def spline_interpolation(vertices: Iterable['Vertex'],
degree: int = 3,
method: str = 'uniform',
power: float = .5,
subdivide: int = 4) -> List[Vector]:
"""
B-spline interpolation, vertices are fit points for the spline definition.
Only method 'uniform', yields vertices at fit points.
Args:
vertices: fit points
degree: degree of B-spline
method: 'uniform', 'distance' or 'centripetal', calculation method for parameter t
power: power for 'centripetal', default is distance ^ .5
subdivide: count of sub vertices + 1, e.g. 4 creates 3 sub-vertices
Returns: list of vertices
"""
vertices = list(vertices)
spline = bspline_control_frame(vertices,
degree=degree,
method=method,
power=power)
return list(spline.approximate(segments=(len(vertices) - 1) * subdivide))
def render_as_fit_points(self,
layout: 'BaseLayout',
degree: int = 3,
method: str = 'distance',
power: float = .5,
dxfattribs: dict = None) -> None:
"""
Render a B-spline as 2D/3D :class:`~ezdxf.entities.Polyline`, where the definition points are fit points.
- 2D spline vertices uses: :meth:`~ezdxf.layouts.BaseLayout.add_polyline2d`
- 3D spline vertices uses: :meth:`~ezdxf.layouts.BaseLayout.add_polyline3d`
Args:
layout: :class:`~ezdxf.layouts.BaseLayout` object
degree: degree of B-spline (order = `degree` + 1)
method: ``'uniform'``, ``'distance'`` or ``'centripetal'``, calculation method for parameter t
power: power for ``'centripetal'``, default = ``0.5``
dxfattribs: DXF attributes for :class:`~ezdxf.entities.Polyline`
"""
spline = bspline_control_frame(self.points,
degree=degree,
method=method,
power=power)
vertices = list(spline.approximate(self.segments))
if any(vertex.z != 0. for vertex in vertices):
layout.add_polyline3d(vertices, dxfattribs=dxfattribs)
else:
layout.add_polyline2d(vertices, dxfattribs=dxfattribs)
def render_as_fit_points(self, layout: 'GenericLayoutType', degree: int = 3, method: str = 'distance',
power: float = .5, dxfattribs: dict = None) -> None:
"""
Render a B-spline as 2d/3d polyline, where the definition points are fit points.
- 2d points in -> add_polyline2d()
- 3d points in -> add_polyline3d()
To get vertices at fit points, use method='uniform' and use Spline.subdivide(count), where
count is the sub-segment count, count=4, means 4 line segments between two definition points.
Args:
layout: ezdxf layout
degree: degree of B-spline
method: 'uniform', 'distance' or 'centripetal', calculation method for parameter t
power: power for 'centripetal', default is distance ^ .5
dxfattribs: DXF attributes for POLYLINE
"""
spline = bspline_control_frame(self.points, degree=degree, method=method, power=power)
vertices = list(spline.approximate(self.segments))
if any(vertex.z != 0. for vertex in vertices):
layout.add_polyline3d(vertices, dxfattribs=dxfattribs)
else:
layout.add_polyline2d(vertices, dxfattribs=dxfattribs)
def test_check_values():
test_points = [(0., 0.), (1., 2.), (3., 1.), (5., 3.)]
spline = bspline_control_frame(test_points, degree=3, method='distance')
result = list(spline.approximate(49))
assert len(result) == 50
for p1, p2 in zip(result, expected):
assert isclose(p1[0], p2[0], abs_tol=1e-6)
assert isclose(p1[1], p2[1], abs_tol=1e-6)
def test_control_frame(fit_points):
spline = bspline_control_frame(fit_points, degree=3)
assert len(spline.control_points) == len(fit_points)
assert spline.t_array[0] == 0.
assert spline.t_array[-1] == 1.
assert len(spline.t_array) == len(fit_points)
t_points = [spline.point(t) for t in spline.t_array]
for p1, p2 in zip(t_points, fit_points):
assert p1 == p2
def add_spline_control_frame(self, fit_points: Iterable[Tuple[float, float]],
degree: int = 3,
method: str = 'distance',
power: float = .5) -> 'SplineEdge':
bspline = bspline_control_frame(fit_points=fit_points, degree=degree, method=method, power=power)
return self.add_spline(
fit_points=fit_points,
control_points=bspline.control_points,
knot_values=bspline.knot_values(),
)
def add_spline(degree=2, color=3):
spline = bspline_control_frame(fit_points,
degree=degree,
method='distance')
msp.add_polyline2d(spline.control_points,
dxfattribs={
'color': color,
'linetype': 'DASHED'
})
msp.add_open_spline(spline.control_points,
degree=spline.degree,
dxfattribs={'color': color})
def bspline(self, length: float, segments: int = 10, degree: int = 3, method: str = 'uniform') -> BSpline:
"""
Approximate euler spiral by B-spline.
Args:
length: length of euler spiral
segments: count of fit points for B-spline calculation
degree: degree of BSpline
method: calculation method for parameter vector t
"""
fit_points = list(self.approximate(length, segments=segments))
spline = bspline_control_frame(fit_points, degree, method=method)
knots = [v * length for v in spline.knot_values()] # scale knot values to length
spline.basis.knots = knots
return spline