• Explore
• My scripts
• Calculator

from vector1 import AC, r, reduce

'''revised 190227'''
'''vector operations'''

'''zero vector'''
O = [0, 0, 0]

'''basis vectors'''
I = [1, 0, 0]
J = [0, 1, 0]
K = [0, 0, 1]


def va(a, b):
    '''vector addition'''
    return [a_i + b_i for (a_i, b_i) in zip(a, b)]

def vs(aList):
    '''vector sum: add together a list of vectors'''
    return reduce(va, aList)

def vm(a, n):
    '''multiplication of vector a by scalar n'''
    return [n * i for i in a]

def vdist(a, b):
    '''distance from a to b, i.e. b - a'''
    return va(b, vm(a, -1))

def u(a):
    '''unit vector'''
    return vm(a, 1.0/r(a))

def md2v(m, d):
    '''magnitude (m) and direction (d) to vector'''
    return vm(u(d), m)

def cp(a, b):
    '''cross product'''
    if len(a) == 2:
        return a[0]*b[1] - a[1]*b[0]
    if len(a) == 3:
        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 dp(a, b):
    '''dot product'''
    return sum([i * j for (i, j) in zip(a, b)])

def stp(a, b, c):
    '''scalar triple product'''
    return dp(a, cp(b, c))

def ang(a, b):
    '''angle between a and b'''
    return AC(dp(a, b) / (r(a) * r(b)))

def axangs(a):
    '''angles between vector a and each axis'''
    return [ang(a, i) for i in (I, J, K)]

def comp(a, b):
    '''scalar projection of a onto b'''
    return dp(a, u(b))

def proj(a, b):
    '''vector projection of a onto b'''
    return vm(u(b), comp(a, b))

def orth(a, b):
    '''proj(a, b) + orth(a, b) == a'''
    return vdist(proj(a, b), a)