def bernstein(n, k, t):
"""k:sup:`th` of `n` + 1 Bernstein basis polynomials of degree `n`. A
weighted linear combination of these basis polynomials is called a Bernstein
polynomial [wikipedia2017k]_.
Notes
-----
When constructing Bezier curves, the weights are simply the coordinates
of the control points of the curve.
Parameters
----------
n : int
The degree of the polynomial.
k : int
The number of the basis polynomial.
t : float
The variable.
Returns
-------
float
The value of the Bernstein basis polynomial at `t`.
"""
if k < 0:
return 0
if k > n:
return 0
return binomial_coefficient(n, k) * t**k * (1 - t)**(n - k)
def test_binomial(n, k, result):
assert binomial_coefficient(n, k) == pytest.approx(result)
def test_binomial_raises_when_input_is_invalid(n, k):
with pytest.raises(ValueError):
binomial_coefficient(n, k)