254 lines
8.9 KiB
Python
254 lines
8.9 KiB
Python
from typing import Any, Callable, List, NamedTuple, Optional, Tuple
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import math
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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 __hash__(self) -> int:
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return hash((self.l, self.r))
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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 approximately_equal(self, other: 'Segment') -> float:
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return (math.isclose(self.l.y, other.l.y, rel_tol=1e-5) and
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math.isclose(self.r.y, other.r.y, rel_tol=1e-5))
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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 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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# We compute the x-coordinate of every intersection point. We sort the
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# x-coordinates and for every x, we compute the highest line at that point.
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xs: List[float] = [0.0, 1.0]
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for (i, s1) in enumerate(segments):
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for (j, s2) in enumerate(segments[i + 1:], i + 1):
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p = s1.intersection(s2)
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if p is not None:
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xs.append(p.x)
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xs.sort()
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return [(x, max(segments, key=lambda s: s(x))(x)) for x in xs]
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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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def is_subset(xs: List[Any], ys: List[Any]) -> bool:
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return all(x in ys for x in xs)
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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.assertTrue(is_subset(path, max_of_segments(segments)))
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self.assertTrue(is_subset(path, max_of_segments(segments[::-1])))
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if __name__ == '__main__':
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unittest.main()
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