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from visual import box, sphere, vector
def read_points(filename):
    Read points from file filename.
    >>> read_points("testdata0.txt")
    [[0.0, 0.0], [1.0, -1.0], [2.0, 3.0]]
    file = open(filename, 'r')
    points = []                             #initialize our list of points
    for line in file:
        point = []                          #a point is just a list of numbers
        str_coords = line.split()           #split the line
                                            #"2 3 4" -> ["2", "3", "4"]
        for str_coord in str_coords:        
            coord = float(str_coord)        #convert coordinate to number
            point.append(coord)             #add coordinate to point
        points.append(point)                #add point to the list of points
    return points
def save_points(points, fname):
    Given a list of points, save them to the file named fname. These 
    points can be read back in with read_points(fname).
    >>> save_points([[0,0],[1,-1],[2,3]], "testdata0.txt")
    file = open(fname, 'w')
    for point in points:
        for coord in point:
            print >>file, coord,
        print >>file
def show_points(points, color=(0,1,0)):
    Given a list of 2D or 3D points, draw them as spheres in the active 
    VPython window.  If no color is given, the spheres will be green.
    #>>> show_points([[0,0],[1,-1],[2,3]])
    for point in points:
        sphere(pos=point, radius=.5, color=color)
def show_box(p1, p2, color=(0,0,1)):
    Given two points p1 and p2, draw a box in the active VPython window
    indicating the rectangle outlined by p1 and p2. If no color is given, 
    the box will be blue.
    #>>> show_box([0,0], [5,5])
    # convert the points to vectors to make math much more convenient
    p1 = vector(p1)
    p2 = vector(p2)
    # pos gives the center of the box, so we want it to be the average
    #     of p1 and p2
    # size gives the size of the box, so we want it to be the distance
    #     between p1 and p2
    box(pos=(p1+p2)/2, size=(p1-p2), color=color)
def random_points(n, d):
    Generate a list of n random points in d-dimensional space.  For example,
    if d=2, then the points will be in 2D space (they will have two
    coordinates).  The space that the points are placed in scales with n and d.
    >>> len(random_points(5, 3))
    from random import uniform
    r = int(n**(1./d)+1)                # we use this so there is roughly
                                        # the same density of points
                                        # regardless of n or d
    points = []                         # initialize our list of points
    for i in range(n):                  # n times...
        point = []                      #  initialize our point 
                                        #    (which is just a list of coords)
        for j in range(d):              #  for each dimension...
            point.append(uniform(-r, r))#    add a random number to the point
        points.append(point)            #  add our completed point to the list
    return points                       
# Self-test code if this module is run directly...
if __name__ == "__main__":
    import doctest
    doctest.master = None