):	return (a[0]-n, a[1]-n, a[2]-n)
def mulN(a,n):	return (a[0]*n, a[1]*n, a[2]*n)
def modN(a,n):	return (a[0]%n, a[1]%n, a[2]%n)
def divN(a,n):	return (a[0]/n, a[1]/n, a[2]/n)

def sqr(a):			return dot(a,a)
def length(a):		return sqrt(sqr(a))
def normalize(a):	return mulN(a, 1.0/length(a))
def avg(a,b):		return mulN(add(a,b),0.5)
def distance(a,b):	return length(sub(a,b))

def cross(a, b):
	return (a[1]*b[2] - a[2]*b[1],
			a[2]*b[0] - a[0]*b[2],
			a[0]*b[1] - a[1]*b[0])
def reflect(a, b):
	return sub(mulN(b, dot(a, b)*2), a)

def lerp(a,b,t):
	return add(mulN(a,1.0-t), mulN(b, t))

def min((a0,a1,a2),(b0,b1,b2)):
	return (_min(a0,b0),_min(a1,b1),_min(a2,b2))
def max((a0,a1,a2),(b0,b1,b2)):
	return (_max(a0,b0),_max(a1,b1),_max(a2,b2))

def toint(a):
	return (int(a[0]), int(a[1]), int(a[2]))
def tofloor(a):
	return (floor(a[0]), floor(a[1]), floor(a[2]))
def toceil(a):
	return (ceil(a[0]), ceil(a[1]), ceil(a[2]))

def sumlist(l):
	return reduce(add, l)
def avglist(l):
	return mulN(sumlist(l), 1.0/len(l))