coordinateMathSoln

import math class Triad : """ Calculate angles and distances among a triad of points.

Author: David Bernick
Date: March 21, 2013
Points can be supplied in any dimensional space as long as they are consistent.
Points are supplied as tupels in n-dimensions, and there should be three
of those to make the triad. Each point is positionally named as p,q,r
and the corresponding angles are then angleP, angleQ and angleR.
Distances are given by dPQ(), dPR() and dQR()

Required Modules: math
initialized: 3 positional tuples representing Points in n-space
         p1 = Triad( p=(1,0,0), q=(0,0,0), r=(0,1,0) )
attributes: p,q,r the 3 tuples representing points in N-space
methods:  angleP(), angleR(), angleQ() angles measured in radians
      dPQ(), dPR(), dQR() distances in the same units of p,q,r

"""

def __init__(self,p,q,r) :
    """ Construct a Triad. 
    
    Example construction:
        p1 = Triad( p=(1.,0.,0.), q=(0.,0.,0.), r=(0.,0.,0.) ). 
    """
    self.p = p
    self.q = q
    self.r = r

private helper methods

def d2 (self,a,b) : # calculate squared distance of point a to b
    return float(sum((ia-ib)*(ia-ib)  for  ia,ib in zip (a,b)))

def dot (self,a,b) : # dotProd of standard vectors a,b
    return float(sum(ia*ib for ia,ib in zip(a,b)))

def ndot (self,a,b,c) : # dotProd of vec. a,c standardized to b
    return float(sum((ia-ib)*(ic-ib) for ia,ib,ic in zip (a,b,c)))

calculate lengths(distances) of segments PQ, PR and QR

def dPQ (self):
    """ Provides the distance between point p and point q """
    return math.sqrt(self.d2(self.p,self.q))

def dPR (self):
    """ Provides the distance between point p and point r """
    return math.sqrt(self.d2(self.p,self.r))

def dQR (self):
    """ Provides the distance between point q and point r """
    return math.sqrt(self.d2(self.q,self.r))

def angleP (self) :
    """ Provides the angle made at point p by segments pq and pr (radians). """
    return math.acos(self.ndot(self.q,self.p,self.r) /   math.sqrt(self.d2(self.q,self.p)*self.d2(self.r,self.p)))

def angleQ (self) :
    """ Provides the angle made at point q by segments qp and qr (radians). """
    return math.acos(self.ndot(self.p,self.q,self.r) /  math.sqrt(self.d2(self.p,self.q)*self.d2(self.r,self.q)))

def angleR (self) :
    """ Provides the angle made at point r by segments rp and rq (radians). """
    return math.acos(self.ndot(self.p,self.r,self.q) /  math.sqrt(self.d2(self.p,self.r)*self.d2(self.q,self.r)))

def main(): ''' Function docstring goes here''' #we will take input of the cordinates points=input('Cordinate Points:') points=points.replace('(','') points=points.replace(',','') points=points.replace('=','') points=points.split(') ') p=points[0].split() q=points[1].split() r=points[2].replace(')','').split()

We will construct a Dictionary with key as the cordinate name, C,N,Ca and Value as the 3D point

diction={}
diction[p[0]]=float(p[1]),float(p[2]),float(p[3])
diction[q[0]]=float(q[1]),float(q[2]),float(q[3])
diction[r[0]]=float(r[1]),float(r[2]),float(r[3])
thisCord=Triad(diction['C'],diction['N'],diction['Ca'])
print('N-C bond length = {0:0.2f}'.format(thisCord.dPQ()))
print('N-Ca bond length = {0:0.2f}'.format(thisCord.dQR()))
print('C-N-Ca bond angle = {0:0.1f}'.format(thisCord.angleQ()*180/3.142))

main()