90 lines
3.8 KiB
Python
90 lines
3.8 KiB
Python
import math
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import random
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import pytest
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from flight_map.curves import Cubic, interpolate
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def test_spline_interpolates_samples_with_continuous_tangent() -> None:
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points = [(0.0, 0.0), (1.0, 2.0), (5.0, 3.0), (6.0, -1.0)]
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curves = interpolate(points)
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assert len(curves) == len(points) - 1
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for index, curve in enumerate(curves):
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assert curve.point(0) == pytest.approx(points[index])
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assert curve.point(1) == pytest.approx(points[index + 1])
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for first, second in zip(curves, curves[1:], strict=False):
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incoming = (first.end[0] - first.control2[0], first.end[1] - first.control2[1])
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outgoing = (second.control1[0] - second.start[0], second.control1[1] - second.start[1])
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cross = incoming[0] * outgoing[1] - incoming[1] * outgoing[0]
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dot = incoming[0] * outgoing[0] + incoming[1] * outgoing[1]
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assert abs(cross) < 1e-10 and dot > 0
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# A non-collinear path must actually curve, not just encode straight lines as cubics.
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assert curves[0].point(0.5) != pytest.approx((0.5, 1.0))
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def test_two_points_remain_a_straight_path_and_duplicates_are_finite() -> None:
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curve = interpolate([(0, 0), (9, 6)])[0]
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assert curve.point(0.5) == pytest.approx((4.5, 3))
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for segment in interpolate([(0, 0), (0, 0), (1, 2), (1, 2), (3, 0)]):
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assert all(math.isfinite(coordinate) for p in segment.points for coordinate in p)
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assert interpolate([]) == []
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assert interpolate([(0, 0)]) == []
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def test_curve_portion_preserves_original_shape() -> None:
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curve = Cubic((-2, 0), (1, 5), (3, -5), (6, 0))
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portion = curve.portion(0.2, 0.8)
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for fraction in (0, 0.1, 0.5, 0.8, 1):
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assert portion.point(fraction) == pytest.approx(curve.point(0.2 + fraction * 0.6))
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with pytest.raises(ValueError):
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curve.portion(0.8, 0.2)
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def test_curve_can_enter_bounds_when_both_endpoints_are_outside() -> None:
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curve = Cubic((-2, 0), (-1, 3), (1, 3), (2, 0))
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rectangle = (-1.0, 1.0, 1.0, 3.0)
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portions = curve.clipped(rectangle)
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assert len(portions) == 1
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assert portions[0].start[0] == pytest.approx(-1)
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assert portions[0].end[0] == pytest.approx(1)
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assert portions[0].point(0.5)[1] > 2
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def test_clipping_handles_multiple_entries_tangency_and_boundary_lines() -> None:
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curve = Cubic((-2, 0), (4, 0), (-4, 0), (2, 0))
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rectangle = (-0.1, -1.0, 0.1, 1.0)
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assert len(curve.inside_intervals(rectangle)) == 3
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boundary = Cubic((-2, 0), (-1, 0), (1, 0), (2, 0))
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assert len(boundary.clipped((-1, 0, 1, 1))) == 1
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# Only touches the lower edge; it has no visible interval inside the rectangle.
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tangent = Cubic((0, -3), (1, 1), (2, 1), (3, -3))
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assert tangent.clipped((-1, 0, 4, 4)) == []
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def test_random_clipping_matches_dense_curve_membership() -> None:
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randomizer = random.Random(42)
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rectangle = (-1.0, -1.0, 1.0, 1.0)
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for _ in range(100):
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points = [(randomizer.uniform(-3, 3), randomizer.uniform(-3, 3)) for _ in range(4)]
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curve = Cubic(*points)
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intervals = curve.inside_intervals(rectangle)
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for index in range(201):
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t = index / 200
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x, y = curve.point(t)
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inside = -1 <= x <= 1 and -1 <= y <= 1
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selected = any(first - 1e-10 <= t <= last + 1e-10 for first, last in intervals)
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assert selected == inside
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for portion in curve.clipped(rectangle):
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for index in range(51):
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x, y = portion.point(index / 50)
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assert -1 - 1e-8 <= x <= 1 + 1e-8 and -1 - 1e-8 <= y <= 1 + 1e-8
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def test_transformation_preserves_bezier_shape() -> None:
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curve = Cubic((0, 0), (1, 2), (2, -1), (3, 0))
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transformed = curve.transform([2, 0, 0, -2, 10, 20])
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for t in (0, 0.1, 0.6, 1):
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x, y = curve.point(t)
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assert transformed.point(t) == pytest.approx((2 * x + 10, -2 * y + 20))
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