from numpy import array, dot
import math 

def generateSeparations (symmetry_points, route):
    """
    Given a dict of 3D vector points and the route which
    connects them, generate the so-called separations and
    separation sums.
    """
    separations = []
    # The first point is always placed at x=0
    separationsums = [0.0]
    # The last symmetry point is of course not included
    # except as endpoint for the last segment
    for p in range(len(route)-1):
        delta = array(symmetry_points[route[p+1]]) - array(symmetry_points[route[p]])
        # Calculate and store the vector distance between subsequent points
        separations.append(math.sqrt(dot(delta,delta)))
        # Cumulative sum of the distances
        separationsums.append(separationsums[-1] + separations[-1])
    return separations, separationsums

def convertVectorPointToX (N, id, separations, separationsums):
    """
    Use the separations and separation sums to map 3D vector
    points onto a one-dimensional dummy coordinate for the
    horizontal axis, e.g. to be used in a bandstructure plot.
    id is the segment number.
    """
    x = []
    for i in range(N):
        # If changes are made to the definition of the vector points
        # in generateLineBetweenVectorsPoints below,
        # the denominator here must be changed accordingly
        x.append(float(i)/(N-1)*separations[id] + separationsums[id])
    return x

def generateLineBetweenVectorsPoints (start_point,end_point,N):
    """
    Given two points (given as lists), generate a sequence of
    N points between them, evenly distributed and return in a list.
    """
    b = []
    for i in range(N):
        # The end-point is included; to exclude it, use N in the denominator instead
        # If this is changed, the change should be mirrored in convertVectorPointToX above
        a = (float(i)/(N-1),)*3*(array(end_point)-array(start_point)) + start_point
        b.append(a)
    return b