def test_lr_spline_insert_line_multiple():
LR = init_tensor_product_LR_spline(1, 1, [0, 1, 2, 3], [0, 1, 2])
M1 = Meshline(0, 2, constant_value=0.5, axis=1) # horizontal split
M2 = Meshline(0, 1, constant_value=1.5, axis=0) # vertical split
LR.insert_line(M1)
LR.insert_line(M2)
# expected functions
b1 = BSpline(1, 1, [0, 1, 1.5], [0, 0.5, 1])
b2 = BSpline(1, 1, [1, 1.5, 2], [0, 0.5, 1])
b3 = BSpline(1, 1, [0, 1, 2], [0.5, 1, 2])
b4 = BSpline(1, 1, [1, 2, 3], [0, 1, 2])
assert b1 in LR.S
assert b2 in LR.S
assert b3 in LR.S
assert b3 in LR.S
assert len(LR.S) == 4
expected_elements = [
Element(0, 0, 1, 0.5),
Element(1, 0, 1.5, 0.5),
Element(1.5, 0, 2, 0.5),
Element(0, 0.5, 1, 1),
Element(1, 0.5, 1.5, 1),
Element(1.5, 0.5, 2, 1),
Element(2, 0, 3, 1),
Element(0, 1, 1, 2),
Element(1, 1, 2, 2),
Element(2, 1, 3, 2)
]
assert all([LR.contains_element(e) for e in expected_elements])
assert len(LR.M) == 10
def test_element_equality():
e1 = Element(0, 0, 1, 1)
e2 = Element(0, 0, 1, 1)
e3 = Element(0, 0, 1, 1.1)
assert e1 == e2
assert e1 != e3
def test_element_intersects():
e1 = Element(0, 0, 1, 1)
e2 = Element(0.25, 0.25, 0.75, 0.75)
e3 = Element(0.5, 0.5, 1.5, 1.5)
e4 = Element(1, 0, 2, 1)
assert e1.intersects(e2) and e2.intersects(e1)
assert e1.intersects(e3) and e3.intersects(e1)
assert not e1.intersects(e4)
e5 = e1.split(axis=0, split_value=.5)
assert not e1.intersects(e5)
def test_lr_spline_minimal_span_line_superficial():
"""
Constructed example, won't occur in practice.
"""
element = Element(0.5, 0, 1, 2)
ku1 = [-1, 0, 1]
kv1 = [0, 1, 2]
ku2 = [0, 0.5, 1]
kv2 = [0, 1, 3]
b1 = BSpline(1, 1, ku1, kv1)
b2 = BSpline(1, 1, ku2, kv2)
element.add_supported_b_spline(b1)
element.add_supported_b_spline(b2)
small_span_meshline_vertical = LRSpline.get_minimal_span_meshline(element,
axis=0)
small_span_meshline_horizontal = LRSpline.get_minimal_span_meshline(
element, axis=1)
assert small_span_meshline_vertical.start == 0
assert small_span_meshline_vertical.stop == 2
assert small_span_meshline_vertical.constant_value == 0.75
assert small_span_meshline_horizontal.start == 0
assert small_span_meshline_horizontal.stop == 1
assert small_span_meshline_horizontal.constant_value == 1
def test_element_containment():
e = Element(0, 0, 1, 1)
assert e.contains(0.5, 0.5)
assert e.contains(0.5, 0)
assert not e.contains(-1, 0.5)
assert not e.contains(0, -1.0e-14)
def test_element_support():
e = Element(0, 0, 1, 1)
e.add_supported_b_spline(max)
assert e.has_supported_b_spline(max)
assert e.get_supported_b_spline(0) == max
e.remove_supported_b_spline(max)
assert len(e.supported_b_splines) == 0
def test_meshline_splits_element():
start = 0
stop = 1
constant_value = 0.5
m1 = Meshline(start, stop, constant_value, 0)
m2 = Meshline(start, stop, constant_value, 1)
e1 = Element(0, 0, 1, 1)
e2 = Element(0, 0, 0.4, 1)
e3 = Element(0, 0, 0.5, 1)
assert m1.splits_element(e1)
assert not m1.splits_element(e2)
assert not m1.splits_element(e3)
assert m2.splits_element(e1)
assert m2.splits_element(e2)
assert m2.splits_element(e3)
def test_element_area():
e1 = Element(0, 0, 1, 1)
assert e1.area == 1
def test_element_midpoint():
e1 = Element(0, 0, 1, 1)
mp = e1.midpoint
assert mp == (0.5, 0.5)
def test_element_init():
e = Element(0, 0, 1, 1)
assert e.u_min == 0 and e.u_max == 1 and e.v_min == 0 and e.v_max == 1 and e.supported_b_splines == []
def test_element_invalid():
e1 = Element(0, 0, 1, 1)
e2 = e1.split(0, 1)
assert e2 is None
assert e1.u_min == 0 and e1.u_max == 1 and e1.v_min == 0 and e1.v_max == 1
def test_element_split():
e1 = Element(0, 0, 1, 1)
e2 = e1.split(0, 0.5)
assert e1.u_min == 0 and e1.v_min == 0 and e1.u_max == 0.5 and e1.v_max == 1
assert e2.u_min == 0.5 and e2.v_min == 0 and e2.u_max == 1 and e2.v_max == 1
def init_tensor_product_LR_spline(d1: int, d2: int, ku: Vector,
kv: Vector) -> 'LRSpline':
"""
Initializes an LR spline at the tensor product level of bidegree (d1, d2).
:param d1: first component degree
:param d2: second component degree
:param ku: knots in u_direction
:param kv: knots in v_direction
:return: corresponding LR_spline
"""
elements = []
basis = []
meshlines = []
unique_ku = np.unique(ku)
unique_kv = np.unique(kv)
for i in range(len(unique_ku) - 1):
for j in range(len(unique_kv) - 1):
elements.append(
Element(unique_ku[i], unique_kv[j], unique_ku[i + 1],
unique_kv[j + 1]))
for i in range(len(ku) - d1 - 1):
for j in range(len(kv) - d2 - 1):
end_u = _at_end(ku, i + d1 + 1)
end_v = _at_end(kv, j + d2 + 1)
# TODO: This only works if the knot vectors are p+1-extended.
north = j == len(kv) - d2 - 2
south = j == 0
east = i == len(ku) - d1 - 2
west = i == 0
basis.append(
BSpline(d1,
d2,
ku[i:i + d1 + 2],
kv[j:j + d2 + 2],
end_u=end_u,
end_v=end_v,
north=north,
south=south,
east=east,
west=west))
for b in basis:
for e in elements:
if b.add_to_support_if_intersects(e):
e.add_supported_b_spline(b)
for i in range(len(unique_ku)):
for j in range(len(unique_kv) - 1):
new_m = Meshline(start=unique_kv[j],
stop=unique_kv[j + 1],
constant_value=unique_ku[i],
axis=0)
new_m.set_multiplicity(ku)
meshlines.append(new_m)
for i in range(len(unique_kv)):
for j in range(len(unique_ku) - 1):
new_m = Meshline(start=unique_ku[j],
stop=unique_ku[j + 1],
constant_value=unique_kv[i],
axis=1)
new_m.set_multiplicity(kv)
meshlines.append(new_m)
u_range = [ku[0], ku[-1]]
v_range = [kv[0], kv[-1]]
return LRSpline(elements, basis, meshlines, u_range, v_range, unique_ku,
unique_kv)