def evaluate_cartesian(self, s, t, _verify=True):
r"""Compute a point on the triangle.
Evaluates :math:`B\left(1 - s - t, s, t\right)` by calling
:meth:`evaluate_barycentric`:
This method acts as a (partial) inverse to :meth:`locate`.
.. testsetup:: triangle-cartesian
import numpy as np
import bezier
.. doctest:: triangle-cartesian
:options: +NORMALIZE_WHITESPACE
>>> nodes = np.asfortranarray([
... [0.0, 0.5, 1.0 , 0.0, 0.5, 0.25],
... [0.0, 0.5, 0.625, 0.5, 0.5, 1.0 ],
... ])
>>> triangle = bezier.Triangle(nodes, degree=2)
>>> point = triangle.evaluate_cartesian(0.125, 0.375)
>>> point
array([[0.16015625],
[0.44726562]])
>>> triangle.evaluate_barycentric(0.5, 0.125, 0.375)
array([[0.16015625],
[0.44726562]])
Args:
s (float): Parameter along the reference triangle.
t (float): Parameter along the reference triangle.
_verify (Optional[bool]): Indicates if the coordinates should be
verified inside of the reference triangle. Defaults to
:data:`True`.
Returns:
numpy.ndarray: The point on the triangle (as a two dimensional
NumPy array).
"""
if _verify:
self._verify_cartesian(s, t)
return _triangle_helpers.evaluate_barycentric(self._nodes,
self._degree,
1.0 - s - t, s, t)
def evaluate_barycentric(self, lambda1, lambda2, lambda3, _verify=True):
r"""Compute a point on the triangle.
Evaluates :math:`B\left(\lambda_1, \lambda_2, \lambda_3\right)`.
.. image:: ../../images/triangle_evaluate_barycentric.png
:align: center
.. testsetup:: triangle-barycentric, triangle-barycentric-fail1,
triangle-barycentric-fail2,
triangle-barycentric-no-verify
import numpy as np
import bezier
nodes = np.asfortranarray([
[0.0, 0.5, 1.0 , 0.125, 0.375, 0.25],
[0.0, 0.0, 0.25, 0.5 , 0.375, 1.0 ],
])
triangle = bezier.Triangle(nodes, degree=2)
.. doctest:: triangle-barycentric
:options: +NORMALIZE_WHITESPACE
>>> nodes = np.asfortranarray([
... [0.0, 0.5, 1.0 , 0.125, 0.375, 0.25],
... [0.0, 0.0, 0.25, 0.5 , 0.375, 1.0 ],
... ])
>>> triangle = bezier.Triangle(nodes, degree=2)
>>> point = triangle.evaluate_barycentric(0.125, 0.125, 0.75)
>>> point
array([[0.265625 ],
[0.73046875]])
.. testcleanup:: triangle-barycentric
import make_images
make_images.triangle_evaluate_barycentric(triangle, point)
However, this can't be used for points **outside** the
reference triangle:
.. doctest:: triangle-barycentric-fail1
>>> triangle.evaluate_barycentric(-0.25, 0.75, 0.5)
Traceback (most recent call last):
...
ValueError: ('Weights must be positive', -0.25, 0.75, 0.5)
or for non-barycentric coordinates;
.. doctest:: triangle-barycentric-fail2
>>> triangle.evaluate_barycentric(0.25, 0.25, 0.25)
Traceback (most recent call last):
...
ValueError: ('Weights do not sum to 1', 0.25, 0.25, 0.25)
However, these "invalid" inputs can be used if ``_verify`` is
:data:`False`.
.. doctest:: triangle-barycentric-no-verify
:options: +NORMALIZE_WHITESPACE
>>> triangle.evaluate_barycentric(-0.25, 0.75, 0.5, _verify=False)
array([[0.6875 ],
[0.546875]])
>>> triangle.evaluate_barycentric(0.25, 0.25, 0.25, _verify=False)
array([[0.203125],
[0.1875 ]])
Args:
lambda1 (float): Parameter along the reference triangle.
lambda2 (float): Parameter along the reference triangle.
lambda3 (float): Parameter along the reference triangle.
_verify (Optional[bool]): Indicates if the barycentric coordinates
should be verified as summing to one and all non-negative (i.e.
verified as barycentric). Can either be used to evaluate at
points outside the domain, or to save time when the caller
already knows the input is verified. Defaults to :data:`True`.
Returns:
numpy.ndarray: The point on the triangle (as a two dimensional
NumPy array with a single column).
Raises:
ValueError: If the weights are not valid barycentric
coordinates, i.e. they don't sum to ``1``. (Won't raise if
``_verify=False``.)
ValueError: If some weights are negative. (Won't raise if
``_verify=False``.)
"""
if _verify:
self._verify_barycentric(lambda1, lambda2, lambda3)
return _triangle_helpers.evaluate_barycentric(self._nodes,
self._degree, lambda1,
lambda2, lambda3)