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import fontTools.misc.bezierTools as bezierTools
from fontTools.misc.bezierTools import (
calcQuadraticBounds,
calcQuadraticArcLength,
calcCubicBounds,
curveLineIntersections,
segmentPointAtT,
splitLine,
splitQuadratic,
splitCubic,
splitQuadraticAtT,
splitCubicAtT,
solveCubic,
)
import pytest
def test_calcQuadraticBounds():
assert calcQuadraticBounds((0, 0), (50, 100), (100, 0)) == (0, 0, 100, 50.0)
assert calcQuadraticBounds((0, 0), (100, 0), (100, 100)) == (0.0, 0.0, 100, 100)
def test_calcCubicBounds():
assert calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0)) == (
(0, 0, 100, 75.0)
)
assert calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100)) == (
0.0,
0.0,
100,
100,
)
assert calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0)) == pytest.approx(
(35.566243, 0.000000, 64.433757, 75.000000)
)
def test_splitLine():
assert splitLine((0, 0), (100, 100), where=50, isHorizontal=True) == [
((0, 0), (50.0, 50.0)),
((50.0, 50.0), (100, 100)),
]
assert splitLine((0, 0), (100, 100), where=100, isHorizontal=True) == [
((0, 0), (100, 100))
]
assert splitLine((0, 0), (100, 100), where=0, isHorizontal=True) == [
((0, 0), (0, 0)),
((0, 0), (100, 100)),
]
assert splitLine((0, 0), (100, 100), where=0, isHorizontal=False) == [
((0, 0), (0, 0)),
((0, 0), (100, 100)),
]
assert splitLine((100, 0), (0, 0), where=50, isHorizontal=False) == [
((100, 0), (50, 0)),
((50, 0), (0, 0)),
]
assert splitLine((0, 100), (0, 0), where=50, isHorizontal=True) == [
((0, 100), (0, 50)),
((0, 50), (0, 0)),
]
assert splitLine((0, 100), (100, 100), where=50, isHorizontal=True) == [
((0, 100), (100, 100))
]
def assert_curves_approx_equal(actual_curves, expected_curves):
assert len(actual_curves) == len(expected_curves)
for acurve, ecurve in zip(actual_curves, expected_curves):
assert len(acurve) == len(ecurve)
for apt, ept in zip(acurve, ecurve):
assert apt == pytest.approx(ept)
def test_splitQuadratic():
assert splitQuadratic(
(0, 0), (50, 100), (100, 0), where=150, isHorizontal=False
) == [((0, 0), (50, 100), (100, 0))]
assert splitQuadratic(
(0, 0), (50, 100), (100, 0), where=50, isHorizontal=False
) == [((0, 0), (25, 50), (50, 50)), ((50, 50), (75, 50), (100, 0))]
assert splitQuadratic(
(0, 0), (50, 100), (100, 0), where=25, isHorizontal=False
) == [((0, 0), (12.5, 25), (25, 37.5)), ((25, 37.5), (62.5, 75), (100, 0))]
assert_curves_approx_equal(
splitQuadratic((0, 0), (50, 100), (100, 0), where=25, isHorizontal=True),
[
((0, 0), (7.32233, 14.64466), (14.64466, 25)),
((14.64466, 25), (50, 75), (85.3553, 25)),
((85.3553, 25), (92.6777, 14.64466), (100, -7.10543e-15)),
],
)
# XXX I'm not at all sure if the following behavior is desirable
assert splitQuadratic((0, 0), (50, 100), (100, 0), where=50, isHorizontal=True) == [
((0, 0), (25, 50), (50, 50)),
((50, 50), (50, 50), (50, 50)),
((50, 50), (75, 50), (100, 0)),
]
def test_splitCubic():
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=150, isHorizontal=False
) == [((0, 0), (25, 100), (75, 100), (100, 0))]
