def test_reparam(self):
# non-uniform knot vector of a squiggly quadratic n=4 curve
controlpoints = [[0, 0, 0], [1, 1, 0], [2, -1, 0], [3, 0, 0]]
crv = Curve(BSplineBasis(3, [0, 0, 0, 1.32, 3, 3, 3]), controlpoints)
# get some info on the initial curve
knots1 = crv.knots(0)
evaluation_point1 = crv(1.20)
self.assertEqual(knots1[0], 0)
self.assertEqual(knots1[-1], 3)
# reparametrize
crv.reparam((6.0, 9.0))
# get some info on the reparametrized curve
knots2 = crv.knots(0)
evaluation_point2 = crv(7.20)
self.assertEqual(knots2[0], 6)
self.assertEqual(knots2[-1], 9)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# normalize, i.e. set domain to [0,1]
crv.reparam()
# get some info on the normalized curve
knots3 = crv.knots(0)
evaluation_point3 = crv(0.40)
self.assertEqual(knots3[0], 0)
self.assertEqual(knots3[-1], 1)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point3[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point3[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point3[2])
# test errors and exceptions
with self.assertRaises(ValueError):
crv.reparam((9, 3))
with self.assertRaises(TypeError):
crv.reparam(("one", "two"))
def test_reparam(self):
# non-uniform knot vector of a squiggly quadratic n=4 curve
controlpoints = [[0, 0, 0], [1, 1, 0], [2, -1, 0], [3, 0, 0]]
crv = Curve(BSplineBasis(3, [0, 0, 0, 1.32, 3, 3, 3]), controlpoints)
# get some info on the initial curve
knots1 = crv.knots(0)
evaluation_point1 = crv(1.20)
self.assertEqual(knots1[0], 0)
self.assertEqual(knots1[-1], 3)
# reparametrize
crv.reparam((6.0, 9.0))
# get some info on the reparametrized curve
knots2 = crv.knots(0)
evaluation_point2 = crv(7.20)
self.assertEqual(knots2[0], 6)
self.assertEqual(knots2[-1], 9)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# normalize, i.e. set domain to [0,1]
crv.reparam()
# get some info on the normalized curve
knots3 = crv.knots(0)
evaluation_point3 = crv(0.40)
self.assertEqual(knots3[0], 0)
self.assertEqual(knots3[-1], 1)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point3[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point3[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point3[2])
# test errors and exceptions
with self.assertRaises(ValueError):
crv.reparam((9, 3))
with self.assertRaises(TypeError):
crv.reparam(("one", "two"))
def test_insert_knot(self):
# non-uniform knot vector of a squiggly quadratic n=5 curve in 3D
controlpoints = [[0, 0, 0], [1, 1, 1], [2, -1, 0], [3, 0, -1], [0, 0, -5]]
crv = Curve(BSplineBasis(3, [0, 0, 0, .3, .4, 1, 1, 1]), controlpoints)
evaluation_point1 = crv(0.37)
crv.insert_knot(.2)
crv.insert_knot(.3)
crv.insert_knot(.9)
evaluation_point2 = crv(0.37)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
self.assertEqual(len(crv.knots(0, with_multiplicities=True)), 11)
# test knot insertion on single knot span
crv = Curve(BSplineBasis(5), [[0, 0, 0], [1, 1, 1], [2, -1, 0], [3, 0, -1], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.2)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion on first of two-knot span
crv = Curve(
BSplineBasis(3, [0, 0, 0, .5, 1, 1, 1]), [[0, 0, 0], [2, -1, 0], [3, 0, -1], [0, 0, -5]
])
evaluation_point1 = crv(0.27)
crv.insert_knot(.2)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion on last of two-knot span
crv = Curve(
BSplineBasis(3, [0, 0, 0, .5, 1, 1, 1]), [[0, 0, 0], [2, -1, 0], [3, 0, -1], [0, 0, -5]
])
evaluation_point1 = crv(0.27)
crv.insert_knot(.9)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion down to C0 basis
