def test_from_quadratic_not_elevated(self):
from bezier import _curve_helpers
nodes = np.asfortranarray([[0.0, 1.0, 2.0], [0.0, 1.5, 0.0]])
result = self._call_function_under_test(nodes)
expected = np.asfortranarray([[0.0, 2.0], [0.5, 0.5]])
self.assertEqual(result, expected)
re_elevated = _curve_helpers.elevate_nodes(result)
self.assertTrue(np.any(nodes != re_elevated))
def elevate(self):
r"""Return a degree-elevated version of the current curve.
Does this by converting the current nodes :math:`v_0, \ldots, v_n`
to new nodes :math:`w_0, \ldots, w_{n + 1}` where
.. math::
\begin{align*}
w_0 &= v_0 \\
w_j &= \frac{j}{n + 1} v_{j - 1} + \frac{n + 1 - j}{n + 1} v_j \\
w_{n + 1} &= v_n
\end{align*}
.. image:: ../images/curve_elevate.png
:align: center
.. testsetup:: curve-elevate
import numpy as np
import bezier
.. doctest:: curve-elevate
:options: +NORMALIZE_WHITESPACE
>>> nodes = np.asfortranarray([
... [0.0, 0.0],
... [1.5, 1.5],
... [3.0, 0.0],
... ])
>>> curve = bezier.Curve(nodes, degree=2)
>>> elevated = curve.elevate()
>>> elevated
<Curve (degree=3, dimension=2)>
>>> elevated.nodes
array([[ 0., 0.],
[ 1., 1.],
[ 2., 1.],
[ 3., 0.]])
.. testcleanup:: curve-elevate
import make_images
make_images.curve_elevate(curve, elevated)
Returns:
Curve: The degree-elevated curve.
"""
new_nodes = _curve_helpers.elevate_nodes(self._nodes, self._degree,
self._dimension)
root = None if self._root is self else self._root
return Curve(new_nodes,
self._degree + 1,
start=self._start,
end=self._end,
root=root,
_copy=False)
def _actually_inverse_helper(self, degree):
from bezier import _curve_helpers
from bezier import _helpers
nodes = np.eye(degree + 2, order="F")
reduction_mat = self._call_function_under_test(nodes)
id_mat = np.eye(degree + 1, order="F")
elevation_mat = _curve_helpers.elevate_nodes(id_mat)
result = _helpers.matrix_product(elevation_mat, reduction_mat)
return result, id_mat
def _call_function_under_test(nodes, degree, dimension):
from bezier import _curve_helpers
return _curve_helpers.elevate_nodes(nodes, degree, dimension)
