def bspline(self,
length: float,
segments: int = 10,
degree: int = 3,
method: str = 'uniform') -> BSpline:
"""
Approximate euler spiral as 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
Returns:
:class:`BSpline`
"""
fit_points = list(self.approximate(length, segments=segments))
spline = global_bspline_interpolation(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
def render_as_fit_points(self,
layout: 'BaseLayout',
degree: int = 3,
method: str = 'chord',
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"/"chord", "centripetal"/"sqrt_chord" or "arc"
calculation method for parameter t
dxfattribs: DXF attributes for :class:`~ezdxf.entities.Polyline`
"""
spline = global_bspline_interpolation(self.points,
degree=degree,
method=method)
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 = global_bspline_interpolation(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_bspline_interpolation(fit_points):
spline = global_bspline_interpolation(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(degree=2, color=3):
spline = global_bspline_interpolation(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 spline_interpolation(vertices: Iterable['Vertex'], degree: int = 3, method: str = 'chord',
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", "chord"/"distance", "centripetal"/"sqrt_chord" or "arc" calculation method for parameter t
subdivide: count of sub vertices + 1, e.g. 4 creates 3 sub-vertices
Returns: list of vertices
"""
vertices = list(vertices)
spline = global_bspline_interpolation(vertices, degree=degree, method=method)
return list(spline.approximate(segments=(len(vertices) - 1) * subdivide))
def bspline(
self,
length: float,
segments: int = 10,
degree: int = 3,
method: str = "uniform",
) -> BSpline:
"""Approximate euler spiral as 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
Returns:
:class:`BSpline`
"""
length = float(length)
fit_points = list(self.approximate(length, segments=segments))
derivatives = [
# Scaling derivatives by chord length (< real length) is suggested
# by Piegl & Tiller.
self.tangent(t).normalize(length)
for t in _params(length, segments)
]
spline = global_bspline_interpolation(
fit_points, degree, method=method, tangents=derivatives
)
return BSpline(
spline.control_points,
spline.order,
# Scale knot values to length:
[v * length for v in spline.knots()],
)
def test_bspline_interpolation_first_derivatives(fit_points):
tangents = estimate_tangents(fit_points)
spline = global_bspline_interpolation(fit_points,
degree=3,
tangents=tangents)
assert len(spline.control_points) == 2 * len(fit_points)
def add_spline(degree=2, color=3):
spline = global_bspline_interpolation(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})