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#!/usr/bin/env python
def get_fixpoint_before(fixpoints, x):
"""
Find the fix point directly before the provided position.
"""
assert len(fixpoints) > 0
assert x >= 0
return filter(lambda f: f[0] <= x, fixpoints)[-1]
def get_fixpoint_after(fixpoints, x):
"""
Find the fix point directly after the provided position.
"""
assert len(fixpoints) > 0
assert x >= 0
return filter(lambda f: f[0] >= x, fixpoints)[0]
def make_fixpoints_cyclic(fixpoints, cyclesize):
"""Adapts the fixpoints for the cyclic use-case, by doing the following:
- Sort the fixpoints by x value
- Copy the last fixpoint as first fixpoint
- Copy the first fixpoint as the last fixpoint
"""
# Sort fix points by x value
fixpoints = sorted(fixpoints, key=lambda f: f[0])
last_fixpoint = fixpoints[-1]
first_fixpoint = fixpoints[0]
return [
((cyclesize - last_fixpoint[0]) * -1, last_fixpoint[1])
] + fixpoints + [
((cyclesize + first_fixpoint[0]), first_fixpoint[1])
]
def interpolate_value(fixpoints, cyclesize, x):
"""
Interpolates the value at the provided position. It uses the fixpoints provided
for the interpolation and assumes that the x axis is from 0 till cyclesize-1
inclusive.
"""
assert len(fixpoints) > 0
assert x >= 0
assert x < cyclesize
modified_fixpoints = make_fixpoints_cyclic(fixpoints, cyclesize)
before = get_fixpoint_before(modified_fixpoints, x)
after = get_fixpoint_after(modified_fixpoints, x)
# If we are directly on a fix point, return it
# In this case before == after == x
if x == before[0]:
return before[1]
# Compute Slope
delta_x = after[0] - before[0]
delta_y = after[1] - before[1]
slope = float(delta_y) / float(delta_x)
# Compute Increment
increment = (x - before[0]) * slope
return before[1] + increment
import unittest
import random
# Circle runs from 0 to 99
TEST_CYCLE_SIZE = 100
# Format (x, y)
TEST_FIX_POINTS = [
(5, 50),
(25, 25),
(30, 25),
(40, 1025),
(75, 525),
(80, 30),
(90, 100)
]
class TestHelpers(unittest.TestCase):
def test_get_fixpoint_before(self):
# If you are on a fix point, this point is taken
for (p, v) in TEST_FIX_POINTS:
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, p), (p, v))
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, 15), (5, 50))
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, 24), (5, 50))
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, 34), (30, 25))
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, 83), (80, 30))
self.assertEquals(get_fixpoint_before(TEST_FIX_POINTS, 92), (90, 100))
def test_get_fixpoint_after(self):
# If you are on a fix point, this point is taken
for (p, v) in TEST_FIX_POINTS:
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, p), (p, v))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 1), (5, 50))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 6), (25, 25))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 24), (25, 25))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 34), (40, 1025))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 78), (80, 30))
self.assertEquals(get_fixpoint_after(TEST_FIX_POINTS, 83), (90, 100))
def test_make_fixpoints_cyclic(self):
self.assertEquals(make_fixpoints_cyclic(TEST_FIX_POINTS, TEST_CYCLE_SIZE), [(-10, 100)] +
TEST_FIX_POINTS + [(105, 50)])
def test_make_fixpoints_cyclic_random(self):
self.assertEquals(make_fixpoints_cyclic(random.sample(TEST_FIX_POINTS, len(TEST_FIX_POINTS)), TEST_CYCLE_SIZE), [(-10, 100)] +
TEST_FIX_POINTS + [(105, 50)])
class TestCircleInterpolation(unittest.TestCase):
def test_fixpoints(self):
# All the fixpoints should return their values
for (p, v) in TEST_FIX_POINTS:
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, p), v)
def test_simple(self):
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 13), 40)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 22), 28.75)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 26), 25)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 29), 25)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 31), 125)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 32), 225)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 38), 825)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 39), 925)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 55), 810.71, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 70), 596.428, 2)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 76), 426)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 77), 327)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 78), 228)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 79), 129)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 85), 65)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 88), 86)
self.assertEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 89), 93)
def test_wraparound(self):
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 91), 96.666, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 92), 93.333, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 93), 90, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 94), 86.666, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 95), 83.333, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 96), 80, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 97), 76.666, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 98), 73.333, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 99), 70, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 0), 66.666, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 1), 63.333, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 2), 60, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 3), 56.666, 2)
self.assertAlmostEqual(interpolate_value(TEST_FIX_POINTS, TEST_CYCLE_SIZE, 4), 53.333, 2)
if __name__ == '__main__':
unittest.main()
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