def test_local_cubic_bspline_interpolation_from_tangents():
points = Vec3.list(POINTS1)
tangents = estimate_tangents(points)
control_points, knots = local_cubic_bspline_interpolation_from_tangents(
points, tangents)
assert len(control_points) == 8
assert len(knots) == 8 + 4 # count + order
def test_estimate_tangents_5p():
tangents = estimate_tangents(Vec3.list(POINTS1), method="5-points")
assert len(tangents) == 4
# Reference curve as fine approximation
msp.add_lwpolyline(sine_wave(count=800, scale=2.0),
dxfattribs={
'color': 1,
'layer': 'Reference curve (LWPolyline)'
})
# AutoCAD/BricsCAD interpolation
msp.add_spline(data, dxfattribs={'layer': 'BricsCAD B-spline', 'color': 2})
# tangent estimation method
METHOD = '5-p'
# create not normalized tangents (default is normalized)
tangents = estimate_tangents(data, METHOD, normalize=False)
# show tangents
for p, t in zip(data, tangents):
msp.add_line(p,
p + t,
dxfattribs={
'color': 5,
'layer': f'Estimated tangents ({METHOD})'
})
# local interpolation: a normalized tangent vector for each data point is required,
s = local_cubic_bspline_interpolation(
data, tangents=[t.normalize() for t in tangents])
# or set argument 'method' for automatic tangent estimation, default method is '5-points' interpolation
# s = local_cubic_bspline_interpolation(data, method=METHOD)
dxfattribs={
'layer': 'BricsCAD B-spline',
'color': 2
})
spline.dxf.start_tangent = Vec3.from_deg_angle(100)
spline.dxf.end_tangent = Vec3.from_deg_angle(-100)
zoom.extents(msp)
doc.saveas(DIR / 'concept-1-fit-points-and-tangents.dxf')
# 3. Need control vertices to render the B-spline but start- and
# end tangents are not stored in the DXF file like in scenario 1.
# Estimation of start- and end tangents is required, best result by:
# "5 Point Interpolation" from "The NURBS Book", Piegl & Tiller
doc, msp = setup()
tangents = estimate_tangents(points, method='5-points')
# Estimated tangent angles: (108.43494882292201, -108.43494882292201) degree
m1, m2 = estimate_end_tangent_magnitude(points, method='chord')
start_tangent = tangents[0].normalize(m1)
end_tangent = tangents[-1].normalize(m2)
# Interpolate control vertices from fit points and end derivatives as constraints
s = global_bspline_interpolation(points,
degree=3,
tangents=(start_tangent, end_tangent))
msp.add_spline(dxfattribs={
'color': 4,
'layer': 'Global Interpolation'
}).apply_construction_tool(s)
# Result does not matches the BricsCAD interpolation
# tangents angle: (101.0035408517495, -101.0035408517495) degree
msp.add_spline(points,
# tangents are stored explicit in the DXF file.
spline = msp.add_spline(
points, degree=3, dxfattribs={"layer": "BricsCAD B-spline", "color": 2}
)
spline.dxf.start_tangent = Vec3.from_deg_angle(100)
spline.dxf.end_tangent = Vec3.from_deg_angle(-100)
zoom.extents(msp)
doc.saveas(DIR / "concept-1-fit-points-and-tangents.dxf")
# 3. Need control vertices to render the B-spline but start- and
# end tangents are not stored in the DXF file like in scenario 1.
# Estimation of start- and end tangents is required, best result by:
# "5 Point Interpolation" from "The NURBS Book", Piegl & Tiller
doc, msp = setup()
tangents = estimate_tangents(points, method="5-points")
# Estimated tangent angles: (108.43494882292201, -108.43494882292201) degree
m1, m2 = estimate_end_tangent_magnitude(points, method="chord")
start_tangent = tangents[0].normalize(m1)
end_tangent = tangents[-1].normalize(m2)
# Interpolate control vertices from fit points and end derivatives as constraints
s = global_bspline_interpolation(
points, degree=3, tangents=(start_tangent, end_tangent)
)
msp.add_spline(
dxfattribs={"color": 4, "layer": "Global Interpolation"}
).apply_construction_tool(s)
# Result does not matches the BricsCAD interpolation
# tangents angle: (101.0035408517495, -101.0035408517495) degree
msp.add_spline(
points, degree=3, dxfattribs={"layer": "BricsCAD B-spline", "color": 2}
def test_estimate_tangents_5p():
tangents = estimate_tangents(Vector.list(POINTS1), method='5-points')
assert len(tangents) == 4
def test_estimate_tangents_3p():
tangents = estimate_tangents(Vec3.list(POINTS1), method='3-points')
assert len(tangents) == 4
