Ryan Malloy
55a869ef7d
Ports Direction/IntDirection (equivalence classes of vectors, gcd- normalized, exact angular compare) and Line. Line.side_of uses an exact integer determinant; Line.intersection returns an IntPoint when the crossing is integral and a RationalPoint otherwise, with the orthogonal and 45-degree fast paths from the source preserved. Parallel lines yield a point at infinity (z=0). BigIntDirection is folded into IntDirection since unbounded int always fits. Tests cover integral and rational intersections, parallel-line infinity, exactness beyond double precision (verified via exact collinearity of the result), and direction normalization/ordering.
103 lines
3.5 KiB
Python
103 lines
3.5 KiB
Python
"""Tests for lines, emphasizing exact intersection.
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Oracles hand-derived from ``geometry/planar/Line.java``.
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"""
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from __future__ import annotations
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from freeroute.geometry import IntPoint, Line, RationalPoint, Side
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def test_side_of_point():
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# Line.side_of reports where the *line* is relative to the point
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# (point.side_of(line).negate() in the source): a point above a +x line has
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# the line on its right.
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line = Line.from_coords(0, 0, 2, 0) # along +x
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assert line.side_of(IntPoint(1, 1)) == Side.ON_THE_RIGHT
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assert line.side_of(IntPoint(1, -1)) == Side.ON_THE_LEFT
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assert line.side_of(IntPoint(5, 0)) == Side.COLLINEAR
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def test_integral_intersection_fast_paths():
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# vertical x horizontal
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v = Line.from_coords(3, 0, 3, 9)
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h = Line.from_coords(0, 4, 9, 4)
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assert v.intersection(h) == IntPoint(3, 4)
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# horizontal x right-diagonal (y=x): y=4 -> (4,4)
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diag = Line.from_coords(0, 0, 5, 5)
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assert h.intersection(diag) == IntPoint(4, 4)
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def test_general_integral_intersection():
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# y = x/2 and y = 1 -> x = 2
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a = Line.from_coords(0, 0, 2, 1)
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b = Line.from_coords(0, 1, 4, 1)
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assert a.intersection(b) == IntPoint(2, 1)
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def test_rational_intersection_exact():
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# y = 2x/3 and y = 1 -> x = 1.5 -> RationalPoint (3,2,2)
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a = Line.from_coords(0, 0, 3, 2)
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b = Line.from_coords(0, 1, 5, 1)
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result = a.intersection(b)
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assert isinstance(result, RationalPoint)
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assert result == RationalPoint(3, 2, 2)
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assert not result.is_infinite()
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# float approximation agrees
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fp = result.to_float()
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assert abs(fp.x - 1.5) < 1e-9 and abs(fp.y - 1.0) < 1e-9
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def test_parallel_intersection_is_infinite():
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a = Line.from_coords(0, 0, 1, 0)
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b = Line.from_coords(0, 5, 1, 5)
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result = a.intersection(b)
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assert result.is_infinite()
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assert a.is_parallel(b)
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def test_intersection_exact_beyond_double_precision():
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# Two nearly-parallel steep lines crossing at a non-integer point far out.
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# Coordinates chosen so a double determinant would lose bits; int stays exact.
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a = Line.from_coords(0, 0, 1000000, 999999)
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b = Line.from_coords(0, 1, 1000000, 1000000)
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result = a.intersection(b)
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assert isinstance(result, RationalPoint)
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# Verify exactness: the intersection lies on both lines (exact side test).
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assert a.side_of(result) == Side.COLLINEAR
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assert b.side_of(result) == Side.COLLINEAR
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def test_intersection_approx_matches_exact():
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a = Line.from_coords(0, 0, 3, 2)
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b = Line.from_coords(0, 1, 5, 1)
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approx = a.intersection_approx(b)
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assert abs(approx.x - 1.5) < 1e-9
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assert abs(approx.y - 1.0) < 1e-9
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def test_translate_and_opposite():
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line = Line.from_coords(0, 0, 4, 0)
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assert line.opposite().direction().equals(line.direction()) is False
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from freeroute.geometry import IntVector
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moved = line.translate_by(IntVector(0, 5))
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assert moved.side_of(IntPoint(2, 5)) == Side.COLLINEAR
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def test_perpendicular_and_parallel_predicates():
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horizontal = Line.from_coords(0, 0, 1, 0)
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vertical = Line.from_coords(0, 0, 0, 1)
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assert horizontal.is_perpendicular(vertical)
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assert not horizontal.is_parallel(vertical)
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assert horizontal.is_parallel(Line.from_coords(3, 7, 10, 7))
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def test_line_equality_same_set_same_direction():
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a = Line.from_coords(0, 0, 2, 0)
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b = Line.from_coords(-5, 0, 9, 0) # same line, same direction
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c = Line.from_coords(9, 0, -5, 0) # same set, opposite direction
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assert a == b
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assert a != c
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assert a.is_equal_or_opposite(c)
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