Added some geometry code.
I'll use this for load vs read fraction plots.
This commit is contained in:
Michael Whittaker
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900b69d8d1
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1 changed files with 263 additions and 0 deletions
263
quorums/geometry.py
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263
quorums/geometry.py
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from typing import Any, Callable, List, NamedTuple, Optional, Tuple
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import unittest
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class Point(NamedTuple):
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x: float
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y: float
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class Segment:
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def __init__(self, l: Point, r: Point) -> None:
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assert l != r
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assert l.x < r.x
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self.l = l
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self.r = r
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def __str__(self) -> str:
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return f'{tuple(self.l)} -> {tuple(self.r)}'
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def __repr__(self) -> str:
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return f'Segment({self.l}, {self.r})'
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def __eq__(self, other) -> bool:
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if isinstance(other, Segment):
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return (self.l, self.r) == (other.l, other.r)
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else:
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return False
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def compatible(self, other: 'Segment') -> float:
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return self.l.x == other.l.x and self.r.x == other.r.x
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def __call__(self, x: float) -> float:
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assert self.l.x <= x <= self.r.x
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return self.slope() * (x - self.l.x) + self.l.y
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def slope(self) -> float:
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return (self.r.y - self.l.y) / (self.r.x - self.l.x)
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def above(self, other: 'Segment') -> bool:
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assert self.compatible(other)
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return self != other and self.l.y >= other.l.y and self.r.y >= other.r.y
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def above_eq(self, other: 'Segment') -> bool:
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assert self.compatible(other)
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return self == other or self.above(other)
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def intersects(self, other: 'Segment') -> bool:
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assert self.compatible(other)
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if self == other:
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return True
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elif self.l.y == other.l.y or self.r.y == other.r.y:
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return True
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elif self.above(other) or other.above(self):
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return False
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else:
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return True
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def intersection(self, other: 'Segment') -> Optional[Point]:
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assert self.compatible(other)
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if self == other or not self.intersects(other):
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return None
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x = ((other.l.y - self.l.y) /
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(self.r.y - other.r.y + other.l.y - self.l.y))
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return Point(x, self(x))
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def max_of_segments(segments: List[Segment]) -> List[Tuple[float, float]]:
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assert len(segments) > 0
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assert len({segment.l.x for segment in segments}) == 1
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assert len({segment.r.x for segment in segments}) == 1
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# First, we remove any segments that are subsumed by other segments.
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non_dominated: List[Segment] = []
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for segment in segments:
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if any(other.above_eq(segment) for other in non_dominated):
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# If this segment is dominated by another, we exclude it.
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pass
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else:
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# Otherwise, we add this segment and remove any that it dominates.
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non_dominated = [other
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for other in non_dominated
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if not segment.above_eq(other)]
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non_dominated.append(segment)
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# Next, we start at the leftmost segment and continually jump over to the
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# segment with the first intersection.
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segment = max(non_dominated, key=lambda segment: segment.l.y)
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path: List[Point] = [segment.l]
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while True:
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intersections: List[Tuple[Point, Segment]] = []
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for other in non_dominated:
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p = segment.intersection(other)
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if p is not None and p.x > path[-1].x:
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intersections.append((p, other))
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if len(intersections) == 0:
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path.append(segment.r)
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return [(p.x, p.y) for p in path]
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intersection, segment = min(intersections, key=lambda t: t[0].x)
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path.append(intersection)
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class TestGeometry(unittest.TestCase):
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def test_eq(self):
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l = Point(0, 1)
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r = Point(1, 1)
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m = Point(0.5, 0.5)
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self.assertEqual(Segment(l, r), Segment(l, r))
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self.assertNotEqual(Segment(l, r), Segment(l, m))
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def test_compatible(self):
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s1 = Segment(Point(0, 1), Point(1, 2))
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s2 = Segment(Point(0, 2), Point(1, 1))
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s3 = Segment(Point(0.5, 2), Point(1, 1))
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self.assertTrue(s1.compatible(s2))
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self.assertTrue(s2.compatible(s1))
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self.assertFalse(s1.compatible(s3))
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self.assertFalse(s3.compatible(s1))
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self.assertFalse(s2.compatible(s3))
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self.assertFalse(s3.compatible(s2))
