def test_add_curves3():
path = Path()
c1 = Bezier3P(((0, 0), (1, 1), (2, 0)))
c2 = Bezier3P(((2, 0), (1, -1), (0, 0)))
tools.add_bezier3p(path, [c1, c2])
assert len(path) == 2
assert path.end == (0, 0)
def test_add_curves3_with_gap():
path = Path()
c1 = Bezier3P(((0, 0), (1, 1), (2, 0)))
c2 = Bezier3P(((2, -1), (3, -2), (0, -1)))
tools.add_bezier3p(path, [c1, c2])
assert len(path) == 3 # added a line segment between curves
assert path.end == (0, -1)
def quadratic_bezier_from_3p(p1: Vertex, p2: Vertex, p3: Vertex) -> Bezier3P:
"""Returns a quadratic Bèzier curve :class:`Bezier3P` from three points.
The curve starts at `p1`, goes through `p2` and ends at `p3`.
(source: `pomax-2`_)
.. versionadded:: 0.17.2
.. _pomax-2: https://pomax.github.io/bezierinfo/#pointcurves
"""
def u_func(t: float) -> float:
mt = 1.0 - t
mt2 = mt * mt
return mt2 / (t * t + mt2)
def ratio(t: float) -> float:
t2 = t * t
mt = 1.0 - t
mt2 = mt * mt
return abs((t2 + mt2 - 1.0) / (t2 + mt2))
s = Vec3(p1)
b = Vec3(p2)
e = Vec3(p3)
d1 = (s - b).magnitude
d2 = (e - b).magnitude
t = d1 / (d1 + d2)
u = u_func(t)
c = s * u + e * (1.0 - u)
a = b + (b - c) / ratio(t)
return Bezier3P([s, a, e])
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)
def test_curve3_to(self):
bez3 = Bezier3P([(0, 0), (2, 1), (4, 0)])
p = path.Path()
p.curve3_to(bez3.control_points[2], bez3.control_points[1])
qpath = path.to_qpainter_path([p])
# Qt converts quadratic bezier curves unto cubic bezier curves
assert qpath.elementCount() == 4
bez4 = quadratic_to_cubic_bezier(bez3)
q1 = qpath.elementAt(1)
assert q1.isCurveTo() # start of cure
assert q1.x, q1.y == bez4.control_points[1]
q2 = qpath.elementAt(2)
assert q2.type == 3 # curve data element
assert q2.x, q2.y == bez4.control_points[2]
q3 = qpath.elementAt(3)
assert q3.type == 3 # curve data element
assert q3.x, q3.y == bez4.control_points[2]
def test_add_curves3_reverse():
path = Path(start=(0, 0))
c1 = Bezier3P(((2, 0), (1, 1), (0, 0)))
tools.add_bezier3p(path, [c1])
assert len(path) == 1
assert path.end == (2, 0, 0)
def to_bsplines_and_vertices(path: Path,
g1_tol: float = G1_TOL) -> Iterable[PathParts]:
""" Convert a :class:`Path` object into multiple cubic B-splines and
polylines as lists of vertices. Breaks adjacent Bèzier without G1
continuity into separated B-splines.
Args:
path: :class:`Path` objects
g1_tol: tolerance for G1 continuity check
Returns:
:class:`~ezdxf.math.BSpline` and lists of :class:`~ezdxf.math.Vec3`
.. versionadded:: 0.16
"""
from ezdxf.math import bezier_to_bspline
def to_vertices():
points = [polyline[0][0]]
for line in polyline:
points.append(line[1])
return points
def to_bspline():
b1 = bezier[0]
_g1_continuity_curves = [b1]
for b2 in bezier[1:]:
if have_bezier_curves_g1_continuity(b1, b2, g1_tol):
_g1_continuity_curves.append(b2)
else:
yield bezier_to_bspline(_g1_continuity_curves)
_g1_continuity_curves = [b2]
b1 = b2
if _g1_continuity_curves:
yield bezier_to_bspline(_g1_continuity_curves)
prev = path.start
curves = []
for cmd in path:
if cmd.type == Command.CURVE3_TO:
curve = Bezier3P([prev, cmd.ctrl, cmd.end])
elif cmd.type == Command.CURVE4_TO:
curve = Bezier4P([prev, cmd.ctrl1, cmd.ctrl2, cmd.end])
elif cmd.type == Command.LINE_TO:
curve = (prev, cmd.end)
else:
raise ValueError
curves.append(curve)
prev = cmd.end
bezier = []
polyline = []
for curve in curves:
if isinstance(curve, tuple):
if bezier:
yield from to_bspline()
bezier.clear()
polyline.append(curve)
else:
if polyline:
yield to_vertices()
polyline.clear()
bezier.append(curve)
if bezier:
yield from to_bspline()
if polyline:
yield to_vertices()
def approx_curve3(s, c, e) -> Iterable[Vec3]:
return Bezier3P((s, c, e)).flattening(distance, segments)
def approx_curve3(s, c, e) -> Iterable[Vec3]:
return Bezier3P((s, c, e)).approximate(segments)
def approx(self):
return ApproxParamT(Bezier3P([(0, 0), (1, 2), (2, 4)]))
def curve(self):
return Bezier3P([(0, 0), (1, 2), (2, 4)])