vector3.py

Created by asness
Created on February 28, 2019
1005 Bytes
from vector1 import r
from vector2 import O, va, vs, vm, vdist, dp, cp, stp

'''revised 190227'''
'''vector operations, continued'''

def pldist(a, b, c):
    '''distance from point a to a line
    containing b and c'''
    ba = vdist(a, b)
    bc = vdist(b, c)
    return r(cp(ba, bc)) / r(bc)

def lldist(p1, d1, p2, d2):
    '''Distance between two skew lines L1 and L2.
    L_i contains point p_i and its direction is d_i:
    i.e. r_i(t_i) == p_i + t_i * d_i'''
    return stp(vdist(p1, p2), d1, d2) / r(cp(d1, d2))

def fcsys(rs, Fs, PMs=[O]):
    '''Force-couple system given forces and pure moments'''
    R = vs(Fs)
    Ms = [cp(r, F) for (r, F) in zip(rs, Fs)]
    MR = va(vs(Ms), vs(PMs))
    return R, MR
    
def wr(R, M):
    '''Given a force-couple system, find the equivalent
    wrench's pitch p and its closest point to origin R0.
    The pitch axis line can be written as x(t) == R0 + t * R'''
    p = dp(R, M) / r(R)**2
    R0 = vm(cp(R, M), 1/r(R)**2)
    return p, R0