test.py

from numpy import matrix
from numpy.linalg import norm

from spline import bezier, bezier6, curve_constraints, exact_cubic, from_bezier, polynom, spline_deriv_constraint

__EPS = 1e-6

waypoints = matrix([[1., 2., 3.], [4., 5., 6.]]).transpose()
waypoints6 = matrix([[1., 2., 3., 7., 5., 5.], [4., 5., 6., 4., 5., 6.]]).transpose()
time_waypoints = matrix([0., 1.])

# testing bezier curve
a = bezier6(waypoints6)
a = bezier(waypoints, 3.)

assert (a.degree == a.nbWaypoints - 1)
a.min()
a.max()
a(0.4)
assert ((a.derivate(0.4, 0) == a(0.4)).all())
a.derivate(0.4, 2)
a = a.compute_derivate(100)

prim = a.compute_primitive(1)

for i in range(10):
    t = float(i) / 10.
    assert (a(t) == prim.derivate(t, 1)).all()
assert (prim(0) == matrix([0., 0., 0.])).all()

prim = a.compute_primitive(2)
for i in range(10):
    t = float(i) / 10.
    assert (a(t) == prim.derivate(t, 2)).all()
assert (prim(0) == matrix([0., 0., 0.])).all()

waypoints = matrix([[1., 2., 3.], [4., 5., 6.], [4., 5., 6.], [4., 5., 6.], [4., 5., 6.]]).transpose()
a0 = bezier(waypoints)
a1 = bezier(waypoints, 3.)
prim0 = a0.compute_primitive(1)
prim1 = a1.compute_primitive(1)

for i in range(10):
    t = float(i) / 10.
    assert norm(a0(t) - a1(3 * t)) < __EPS
    assert norm(a0.derivate(t, 1) - a1.derivate(3 * t, 1) * 3.) < __EPS
    assert norm(a0.derivate(t, 2) - a1.derivate(3 * t, 2) * 9.) < __EPS
    assert norm(prim0(t) - prim1(t * 3) / 3.) < __EPS
assert (prim(0) == matrix([0., 0., 0.])).all()

# testing bezier with constraints
c = curve_constraints()
c.init_vel = matrix([0., 1., 1.])
c.end_vel = matrix([0., 1., 1.])
c.init_acc = matrix([0., 1., -1.])
c.end_acc = matrix([0., 100., 1.])

waypoints = matrix([[1., 2., 3.], [4., 5., 6.]]).transpose()
a = bezier(waypoints, c)
assert norm(a.derivate(0, 1) - c.init_vel) < 1e-10
assert norm(a.derivate(1, 2) - c.end_acc) < 1e-10

# testing polynom function
a = polynom(waypoints)
a = polynom(waypoints, -1., 3.)
a.min()
a.max()
a(0.4)
assert ((a.derivate(0.4, 0) == a(0.4)).all())
a.derivate(0.4, 2)

# testing exact_cubic function
a = exact_cubic(waypoints, time_waypoints)
a.min()
a.max()
a(0.4)
assert ((a.derivate(0.4, 0) == a(0.4)).all())
a.derivate(0.4, 2)

# testing spline_deriv_constraints
c = curve_constraints()
c.init_vel
c.end_vel
c.init_acc
c.end_acc

c.init_vel = matrix([0., 1., 1.])
c.end_vel = matrix([0., 1., 1.])
c.init_acc = matrix([0., 1., 1.])
c.end_acc = matrix([0., 1., 1.])

a = spline_deriv_constraint(waypoints, time_waypoints)
a = spline_deriv_constraint(waypoints, time_waypoints, c)

# converting bezier to polynom

a = bezier(waypoints)
a_pol = from_bezier(a)
assert norm(a(0.3) - a_pol(0.3)) < __EPS