def test_spatial_arc_from_3p():
start_point_wcs = Vector(0, 1, 0)
end_point_wcs = Vector(1, 0, 0)
def_point_wcs = Vector(0, 0, 1)
ucs = UCS.from_x_axis_and_point_in_xy(origin=def_point_wcs,
axis=end_point_wcs - def_point_wcs,
point=start_point_wcs)
start_point_ucs = ucs.from_wcs(start_point_wcs)
end_point_ucs = ucs.from_wcs(end_point_wcs)
def_point_ucs = Vector(0, 0)
arc = ConstructionArc.from_3p(start_point_ucs, end_point_ucs,
def_point_ucs)
dwg = ezdxf.new('R12')
msp = dwg.modelspace()
dxf_arc = arc.add_to_layout(msp, ucs)
assert dxf_arc.dxftype() == 'ARC'
assert isclose(dxf_arc.dxf.radius, 0.81649658, abs_tol=1e-9)
assert isclose(dxf_arc.dxf.start_angle, -30) # ???
assert isclose(dxf_arc.dxf.end_angle, -150) # ???
assert is_close_points(dxf_arc.dxf.extrusion,
(0.57735027, 0.57735027, 0.57735027),
abs_tol=1e-9)
def circular_arc_3p(self, data: bytes):
bs = ByteStream(data)
attribs = self._build_dxf_attribs()
p1 = Vec3(bs.read_vertex())
p2 = Vec3(bs.read_vertex())
p3 = Vec3(bs.read_vertex())
arc_type = bs.read_struct('L')[0]
arc = ConstructionArc.from_3p(p1, p3, p2)
attribs['center'] = arc.center
attribs['radius'] = arc.radius
attribs['start_angle'] = arc.start_angle
attribs['end_angle'] = arc.end_angle
return self._factory('ARC', dxfattribs=attribs)
def test_arc_from_3p():
p1 = (-15.73335, 10.98719)
p2 = (-12.67722, 8.76554)
p3 = (-8.00817, 12.79635)
arc = ConstructionArc.from_3p(start_point=p1, end_point=p2, def_point=p3)
arc_result = ConstructionArc(
center=(-12.08260, 12.79635),
radius=4.07443,
start_angle=-153.638906,
end_angle=-98.391676,
)
assert arc.center.isclose(arc_result.center, abs_tol=1e-5)
assert isclose(arc.radius, arc_result.radius, abs_tol=1e-5)
assert isclose(arc.start_angle, arc_result.start_angle, abs_tol=1e-4)
assert isclose(arc.end_angle, arc_result.end_angle, abs_tol=1e-4)
# create a 3D arc from 3 points in WCS
start_point_wcs = Vec3(3, 0, 0)
end_point_wcs = Vec3(0, 3, 0)
def_point_wcs = Vec3(0, 0, 3)
# create UCS
ucs = UCS.from_x_axis_and_point_in_xy(origin=def_point_wcs,
axis=start_point_wcs - def_point_wcs,
point=end_point_wcs)
start_point_ucs = ucs.from_wcs(start_point_wcs)
end_point_ucs = ucs.from_wcs(end_point_wcs)
def_point_ucs = Vec3(0, 0) # origin of UCS
# create arc in the xy-plane of the UCS
arc = ConstructionArc.from_3p(start_point_ucs, end_point_ucs, def_point_ucs)
arc.add_to_layout(modelspace, ucs, dxfattribs={'color': 1}) # red arc
arc = ConstructionArc.from_3p(end_point_ucs, start_point_ucs, def_point_ucs)
arc.add_to_layout(modelspace, ucs, dxfattribs={'color': 2}) # yellow arc
p1 = Vec3(0, -18)
p2 = Vec3(0, +18)
arc = ConstructionArc.from_2p_angle(p1, p2, 90)
arc.add_to_layout(modelspace, dxfattribs={'color': 1})
arc = ConstructionArc.from_2p_angle(p1, p2, 90, ccw=False)
arc.add_to_layout(modelspace, dxfattribs={'color': 2})
p1 = Vec3(20, -18)
p2 = Vec3(20, +18)
spline.apply_construction_tool(bspline)
# Recreate ARC from SPLINE, if you ASSUME or KNOW it is an ARC:
# for spline in msp.query("SPLINE):
# ...
# 1. get the B-spline construction tool from the SPLINE entity
bspline = spline.construction_tool()
max_t = bspline.max_t
# calculate 3 significant points and 2 check points of the SPLINE:
start, chk1, middle, chk2, end = bspline.points([
0, max_t * 0.25, max_t * 0.5, max_t * 0.75, max_t
])
# create an arc from 3 points:
arc_tool = ConstructionArc.from_3p(start, end, middle)
arc_tool.add_to_layout(msp, dxfattribs={
"layer": "recreated arc",
"color": ezdxf.const.MAGENTA,
})
# This only works for flat B-splines in the xy-plane, a.k.a. 2D splines!
# Check the assumption:
center = arc_tool.center
radius = arc_tool.radius
err = max(abs(radius - p.distance(center)) for p in (chk1, chk2))
print(f"max error: {err:.6f}")
# Warning: this does not proof that the assumption was correct, it is always
# possible to create a diverging B-spline which matches the check points: