def from_spline(
cls,
spline: BSpline,
start_width: float,
end_width: float,
segments: int,
) -> "CurvedTrace":
"""
Create curved trace from a B-spline.
Args:
spline: :class:`~ezdxf.math.BSpline` object
start_width: start width
end_width: end width
segments: count of segments for approximation
"""
curve_trace = cls()
count = segments + 1
t = linspace(0, spline.max_t, count)
for ((point, derivative),
width) in zip(spline.derivatives(t, n=1),
linspace(start_width, end_width, count)):
normal = Vec2(derivative).orthogonal(True)
curve_trace._append(Vec2(point), normal, width)
return curve_trace
def from_arc(cls,
arc: ConstructionArc,
start_width: float,
end_width: float,
segments: int = 64) -> 'CurvedTrace':
"""
Create curved trace from an arc.
Args:
arc: :class:`~ezdxf.math.ConstructionArc` object
start_width: start width
end_width: end width
segments: count of segments for full circle (360 degree) approximation, partial arcs have proportional
less segments, but at least 3
Raises:
ValueError: if arc.radius <= 0
"""
if arc.radius <= 0:
raise ValueError(f'Invalid radius: {arc.radius}.')
curve_trace = cls()
count = max(math.ceil(arc.angle_span / 360.0 * segments), 3) + 1
center = Vec2(arc.center)
for point, width in zip(arc.vertices(arc.angles(count)),
linspace(start_width, end_width, count)):
curve_trace._append(point, point - center, width)
return curve_trace
def draw_elliptic_arc_entity_3d(self, entity: DXFGraphic) -> None:
dxf, dxftype = entity.dxf, entity.dxftype()
properties = self._resolve_properties(entity)
if dxftype in {'CIRCLE', 'ARC'}:
center = dxf.center # ocs transformation in .from_arc()
radius = dxf.radius
if dxftype == 'CIRCLE':
start_angle = 0
end_angle = 360
else:
start_angle = dxf.start_angle
end_angle = dxf.end_angle
e = ConstructionEllipse.from_arc(center, radius, dxf.extrusion,
start_angle, end_angle)
elif dxftype == 'ELLIPSE':
e = cast(Ellipse, entity).construction_tool()
else:
raise TypeError(dxftype)
# Approximate as 3D polyline
segments = int((e.end_param - e.start_param) / math.tau *
self.circle_approximation_count)
points = list(
e.vertices(
linspace(e.start_param, e.end_param, max(4, segments + 1))))
self.out.start_path()
for a, b in zip(points, points[1:]):
self.out.draw_line(a, b, properties)
self.out.end_path()
def build():
circle = Circle()
vertices = list(circle.vertices(linspace(0, 360, vertex_count, endpoint=False)))
m = Matrix44.chain(
Matrix44.axis_rotate(axis=Vec3.random(), angle=random.uniform(0, math.tau)),
Matrix44.translate(dx=random.uniform(-2, 2), dy=random.uniform(-2, 2), dz=random.uniform(-2, 2)),
)
return synced_transformation(circle, vertices, m)
def circle(radius=1, count=16):
circle_ = Circle.new(dxfattribs={
'center': (0, 0, 0),
'radius': radius
},
doc=doc)
control_vertices = list(circle_.vertices(linspace(0, 360, count)))
return circle_, control_vertices
def test_rational_spline_curve_points_by_nurbs_python():
arc = ConstructionArc(end_angle=90)
spline = rational_bspline_from_arc(end_angle=arc.end_angle)
curve = spline.to_nurbs_python_curve()
t = list(linspace(0, 1, 10))
points = list(spline.points(t))
expected = list(curve.evaluate_list(t))
for p, e in zip(points, expected):
assert p.isclose(e)
def test_rational_spline_derivatives_by_nurbs_python():
arc = ConstructionArc(end_angle=90)
spline = rational_bspline_from_arc(end_angle=arc.end_angle)
curve = spline.to_nurbs_python_curve()
t = list(linspace(0, 1, 10))
derivatives = list(spline.derivatives(t, n=1))
expected = [curve.derivatives(u, 1) for u in t]
for (p, d1), (e, ed1) in zip(derivatives, expected):
assert p.isclose(e)
assert d1.isclose(ed1)
def divide(self, count: int) -> Iterator[Vec3]:
"""Returns `count` interpolated vertices along the polyline.
Argument `count` has to be greater than 2 and the start- and end
vertices are always included.
"""
if count < 2:
raise ValueError(f"invalid count: {count}")
vertex_at = self._vertex_at
for distance in linspace(0.0, self.length, count):
yield vertex_at(distance)
def __init__(
self,
curve: SupportsPointMethod,
*,
max_t: float = 1.0,
segments: int = 100,
):
assert hasattr(curve, "point")
assert segments > 0
self._polyline = ConstructionPolyline(
curve.point(t) for t in linspace(0.0, max_t, segments + 1))
self._max_t = max_t
self._step = max_t / segments
def flattening(self, sagitta: float) -> Iterator[Vec2]:
"""Approximate the circle by vertices, argument `sagitta` is the
max. distance from the center of an arc segment to the center of its
chord. Returns a closed polygon where the start vertex is coincident
with the end vertex!
.. versionadded:: 0.17.1
"""
from .arc import arc_segment_count
count = arc_segment_count(self.radius, math.tau, sagitta)
yield from self.vertices(linspace(0.0, math.tau, count + 1))
def get_params(start: float, end: float, num: int) -> Iterable[float]:
"""Returns `num` params from start- to end param in counter clockwise order.
All params are normalized in the range from [0, 2π).
"""
if num < 2:
raise ValueError("num >= 2")
if end <= start:
end += math.tau
for param in linspace(start, end, num):
yield param % math.tau
def angles(self, num: int) -> Iterable[float]:
""" Returns `num` angles from start- to end angle in degrees in counter clockwise order.
All angles are normalized in the range from [0, 360).
"""
if num < 2:
raise ValueError('num >= 2')
start = self.dxf.start_angle % 360
stop = self.dxf.end_angle % 360
if stop <= start:
stop += 360
for angle in linspace(start, stop, num=num, endpoint=True):
yield angle % 360
def flattening(self, sagitta: float) -> Iterable[Vec3]:
"""Approximate the circle by vertices in WCS, argument `sagitta` is the
max. distance from the center of an arc segment to the center of its
chord. Returns a closed polygon: start vertex == end vertex!
Yields always :class:`~ezdxf.math.Vec3` objects.
.. versionadded:: 0.15
"""
radius = abs(self.dxf.radius)
if radius > 0.0:
count = arc_segment_count(radius, math.tau, sagitta)
yield from self.vertices(linspace(0.0, 360.0, count + 1))
def test_random_ellipse_transformations(sx, sy, sz, start, end):
vertex_count = 8
for angle in linspace(0, math.tau, 19):
for dx, dy, dz in product([2, 0, -2], repeat=3):
axis = Vec3.random() # TODO: fixed rotation axis
config = f"CONFIG sx={sx}, sy={sy}, sz={sz}; " \
f"start={start:.4f}, end={end:.4f}; angle={angle};" \
f"dx={dx}, dy={dy}, dz={dz}; axis={str(axis)}"
ellipse0, vertices0 = build(angle, dx, dy, dz, axis, start, end,
vertex_count)
assert check(ellipse0, vertices0, vertex_count) is True, config
ellipse1, vertices1 = synced_scaling(ellipse0, vertices0, sx, sy,
sz)
assert check(ellipse1, vertices1, vertex_count) is True, config
def profile_bspline_point_new(count, spline):
for _ in range(count):
for t in linspace(0, 1.0, 100):
spline.point(t)
def profile_vertex_calculation(count, spline, num):
for _ in range(count):
for t in linspace(0.0, spline.max_t, num):
spline.point(t)
def test_params():
count = 9
e = ConstructionEllipse(start_param=math.pi / 2, end_param=-math.pi / 2)
params = list(e.params(count))
expected = list(linspace(math.pi / 2, math.pi / 2.0 * 3.0, count))
assert params == expected
def profile_bspline_derivatives_new(count, spline):
for _ in range(count):
list(spline.derivatives(t=linspace(0, 1.0, 100)))
def sine_wave(count: int, scale: float = 1.0) -> Iterable[Vec3]:
for t in linspace(0, math.tau, count):
yield Vec3(t * scale, math.sin(t) * scale)
def t_vector():
return list(linspace(0, max(KNOTS), 20))
def sine_wave(count: int, scale: float = 1.0):
for t in linspace(0, math.tau, count):
yield Vector(t * scale, math.sin(t) * scale)
def bspline_points_rational(cls, count):
for curve in splines:
weights = [1.0] * curve.count
spline = cls(curve, weights)
for u in linspace(0, spline.basis.max_t, count):
spline.point(u)
def bspline_points(cls, count):
for curve in splines:
spline = cls(curve)
for u in linspace(0, spline.basis.max_t, count):
spline.point(u)
def bspline_multi_points(cls, count):
for curve in splines:
spline = cls(curve)
list(spline.points(linspace(0, spline.basis.max_t, count)))
def bspline_multi_derivative(cls, count):
for curve in splines:
spline = cls(curve)
list(spline.derivatives(linspace(0, spline.basis.max_t, count), 1))
def bspline_derivative(cls, count):
for curve in splines:
spline = cls(curve)
for u in linspace(0, spline.basis.max_t, count):
spline.derivative(u, 1)