utils.py

import math


def fluid(method):
    """
    Fluiditize a method
    """

    def func(self, *args, **kwargs):
        method(self, *args, **kwargs)
        return self

    return func


def refine(function, (vmin, vmax, n_points), angle, length):
    """ Evaluates function on the n points between vmin and vmax, refining if necessary,
    making sure the distance between any two consecutive points is less than max_distance
    """
    max_points = 3000
    dt = float(vmax - vmin) / (n_points - 1)
    domain = [vmin + n * dt for n in xrange(n_points)]
    image = map(function, domain)

    def bisect_and_insert(domain, image, i):
        mp = (domain[i] + domain[i + 1]) / 2
        domain.insert(i + 1, mp)
        image.insert(i + 1, function(mp))

    if angle and length:
        i = 0
        n = n_points
        while i < n - 2 and i < max_points:
            if test_angle(image, i) > angle:
                bisect_and_insert(domain, image, i + 1)
                bisect_and_insert(domain, image, i)
                n += 2
            elif distance(image, i) > length:
                bisect_and_insert(domain, image, i)
                n += 1
            elif distance(image, i + 1) > length:
                bisect_and_insert(domain, image, i + 1)
                n += 1
            else:
                i += 1
    return domain, image


def test_angle(points, i):
    delta = 1e-5
    v1 = points[i + 1] - points[i]
    v2 = points[i + 2] - points[i + 1]
    length1 = v1.length()
    length2 = v2.length()
    if length1 < delta or length2 < delta:
        return 0
    return abs(angle(v1, v2))


def adjustArg(arg):
    if arg > 1.0:
        return 1.0
    elif arg < -1.0:
        return -1.0
    return arg


def distance(points, i):
    return (points[i] - points[i + 1]).length()


def angle(v1, v2):
    return math.acos(adjustArg(v1.dot(v2) / (v1.length() * v2.length())))


def to_polar(function):
    """Returns a function whose arguments are in polar coordinates

    @param function:
    """
    def polar_fn(r, t):
        x = r * math.cos(t)
        y = r * math.sin(t)
        return x, y, function(x, y)

    return polar_fn