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

from numpy import matrix
from numpy.linalg import norm

__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