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)
def test_quality_of_bezier_to_bspline_conversion_1():
# This test shows the close relationship between cubic Bézier- and
# cubic B-spline curves.
points0 = B1.approximate(10)
points1 = bezier_to_bspline([B1]).approximate(10)
for p0, p1 in zip(points0, points1):
assert p0.isclose(p1) is True, "conversion should be perfect"
def test_quality_of_bezier_to_bspline_conversion_2():
# This test shows the close relationship between cubic Bézier- and
# cubic B-spline curves.
# Remove duplicate point between the two curves:
points0 = list(B1.approximate(10)) + list(B2.approximate(10))[1:]
points1 = bezier_to_bspline([B1, B2]).approximate(20)
for p0, p1 in zip(points0, points1):
assert p0.isclose(p1) is True, "conversion should be perfect"
def test_bezier_curves_to_bspline_error():
with pytest.raises(ValueError):
bezier_to_bspline([]) # one or more curves expected
def test_bezier_curves_to_bspline(b1, b2):
bspline = bezier_to_bspline([b1, b2])
# Remove duplicate control point between two adjacent curves:
expected = list(b1.control_points) + list(b2.control_points)[1:]
assert bspline.degree == 3, "should be a cubic B-spline"
assert bspline.control_points == tuple(expected)
# http://help.autodesk.com/view/OARX/2018/ENU/?guid=OREF-AcDbSpline__setFitData_AcGePoint3dArray__AcGeVector3d__AcGeVector3d__AcGe__KnotParameterization_int_double
# Remark in the AutoCAD ObjectARX reference for AcDbSpline about construction
# of a B-spline from fit points:
# degree has no effect. A spline with degree=3 is always constructed when
# interpolating a series of fit points.
# Sadly this works only for short simple splines.
doc, msp = setup()
msp.add_spline(points,
degree=2,
dxfattribs={
'layer': 'BricsCAD B-spline',
'color': 2
})
bezier_curves = cubic_bezier_interpolation(points)
s = bezier_to_bspline(bezier_curves)
msp.add_spline(dxfattribs={
'color': 6,
'layer': 'Cubic Bezier Curve Interpolation'
}).apply_construction_tool(s)
zoom.extents(msp)
doc.saveas(DIR / 'concept-4-cubic-bezier-curves.dxf')
# ----------------------------------------------------------------------------
# A better way to create a SPLINE defined by control vertices from fit points
# without given end tangents for SHORT B-splines:
# ----------------------------------------------------------------------------
doc, msp = setup()
# Create SPLINE defined by fit points only: