def coons(curves, tol=1.e-10):
"""
C[1,1]
o--------------o
| v |
| ^ |
C[0,0] | | | C[0,1]
| | |
| +------> u |
o--------------o
C[1,0]
"""
(C00, C01), (C10, C11) = curves
assert C00.dim == C01.dim == 1
assert C10.dim == C11.dim == 1
#
(C00, C01) = compat(C00, C01)
(C10, C11) = compat(C10, C11)
#
p, U = C10.degree[0], C10.knots[0]
u0, u1 = U[p], U[-p-1]
P = np.zeros((2,2,3), dtype='d')
P[0,0] = C10(u0)
P[1,0] = C10(u1)
P[0,1] = C11(u0)
P[1,1] = C11(u1)
#
q, V = C00.degree[0], C00.knots[0]
v0, v1 = V[q], V[-q-1]
Q = np.zeros((2,2,3), dtype='d')
Q[0,0] = C00(v0)
Q[0,1] = C00(v1)
Q[1,0] = C01(v0)
Q[1,1] = C01(v1)
#
# print "P[0,0] ", P[0,0] , " Q[0,0] ", Q[0,0]
# print "P[1,0] ", P[1,0] , " Q[1,0] ", Q[1,0]
# print "P[0,1] ", P[0,1] , " Q[0,1] ", Q[0,1]
# print "P[1,1] ", P[1,1] , " Q[1,1] ", Q[1,1]
assert np.allclose(P, Q, rtol=0, atol=tol)
#
R0 = ruled(C00, C01).transpose()
R1 = ruled(C10, C11)
B = bilinear(P)
R0, R1, B = compat(R0, R1, B)
control = R0.control + R1.control - B.control
knots = B.knots
return NURBS(knots, control)
def coons(curves, tol=1.e-10):
"""
C[1,1]
o--------------o
| v |
| ^ |
C[0,0] | | | C[0,1]
| | |
| +------> u |
o--------------o
C[1,0]
"""
(C00, C01), (C10, C11) = curves
assert C00.dim == C01.dim == 1
assert C10.dim == C11.dim == 1
#
(C00, C01) = compat(C00, C01)
(C10, C11) = compat(C10, C11)
#
p, U = C10.degree[0], C10.knots[0]
u0, u1 = U[p], U[-p - 1]
P = np.zeros((2, 2, 3), dtype='d')
P[0, 0] = C10(u0)
P[1, 0] = C10(u1)
P[0, 1] = C11(u0)
P[1, 1] = C11(u1)
#
q, V = C00.degree[0], C00.knots[0]
v0, v1 = V[q], V[-q - 1]
Q = np.zeros((2, 2, 3), dtype='d')
Q[0, 0] = C00(v0)
Q[0, 1] = C00(v1)
Q[1, 0] = C01(v0)
Q[1, 1] = C01(v1)
#
# print "P[0,0] ", P[0,0] , " Q[0,0] ", Q[0,0]
# print "P[1,0] ", P[1,0] , " Q[1,0] ", Q[1,0]
# print "P[0,1] ", P[0,1] , " Q[0,1] ", Q[0,1]
# print "P[1,1] ", P[1,1] , " Q[1,1] ", Q[1,1]
assert np.allclose(P, Q, rtol=0, atol=tol)
#
R0 = ruled(C00, C01).transpose()
R1 = ruled(C10, C11)
B = bilinear(P)
R0, R1, B = compat(R0, R1, B)
control = R0.control + R1.control - B.control
knots = B.knots
return NURBS(knots, control)
def coonsInitialize(curves, tol=1.e-3):
[[c1,c3],[c0,c2]] = curves
(c0, c2) = compat(c0, c2)
(c1, c3) = compat(c1, c3)
p, U = c0.degree[0], c0.knots[0]
ub, ue = U[p], U[-p-1]
q, V = c1.degree[0], c1.knots[0]
vb, ve = V[q], V[-q-1]
# c0 and c1 compatibility
P = c0(ub)
Q = c1(vb)
if not np.allclose(P, Q, rtol=0, atol=tol):
c1.reverse()
Q = c1(vb)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c1 and c2 compatibility
P = c1(ve)
Q = c2(ub)
if not np.allclose(P, Q, rtol=0, atol=tol):
c2.reverse()
Q = c2(ub)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c2 and c3 compatibility
P = c2(ue)
Q = c3(ve)
if not np.allclose(P, Q, rtol=0, atol=tol):
c3.reverse()
Q = c3(ve)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c3 and c0 compatibility
P = c3(vb)
Q = c0(ue)
assert np.allclose(P, Q, rtol=0, atol=tol)
return [[c1,c3],[c0,c2]]
def coonsInitialize(curves, tol=1.e-3):
[[c1, c3], [c0, c2]] = curves
(c0, c2) = compat(c0, c2)
(c1, c3) = compat(c1, c3)
p, U = c0.degree[0], c0.knots[0]
ub, ue = U[p], U[-p - 1]
q, V = c1.degree[0], c1.knots[0]
vb, ve = V[q], V[-q - 1]
# c0 and c1 compatibility
P = c0(ub)
Q = c1(vb)
if not np.allclose(P, Q, rtol=0, atol=tol):
c1.reverse()
Q = c1(vb)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c1 and c2 compatibility
P = c1(ve)
Q = c2(ub)
if not np.allclose(P, Q, rtol=0, atol=tol):
c2.reverse()
Q = c2(ub)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c2 and c3 compatibility
P = c2(ue)
Q = c3(ve)
if not np.allclose(P, Q, rtol=0, atol=tol):
c3.reverse()
Q = c3(ve)
assert np.allclose(P, Q, rtol=0, atol=tol)
# c3 and c0 compatibility
P = c3(vb)
Q = c0(ue)
assert np.allclose(P, Q, rtol=0, atol=tol)
return [[c1, c3], [c0, c2]]