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def test_call(self):
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segment = Segment(Point(0, 0), Point(1, 1))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), x)
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segment = Segment(Point(0, 0), Point(1, 2))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), 2*x)
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segment = Segment(Point(1, 2), Point(3, 6))
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for x in [1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0]:
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self.assertEqual(segment(x), 2*x)
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segment = Segment(Point(0, 1), Point(1, 0))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), 1 - x)
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def test_slope(self):
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self.assertEqual(Segment(Point(0, 0), Point(1, 1)).slope(), 1.0)
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self.assertEqual(Segment(Point(0, 1), Point(1, 2)).slope(), 1.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 2)).slope(), 1.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 3)).slope(), 2.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 0)).slope(), -1.0)
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def test_above(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertFalse(s1.above(s1))
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self.assertFalse(s1.above(s2))
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self.assertFalse(s1.above(s3))
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self.assertTrue(s2.above(s1))
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self.assertFalse(s2.above(s2))
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self.assertFalse(s2.above(s3))
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self.assertTrue(s3.above(s1))
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self.assertFalse(s3.above(s2))
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self.assertFalse(s3.above(s3))
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def test_above_eq(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertTrue(s1.above_eq(s1))
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self.assertFalse(s1.above_eq(s2))
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self.assertFalse(s1.above_eq(s3))
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self.assertTrue(s2.above_eq(s1))
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self.assertTrue(s2.above_eq(s2))
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self.assertFalse(s2.above_eq(s3))
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self.assertTrue(s3.above_eq(s1))
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self.assertFalse(s3.above_eq(s2))
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self.assertTrue(s3.above_eq(s3))
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def test_intersects(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertTrue(s1.intersects(s1))
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self.assertFalse(s1.intersects(s2))
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self.assertTrue(s1.intersects(s3))
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self.assertFalse(s2.intersects(s1))
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self.assertTrue(s2.intersects(s2))
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self.assertTrue(s2.intersects(s3))
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self.assertTrue(s3.intersects(s1))
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self.assertTrue(s3.intersects(s2))
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self.assertTrue(s3.intersects(s3))
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def test_intersection(self):
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s1 = Segment(Point(0, 0), Point(1, 1))
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s2 = Segment(Point(0, 1), Point(1, 0))
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s3 = Segment(Point(0, 1), Point(1, 1))
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s4 = Segment(Point(0, 0.25), Point(1, 0.25))
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self.assertEqual(s1.intersection(s1), None)
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self.assertEqual(s1.intersection(s2), Point(0.5, 0.5))
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self.assertEqual(s1.intersection(s3), Point(1, 1))
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self.assertEqual(s1.intersection(s4), Point(0.25, 0.25))
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self.assertEqual(s2.intersection(s1), Point(0.5, 0.5))
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self.assertEqual(s2.intersection(s2), None)
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self.assertEqual(s2.intersection(s3), Point(0, 1))
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self.assertEqual(s2.intersection(s4), Point(0.75, 0.25))
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self.assertEqual(s3.intersection(s1), Point(1, 1))
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self.assertEqual(s3.intersection(s2), Point(0, 1))
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self.assertEqual(s3.intersection(s3), None)
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self.assertEqual(s3.intersection(s4), None)
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self.assertEqual(s4.intersection(s1), Point(0.25, 0.25))
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self.assertEqual(s4.intersection(s2), Point(0.75, 0.25))
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self.assertEqual(s4.intersection(s3), None)
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self.assertEqual(s4.intersection(s4), None)
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def test_max_one_segment(self):
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s1 = Segment(Point(0, 0), Point(1, 1))
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s2 = Segment(Point(0, 1), Point(1, 0))
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s3 = Segment(Point(0, 1), Point(1, 1))
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s4 = Segment(Point(0, 0.25), Point(1, 0.25))
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s5 = Segment(Point(0, 0.75), Point(1, 0.75))
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for s in [s1, s2, s3, s4, s5]:
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self.assertEqual(max_of_segments([s]), [s.l, s.r])
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expected = [
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([s1, s1], [(0, 0), (1, 1)]),
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([s1, s2], [(0, 1), (0.5, 0.5), (1, 1)]),
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([s1, s3], [(0, 1), (1, 1)]),
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([s1, s4], [(0, 0.25), (0.25, 0.25), (1, 1)]),
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([s1, s5], [(0, 0.75), (0.75, 0.75), (1, 1)]),
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([s2, s2], [(0, 1), (1, 0)]),
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([s2, s3], [(0, 1), (1, 1)]),
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([s2, s4], [(0, 1), (0.75, 0.25), (1, 0.25)]),
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([s2, s5], [(0, 1), (0.25, 0.75), (1, 0.75)]),
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([s3, s3], [(0, 1), (1, 1)]),
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([s3, s4], [(0, 1), (1, 1)]),
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([s3, s5], [(0, 1), (1, 1)]),
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([s4, s4], [(0, 0.25), (1, 0.25)]),
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([s4, s5], [(0, 0.75), (1, 0.75)]),
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([s5, s5], [(0, 0.75), (1, 0.75)]),
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([s1, s2, s4], [(0, 1), (0.5, 0.5), (1, 1)]),
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([s1, s2, s5], [(0, 1), (0.25, 0.75), (0.75, 0.75), (1, 1)]),
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]
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for segments, path in expected:
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self.assertEqual(max_of_segments(segments), path, segments)
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self.assertEqual(max_of_segments(segments[::-1]), path, segments)
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if __name__ == '__main__':
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unittest.main()
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