Zovirl Industries

Mark Ivey’s weblog

Interpolated Lookup Tables in Python

Normally there are all kinds of aspects to a simulation that are driven by mathematical functions, like gravity, momentum, population growth rates, economic trends, etc. However, mathematical functions can be difficult to tweak, and I’m finding it much easier to use lookup tables instead. This makes it much easier to make slight modifications: rather than adding additional terms to a function, I just have to modify the values in a table.

I wrapped up the logic for storing a table of points and providing interpolated values between those points into a Python class. Using Python’s __getitem__ method lets my object behave like an array, so I can just index into it when I need a value. Here’s the class:

class InterpolatedArray(object):

  """An array-like object that provides
  interpolated values between set points."""

  def __init__(self, points):
    self.points = sorted(points)

  def __getitem__(self, x):
    if x < self.points[0][0] or x > self.points[-1][0]:
      raise ValueError
    lower_point, upper_point = self._GetBoundingPoints(x)
    return self._Interpolate(x, lower_point, upper_point)

  def _GetBoundingPoints(self, x):
    """Get the lower/upper points that bound x."""
    lower_point = None
    upper_point = self.points[0]
    for point  in self.points[1:]:
      lower_point = upper_point
      upper_point = point
      if x <= upper_point[0]:
    return lower_point, upper_point

  def _Interpolate(self, x, lower_point, upper_point):
    """Interpolate a Y value for x given lower & upper
    bounding points."""
    slope = (float(upper_point[1] - lower_point[1]) /
             (upper_point[0] - lower_point[0]))
    return lower_point[1] + (slope * (x - lower_point[0]))

You use it like this:

points = ((1, 0), (5, 10), (10, 0))
table = InterpolatedArray(points)
print table[1]
print table[3.2]
print table[7]

Here are some examples of the kinds of curves you can easily make:

points = [(0, 0), (2, 9.5), (4, 8.5), (6, 4), (8, 1), (10, 0)]

points = [(0, 10), (2, 10), (4, 9), (6, 7), (8, 4), (10, 0)]

points = [(0, 0), (2, 0), (4, 1.5), (6, 8.5), (8, 10), (10, 10)]

Feel free to use this in your own projects.