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=50, isHorizontal=False
) == [
((0, 0), (12.5, 50), (31.25, 75), (50, 75)),
((50, 75), (68.75, 75), (87.5, 50), (100, 0)),
]
assert_curves_approx_equal(
splitCubic((0, 0), (25, 100), (75, 100), (100, 0), where=25, isHorizontal=True),
[
((0, 0), (2.293792, 9.17517), (4.798045, 17.5085), (7.47414, 25)),
((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667), (92.5259, 25)),
((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517), (100, 1.77636e-15)),
],
)
def test_splitQuadraticAtT():
assert splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5) == [
((0, 0), (25, 50), (50, 50)),
((50, 50), (75, 50), (100, 0)),
]
assert splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5, 0.75) == [
((0, 0), (25, 50), (50, 50)),
((50, 50), (62.5, 50), (75, 37.5)),
((75, 37.5), (87.5, 25), (100, 0)),
]
def test_splitCubicAtT():
assert splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5) == [
((0, 0), (12.5, 50), (31.25, 75), (50, 75)),
((50, 75), (68.75, 75), (87.5, 50), (100, 0)),
]
assert splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5, 0.75) == [
((0, 0), (12.5, 50), (31.25, 75), (50, 75)),
((50, 75), (59.375, 75), (68.75, 68.75), (77.34375, 56.25)),
((77.34375, 56.25), (85.9375, 43.75), (93.75, 25), (100, 0)),
]
def test_solveCubic():
assert solveCubic(1, 1, -6, 0) == [-3.0, -0.0, 2.0]
assert solveCubic(-10.0, -9.0, 48.0, -29.0) == [-2.9, 1.0, 1.0]
assert solveCubic(-9.875, -9.0, 47.625, -28.75) == [-2.911392, 1.0, 1.0]
assert solveCubic(1.0, -4.5, 6.75, -3.375) == [1.5, 1.5, 1.5]
assert solveCubic(-12.0, 18.0, -9.0, 1.50023651123) == [0.5, 0.5, 0.5]
assert solveCubic(9.0, 0.0, 0.0, -7.62939453125e-05) == [-0.0, -0.0, -0.0]
_segmentPointAtT_testData = [
([(0, 10), (200, 100)], 0.0, (0, 10)),
([(0, 10), (200, 100)], 0.5, (100, 55)),
([(0, 10), (200, 100)], 1.0, (200, 100)),
([(0, 10), (100, 100), (200, 50)], 0.0, (0, 10)),
([(0, 10), (100, 100), (200, 50)], 0.5, (100, 65.0)),
([(0, 10), (100, 100), (200, 50)], 1.0, (200, 50.0)),
([(0, 10), (100, 100), (200, 100), (300, 0)], 0.0, (0, 10)),
([(0, 10), (100, 100), (200, 100), (300, 0)], 0.5, (150, 76.25)),
([(0, 10), (100, 100), (200, 100), (300, 0)], 1.0, (300, 0)),
]
@pytest.mark.parametrize("segment, t, expectedPoint", _segmentPointAtT_testData)
def test_segmentPointAtT(segment, t, expectedPoint):
point = segmentPointAtT(segment, t)
assert expectedPoint == point
def test_intersections_straight_line():
curve = ((548, 183), (548, 289), (450, 366), (315, 366))
line1 = ((330, 376), (330, 286))
pt = curveLineIntersections(curve, line1)[0][0]
assert pt[0] == 330
line = (pt, (330, 286))
pt2 = (330.0001018806911, 295.5635754579425)
assert bezierTools._line_t_of_pt(*line, pt2) > 0
s = (19, 0)
e = (110, 0)
pt = (109.05194805194802, 0.0)
assert bezierTools._line_t_of_pt(s, e, pt) == pytest.approx(0.98958184)
def test_calcQuadraticArcLength():
# https://github.com/fonttools/fonttools/issues/3287
assert calcQuadraticArcLength(
(210, 333), (289, 333), (326.5, 290.5)
) == pytest.approx(127.9225)
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