def test_sample_triangle():
"""
We sample a triangle, and assert that the barycentric coordinates of the resulting points are all
positive, hence the points lie inside the triangle.
"""
triangle = np.array([
[0, 0],
[1, 0],
[0, 1]
])
d = 30
points = sample_triangle(triangle, d)
bary_coords = barycentric_coordinates(triangle, points)
assert np.all(bary_coords[bary_coords > 0])
def test_non_zero_splines_evaluation_multiple_quadratic():
"""
Computes all the non-zero quadratic basis splines at a set of points, and asserts
that for each point, the basis functions sum to one.
"""
triangle = np.array([[0, 0], [1, 0], [0, 1]])
d = 2
points = sample_triangle(triangle, 30)
bary_coords = barycentric_coordinates(triangle, points)
k = determine_sub_triangle(bary_coords)
s = evaluate_non_zero_basis_splines(d, bary_coords, k)
expected_sum = np.ones((len(points)))
computed_sum = s.sum(axis=1)
np.testing.assert_almost_equal(expected_sum, computed_sum)
def test_spline_function_evaluation_multiple_linear():
"""
Evaluates the linear spline function with all coefficients equal to one, and assert that the value
is indeed 1 for all points.
"""
triangle = np.array([
[0, 0],
[1, 0],
[0, 1]
])
d = 1
c = np.ones(10)
f = SplineFunction(coefficients=c, degree=d, triangle=triangle)
points = sample_triangle(triangle, 30)
expected_values = np.ones(len(points))
computed_values = f(points)
np.testing.assert_almost_equal(expected_values, computed_values)
def test_spline_function_evaluation_multiple_quadratic():
"""
Computes all the non-zero quadratic basis splines at a set of points, and asserts
that for each point, the basis functions sum to one.
"""
triangle = np.array([
[0, 0],
[1, 0],
[0, 1]
])
d = 2
c = np.ones(12)
f = SplineFunction(coefficients=c, degree=d, triangle=triangle)
points = sample_triangle(triangle, 30)
expected_values = np.ones(len(points))
computed_values = f(points)
np.testing.assert_almost_equal(expected_values, computed_values)