test_helpers.py

"""
    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