def test_arc_segment_count():
radius = 100
max_sagitta = 2
assert arc_segment_count(radius, math.tau, max_sagitta) == 16
alpha = math.tau / 16
l2 = math.sin(alpha / 2) * radius
sagitta = radius - math.sqrt(radius**2 - l2**2)
assert max_sagitta / 2 < sagitta < max_sagitta
def flattening(self, sagitta: float) -> Iterable[Vec3]:
"""Approximate the circle by vertices in WCS, argument `sagitta` is the
max. distance from the center of an arc segment to the center of its
chord. Returns a closed polygon: start vertex == end vertex!
Yields always :class:`~ezdxf.math.Vec3` objects.
.. versionadded:: 0.15
"""
radius = abs(self.dxf.radius)
if radius > 0.0:
count = arc_segment_count(radius, math.tau, sagitta)
yield from self.vertices(linspace(0.0, 360.0, count + 1))