def test_as_bspline():
spiral = EulerSpiral(2.0)
spline = spiral.bspline(5, 10)
assert spline.degree == 3
assert spline.max_t == 5
results = spline.approximate(10)
for expected, result in zip(expected_points, results):
assert is_close_points(Vector(expected), result)
def euler_spiral(count: int, length: float = 1, curvature: float = 1, elevation: float = 0) -> Iterable[Vector]:
"""
Create polygon vertices for an `euler spiral <https://en.wikipedia.org/wiki/Euler_spiral>`_ of a given `length` and
radius of curvature. This is a parametric curve, which always starts
at the origin ``(0, 0)``.
Args:
count: count of polygon vertices
length: length of curve in drawing units
curvature: radius of curvature
elevation: z-axis for all vertices
Returns:
vertices as :class:`~ezdxf.math.Vector` objects
"""
spiral = EulerSpiral(curvature=curvature)
for vertex in spiral.approximate(length, count - 1):
yield vertex.replace(z=elevation)
def euler_spiral(count: int,
length: float = 1,
curvature: float = 1,
elevation: float = 0) -> Iterable[Vector]:
"""
Create polygon vertices for an euler spiral of a given length and
radius of curvature. This is a parametric curve, which always starts
at the origin.
Args:
count: count of polygon vertices
length: length of curve in drawing units
curvature: radius of curvature
elevation: z-axis for all vertices
Returns: yields Vector() objects
"""
spiral = EulerSpiral(curvature=curvature)
for vertex in spiral.approximate(length, count - 1):
yield vertex.replace(z=elevation)
def test_circle_midpoint():
spiral = EulerSpiral(2.0)
m = spiral.circle_midpoint(2.0)
assert is_close_points(m, (0.9917242992178723, 2.082593218533209, 0))
def test_distance():
spiral = EulerSpiral(2.0)
assert isclose(spiral.distance(10), 0.4)
def test_tangent():
spiral = EulerSpiral(2.0)
assert isclose(spiral.tangent(1).angle, 0.125)
def test_radius():
spiral = EulerSpiral(2.0)
assert isclose(spiral.radius(1), 4.)
assert isclose(spiral.radius(0), 0.)
def test_approximate():
spiral = EulerSpiral(2.0)
results = spiral.approximate(5, 10)
for expected, result in zip(expected_points, results):
assert is_close_points(Vector(expected), result)