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# Copyright (c) 2010-2020 Manfred Moitzi
# License: MIT License
import pytest
import random
from ezdxf.math import (
cubic_bezier_interpolation,
Vec3,
Vec2,
Bezier3P,
quadratic_to_cubic_bezier,
Bezier4P,
have_bezier_curves_g1_continuity,
bezier_to_bspline,
split_bezier,
quadratic_bezier_from_3p,
close_vectors,
cubic_bezier_bbox,
quadratic_bezier_bbox,
intersection_ray_cubic_bezier_2d,
)
def test_vertex_interpolation():
points = [(0, 0), (3, 1), (5, 3), (0, 8)]
result = list(cubic_bezier_interpolation(points))
assert len(result) == 3
c1, c2, c3 = result
p = c1.control_points
assert p[0].isclose((0, 0))
assert p[1].isclose((0.9333333333333331, 0.3111111111111111))
assert p[2].isclose((1.8666666666666663, 0.6222222222222222))
assert p[3].isclose((3, 1))
p = c2.control_points
assert p[0].isclose((3, 1))
assert p[1].isclose((4.133333333333334, 1.3777777777777778))
assert p[2].isclose((5.466666666666667, 1.822222222222222))
assert p[3].isclose((5, 3))
p = c3.control_points
assert p[0].isclose((5, 3))
assert p[1].isclose((4.533333333333333, 4.177777777777778))
assert p[2].isclose((2.2666666666666666, 6.088888888888889))
assert p[3].isclose((0, 8))
def test_invalid_bezier_interpolation():
"""At least 3 points are required."""
assert len(list(cubic_bezier_interpolation([(0, 0)]))) == 0
assert len(list(cubic_bezier_interpolation([(0, 0), (1, 0)]))) == 0
def test_quadratic_to_cubic_bezier():
r = random.Random(0)
def random_vec() -> Vec3:
return Vec3(r.uniform(-10, 10), r.uniform(-10, 10), r.uniform(-10, 10))
for i in range(1000):
quadratic = Bezier3P((random_vec(), random_vec(), random_vec()))
quadratic_approx = list(quadratic.approximate(10))
cubic = quadratic_to_cubic_bezier(quadratic)
cubic_approx = list(cubic.approximate(10))
assert len(quadratic_approx) == len(cubic_approx)
for p1, p2 in zip(quadratic_approx, cubic_approx):
assert p1.isclose(p2)
# G1 continuity: normalized end-tangent == normalized start-tangent of next curve
B1 = Bezier4P(Vec2.list([(0, 0), (1, 1), (2, 1), (3, 0)]))
# B1/B2 has G1 continuity:
B2 = Bezier4P(Vec2.list([(3, 0), (4, -1), (5, -1), (6, 0)]))
# B1/B3 has no G1 continuity:
B3 = Bezier4P(Vec2.list([(3, 0), (4, 1), (5, 1), (6, 0)]))
# B1/B4 G1 continuity off tolerance:
B4 = Bezier4P(Vec2.list([(3, 0), (4, -1.03), (5, -1.0), (6, 0)]))
# B1/B5 has a gap between B1 end and B5 start:
B5 = Bezier4P(Vec2.list([(4, 0), (5, -1), (6, -1), (7, 0)]))
def test_g1_continuity_for_bezier_curves():
assert have_bezier_curves_g1_continuity(B1, B2) is True
assert have_bezier_curves_g1_continuity(B1, B3) is False
assert (
have_bezier_curves_g1_continuity(B1, B4, g1_tol=1e-4) is False
), "should be outside of tolerance "
assert (
have_bezier_curves_g1_continuity(B1, B5) is False
), "end- and start point should match"
D1 = Bezier4P(Vec2.list([(0, 0), (1, 1), (3, 0), (3, 0)]))
D2 = Bezier4P(Vec2.list([(3, 0), (3, 0), (5, -1), (6, 0)]))
def test_g1_continuity_for_degenerated_bezier_curves():
assert have_bezier_curves_g1_continuity(D1, B2) is False
assert have_bezier_curves_g1_continuity(B1, D2) is False
assert have_bezier_curves_g1_continuity(D1, D2) is False
@pytest.mark.parametrize("curve", [D1, D2])
def test_flatten_degenerated_bezier_curves(curve):
# Degenerated Bezier curves behave like regular curves!
assert len(list(curve.flattening(0.1))) > 4
@pytest.mark.parametrize(
"b1,b2",
[
(B1, B2), # G1 continuity, the common case
(B1, B3), # without G1 continuity is also a regular B-spline
(B1, B5), # regular B-spline, but first control point of B5 is lost
],
ids=["G1", "without G1", "gap"],
)
def test_bezier_curves_to_bspline(b1, b2):
bspline = bezier_to_bspline([b1, b2])
# Remove duplicate control point between two adjacent curves:
expected = list(b1.control_points) + list(b2.control_points)[1:]
assert bspline.degree == 3, "should be a cubic B-spline"
assert bspline.control_points == tuple(expected)
def test_quality_of_bezier_to_bspline_conversion_1():
# This test shows the close relationship between cubic Bézier- and
# cubic B-spline curves.
points0 = B1.approximate(10)
points1 = bezier_to_bspline([B1]).approximate(10)
for p0, p1 in zip(points0, points1):
assert p0.isclose(p1) is True, "conversion should be perfect"
def test_quality_of_bezier_to_bspline_conversion_2():
# This test shows the close relationship between cubic Bézier- and
# cubic B-spline curves.
# Remove duplicate point between the two curves:
points0 = list(B1.approximate(10)) + list(B2.approximate(10))[1:]
points1 = bezier_to_bspline([B1, B2]).approximate(20)
for p0, p1 in zip(points0, points1):
assert p0.isclose(p1) is True, "conversion should be perfect"
def test_bezier_curves_to_bspline_error():
with pytest.raises(ValueError):
bezier_to_bspline([]) # one or more curves expected
class TestSplitBezier:
@pytest.fixture
def points3(self):
return Vec2.list([(0, 0), (0, 1), (1.5, 0.75), (2, 2)])
@pytest.mark.parametrize("t", [-1, 2])
def test_t_validation(self, points3, t):
with pytest.raises(ValueError):
split_bezier(points3, t)
def test_control_point_validation(self):
with pytest.raises(ValueError):
split_bezier([Vec2(0, 0)], 0.5)
def test_split_cubic_bezier(self, points3):
left, right = split_bezier(points3, 0.5)
assert (
close_vectors(
left,
[(0.0, 0.0), (0.0, 0.5), (0.375, 0.6875), (0.8125, 0.90625)],
)
is True
)
assert (
close_vectors(
right,
[(2.0, 2.0), (1.75, 1.375), (1.25, 1.125), (0.8125, 0.90625)],
)
is True
)
def test_quadratic_bezier_from_3_points():
qbez = quadratic_bezier_from_3p((0, 0), (3, 2), (6, 0))
assert qbez.point(0.5).isclose((3, 2))
def test_cubic_bezier_from_3_points():
cbez = quadratic_bezier_from_3p((0, 0), (3, 2), (6, 0))
assert cbez.point(0.5).isclose((3, 2))
class TestBezierCurveBoundingBox:
def test_linear_curve(self):
bbox = cubic_bezier_bbox(Bezier4P(Vec2.list([(0, 0), (1, 1), (2, 2), (3, 3)])))
assert bbox.extmin == (0, 0, 0)
assert bbox.extmax == (3, 3, 0)
def test_reverse_linear_curve(self):
bbox = cubic_bezier_bbox(
Bezier4P(Vec2.list([(3, 3), (2, 2), (-2, -2), (-3, -3)]))
)
assert bbox.extmin == (-3, -3, 0)
assert bbox.extmax == (3, 3, 0)
def test_cubic_bezier_curve_with_one_extrema(self):
curve = Bezier4P(Vec2.list([(0, 0), (0, 1), (2, 1), (2, 0)]))
bbox = cubic_bezier_bbox(curve)
assert bbox.extmax.y == pytest.approx(0.75)
def test_cubic_bezier_curve_with_two_extrema(self):
curve = Bezier4P(Vec2.list([(0, 0), (0, 1), (2, -1), (2, 0)]))
bbox = cubic_bezier_bbox(curve)
assert bbox.extmin.y == pytest.approx(-0.28867513459481287)
assert bbox.extmax.y == pytest.approx(+0.28867513459481287)
def test_closed_3d_cubic_bezier_curve(self):
curve = Bezier4P(Vec3.list([(0, 0, -1), (2, 3, 0), (-2, 3, 0), (0, 0, -1)]))
bbox = cubic_bezier_bbox(curve)
assert bbox.extmin.x == pytest.approx(-0.5773502691896258)
assert bbox.extmin.z == pytest.approx(-1.0)
assert bbox.extmax.x == pytest.approx(+0.5773502691896258)
assert bbox.extmax.y == pytest.approx(+2.25)
assert bbox.extmax.z == pytest.approx(-0.25)
def test_quadratic_bezier_curve_box(self):
curve = Bezier3P(Vec2.list([(0, 0), (1, 1), (2, 0)]))
bbox = quadratic_bezier_bbox(curve)
assert bbox.extmax.y == pytest.approx(0.5)
class TestRayCubicBezierCurve2dIntersection:
@pytest.fixture(scope="class")
def curve(self):
return Bezier4P(Vec2.list([(0, -2), (2, 6), (4, -6), (6, 2)]))
def test_no_intersection(self, curve):
assert len(intersection_ray_cubic_bezier_2d((0, -6), (1, -6), curve)) == 0
def test_one_intersection_point(self, curve):
points = intersection_ray_cubic_bezier_2d((3, -6), (3, 6), curve)
assert len(points) == 1
assert points[0].isclose((3, 0))
def test_two_intersection_points(self, curve):
points = intersection_ray_cubic_bezier_2d((-1.4, -2.5), (7.1, 3.9), curve)
assert len(points) == 2
expected = (
(0.18851028511733303, -1.3039451970881237),
(2.5249135145844264, 0.4552289992165126),
)
assert all(p.isclose(e) for e, p in zip(expected, points)) is True
def test_three_intersection_points(self, curve):
points = intersection_ray_cubic_bezier_2d((0, 0), (1, 0), curve)
assert len(points) == 3
expected = (
(0.6762099922755492, 0.0),
(3.0, 0.0),
(5.323790007724451, 0.0),
)
assert all(p.isclose(e) for e, p in zip(expected, points)) is True
def test_collinear_ray_and_curve(self):
curve = Bezier4P(Vec2.list([(0, 0), (1, 0), (2, 0), (3, 0)]))
ip = intersection_ray_cubic_bezier_2d((0, 0), (1, 0), curve)
assert len(ip) == 1
assert ip[0].isclose((0, 0)) # ???
@pytest.mark.parametrize("x", [0, 0.5, 1, 3])
def test_linear_ray_and_curve(self, x):
curve = Bezier4P(Vec2.list([(0, 0), (1, 0), (2, 0), (3, 0)]))
# ray defined in +y direction
ip = intersection_ray_cubic_bezier_2d((x, -1), (x, 0), curve)
assert len(ip) == 1
assert ip[0].isclose((x, 0))
# ray defined in -y direction
ip = intersection_ray_cubic_bezier_2d((x, 2), (x, 1), curve)
assert len(ip) == 1
assert ip[0].isclose((x, 0))
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