crv = Curve(BSplineBasis(3), [[0, 0, 0], [2, -1, 0], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.4)
crv.insert_knot(.4)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test rational curves, here a perfect circle represented as n=9, p=2-curve
s = 1.0 / sqrt(2)
controlpoints = [[1, 0, 1], [s, s, s], [0, 1, 1], [-s, s, s], [-1, 0, 1], [-s, -s, s],
[0, -1, 1], [s, -s, s], [1, 0, 1]]
crv = Curve(BSplineBasis(3, [-1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5]), controlpoints, True)
evaluation_point1 = crv(0.37)
crv.insert_knot(.2)
crv.insert_knot(.3)
crv.insert_knot(.9)
evaluation_point2 = crv(0.37)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertEqual(len(crv.knots(0, with_multiplicities=True)), 15)
# test errors and exceptions
with self.assertRaises(TypeError):
crv.insert_knot(1, 2, 3) # too many arguments
with self.assertRaises(ValueError):
crv.insert_knot(1, 2) # direction=2 is illegal for curves
with self.assertRaises(TypeError):
crv.insert_knot() # too few arguments
with self.assertRaises(ValueError):
crv.insert_knot(-0.2) # Outside-domain error
with self.assertRaises(ValueError):
crv.insert_knot(4.4) # Outside-domain error
def test_insert_knot(self):
# non-uniform knot vector of a squiggly quadratic n=5 curve in 3D
controlpoints = [[0, 0, 0], [1, 1, 1], [2, -1, 0], [3, 0, -1],
[0, 0, -5]]
crv = Curve(BSplineBasis(3, [0, 0, 0, .3, .4, 1, 1, 1]), controlpoints)
evaluation_point1 = crv(0.37)
crv.insert_knot(.2)
crv.insert_knot(.3)
crv.insert_knot(.9)
evaluation_point2 = crv(0.37)
# ensure that curve has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
self.assertEqual(len(crv.knots(0, with_multiplicities=True)), 11)
# test knot insertion on single knot span
crv = Curve(BSplineBasis(5),
[[0, 0, 0], [1, 1, 1], [2, -1, 0], [3, 0, -1], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.2)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion on first of two-knot span
crv = Curve(BSplineBasis(3, [0, 0, 0, .5, 1, 1, 1]),
[[0, 0, 0], [2, -1, 0], [3, 0, -1], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.2)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion on last of two-knot span
crv = Curve(BSplineBasis(3, [0, 0, 0, .5, 1, 1, 1]),
[[0, 0, 0], [2, -1, 0], [3, 0, -1], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.9)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test knot insertion down to C0 basis
crv = Curve(BSplineBasis(3), [[0, 0, 0], [2, -1, 0], [0, 0, -5]])
evaluation_point1 = crv(0.27)
crv.insert_knot(.4)
crv.insert_knot(.4)
evaluation_point2 = crv(0.27)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test rational curves, here a perfect circle represented as n=9, p=2-curve
s = 1.0 / sqrt(2)
controlpoints = [[1, 0, 1], [s, s, s], [0, 1, 1], [-s, s, s],
[-1, 0, 1], [-s, -s, s], [0, -1, 1], [s, -s, s],
[1, 0, 1]]
crv = Curve(BSplineBasis(3, [-1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5]),
controlpoints, True)
evaluation_point1 = crv(0.37)
crv.insert_knot(.2)
crv.insert_knot(.3)
crv.insert_knot(.9)
evaluation_point2 = crv(0.37)
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertEqual(len(crv.knots(0, with_multiplicities=True)), 15)
# test errors and exceptions
with self.assertRaises(TypeError):
crv.insert_knot(1, 2, 3) # too many arguments
with self.assertRaises(ValueError):
crv.insert_knot(1, 2) # direction=2 is illegal for curves
with self.assertRaises(TypeError):
crv.insert_knot() # too few arguments
with self.assertRaises(ValueError):
crv.insert_knot(-0.2) # Outside-domain error
with self.assertRaises(ValueError):
crv.insert_knot(4.4) # Outside-domain error
