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test_helpers.py
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"""
Tests for the NURBS-Python package
Released under The MIT License. See LICENSE file for details.
Copyright (c) 2018-2019 Onur Rauf Bingol
Requires "pytest" to run.
"""
from geomdl import helpers
GEOMDL_DELTA = 10e-8
def test_find_span_binsearch():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
num_ctrlpts = len(knot_vector) - degree - 1
knot = 5.0 / 2.0
to_check = helpers.find_span_binsearch(degree, knot_vector, num_ctrlpts, knot)
result = 4 # Value from The Nurbs Book p.68
assert to_check == result
def test_basis_function():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
span = 4
knot = 5.0 / 2.0
to_check = helpers.basis_function(degree, knot_vector, span, knot)
result = [1.0 / 8.0, 6.0 / 8.0, 1.0 / 8.0] # Values from The Nurbs Book p.69
assert abs(to_check[0] - result[0]) < GEOMDL_DELTA
assert abs(to_check[1] - result[1]) < GEOMDL_DELTA
assert abs(to_check[2] - result[2]) < GEOMDL_DELTA
def test_basis_functions():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
spans = [3, 4, 5]
knots = [5.0 / 2.0 for _ in range(len(spans))]
to_check = helpers.basis_functions(degree, knot_vector, spans, knots)
result = [helpers.basis_function(degree, knot_vector, spans[_], knots[_]) for _ in range(len(spans))] # Values from The Nurbs Book p.55
assert abs(to_check[0][0] - result[0][0]) < GEOMDL_DELTA
assert abs(to_check[0][1] - result[0][1]) < GEOMDL_DELTA
assert abs(to_check[0][2] - result[0][2]) < GEOMDL_DELTA
assert abs(to_check[1][0] - result[1][0]) < GEOMDL_DELTA
assert abs(to_check[1][1] - result[1][1]) < GEOMDL_DELTA
assert abs(to_check[1][2] - result[1][2]) < GEOMDL_DELTA
assert abs(to_check[2][0] - result[2][0]) < GEOMDL_DELTA
assert abs(to_check[2][1] - result[2][1]) < GEOMDL_DELTA
assert abs(to_check[2][2] - result[2][2]) < GEOMDL_DELTA
def test_basis_function_all():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
span = 4
knot = 5.0 / 2.0
to_check = helpers.basis_function_all(degree, knot_vector, span, knot)
interm = [helpers.basis_function(_, knot_vector, span, knot) + [None] * (degree - _) for _ in range(0, degree + 1)]
result = [list(_) for _ in zip(*interm)] # Transposing to the same format as to_check
assert abs(to_check[0][0] - result[0][0]) < GEOMDL_DELTA
assert abs(to_check[0][1] - result[0][1]) < GEOMDL_DELTA
assert abs(to_check[0][2] - result[0][2]) < GEOMDL_DELTA
assert to_check[1][0] == result[1][0] # NoneType can't be subtracted
assert abs(to_check[1][1] - result[1][1]) < GEOMDL_DELTA
assert abs(to_check[1][2] - result[1][2]) < GEOMDL_DELTA
assert to_check[2][0] == result[2][0] # None
assert to_check[2][1] == result[2][1] # None
assert abs(to_check[2][2] - result[2][2]) < GEOMDL_DELTA
def test_basis_function_ders():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
span = 4
knot = 5.0 / 2.0
order = 2
to_check = helpers.basis_function_ders(degree, knot_vector, span, knot, order)
result = [[0.125, 0.75, 0.125], [-0.5, 0.0, 0.5], [1.0, -2.0, 1.0]] # Values and formulas from The Nurbs Book p.69 & p.72
assert abs(to_check[0][0] - result[0][0]) < GEOMDL_DELTA
assert abs(to_check[0][1] - result[0][1]) < GEOMDL_DELTA
assert abs(to_check[0][2] - result[0][2]) < GEOMDL_DELTA
assert abs(to_check[1][0] - result[1][0]) < GEOMDL_DELTA
assert abs(to_check[1][1] - result[1][1]) < GEOMDL_DELTA
assert abs(to_check[1][2] - result[1][2]) < GEOMDL_DELTA
assert abs(to_check[2][0] - result[2][0]) < GEOMDL_DELTA
assert abs(to_check[2][1] - result[2][1]) < GEOMDL_DELTA
assert abs(to_check[2][2] - result[2][2]) < GEOMDL_DELTA
def test_find_multiplicity():
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
knots = [0.5, 2, 4, 5]
to_check = [helpers.find_multiplicity(_, knot_vector) for _ in knots]
result = [0, 1, 2, 3]
assert to_check == result
def test_basis_function_one():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
span = 4
knot = 5.0 / 2.0
# Values from basis_function
to_check = [helpers.basis_function_one(degree, knot_vector, span - _, knot) for _ in range(degree, -1, -1)]
result = helpers.basis_function(degree, knot_vector, span, knot)
assert abs(to_check[0] - result[0]) < GEOMDL_DELTA
assert abs(to_check[1] - result[1]) < GEOMDL_DELTA
assert abs(to_check[2] - result[2]) < GEOMDL_DELTA
def test_basis_function_ders_one():
degree = 2
knot_vector = [0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5]
span = 4
knot = 5.0 / 2.0
order = 2
to_check = [helpers.basis_function_ders_one(degree, knot_vector, span - _, knot, order) for _ in range(degree, -1, -1)]
interm = helpers.basis_function_ders(degree, knot_vector, span, knot, order)
result = [list(_) for _ in zip(*interm)]
assert abs(to_check[0][0] - result[0][0]) < GEOMDL_DELTA
assert abs(to_check[0][1] - result[0][1]) < GEOMDL_DELTA
assert abs(to_check[0][2] - result[0][2]) < GEOMDL_DELTA
assert abs(to_check[1][0] - result[1][0]) < GEOMDL_DELTA
assert abs(to_check[1][1] - result[1][1]) < GEOMDL_DELTA
assert abs(to_check[1][2] - result[1][2]) < GEOMDL_DELTA
assert abs(to_check[2][0] - result[2][0]) < GEOMDL_DELTA
assert abs(to_check[2][1] - result[2][1]) < GEOMDL_DELTA
assert abs(to_check[2][2] - result[2][2]) < GEOMDL_DELTA