def insert_knot(self, u_bar, count=1):
# "The NURBS book", 2nd edition, p.5.2, eq. 5.11
s = sv_knotvector.find_multiplicity(self.knotvector, u_bar)
#print(f"I: kv {len(self.knotvector)}{self.knotvector}, u_bar {u_bar} => s {s}")
k = np.searchsorted(self.knotvector, u_bar, side='right') - 1
p = self.degree
u = self.knotvector
new_knotvector = sv_knotvector.insert(self.knotvector, u_bar, count)
N = len(self.control_points)
control_points = self.get_homogenous_control_points()
for r in range(1, count + 1):
prev_control_points = control_points
control_points = []
for i in range(N + 1):
#print(f"I: i {i}, k {k}, p {p}, r {r}, s {s}, k-p+r-1 {k-p+r-1}, k-s {k-s}")
if i <= k - p + r - 1:
point = prev_control_points[i]
#print(f"P[{r},{i}] := {i}{prev_control_points[i]}")
elif k - p + r <= i <= k - s:
denominator = u[i + p - r + 1] - u[i]
alpha = (u_bar - u[i]) / denominator
point = alpha * prev_control_points[i] + (
1.0 - alpha) * prev_control_points[i - 1]
#print(f"P[{r},{i}]: alpha {alpha}, pts {i}{prev_control_points[i]}, {i-1}{prev_control_points[i-1]} => {point}")
else:
point = prev_control_points[i - 1]
#print(f"P[{r},{i}] := {i-1}{prev_control_points[i-1]}")
control_points.append(point)
N += 1
control_points, weights = from_homogenous(np.array(control_points))
curve = SvNativeNurbsCurve(self.degree, new_knotvector, control_points,
weights)
return curve
def insert_knot(self, u_bar, count=1, if_possible=False):
# "The NURBS book", 2nd edition, p.5.2, eq. 5.11
N = len(self.control_points)
u = self.get_knotvector()
s = sv_knotvector.find_multiplicity(u, u_bar)
#print(f"I: kv {len(u)}{u}, u_bar {u_bar} => s {s}")
#k = np.searchsorted(u, u_bar, side='right')-1
k = sv_knotvector.find_span(u, N, u_bar)
p = self.get_degree()
new_knotvector = sv_knotvector.insert(u, u_bar, count)
control_points = self.get_homogenous_control_points()
if (u_bar == u[0] or u_bar == u[-1]):
if s + count > p + 1:
if if_possible:
count = (p + 1) - s
else:
raise CantInsertKnotException(
f"Can't insert first/last knot t={u_bar} for {count} times"
)
else:
if s + count > p:
if if_possible:
count = p - s
else:
raise CantInsertKnotException(
f"Can't insert knot t={u_bar} for {count} times")
for r in range(1, count + 1):
prev_control_points = control_points
control_points = []
for i in range(N + 1):
#print(f"I: i {i}, k {k}, p {p}, r {r}, s {s}, k-p+r-1 {k-p+r-1}, k-s {k-s}")
if i <= k - p + r - 1:
point = prev_control_points[i]
#print(f"P[{r},{i}] := {i}{prev_control_points[i]}")
elif k - p + r <= i <= k - s:
denominator = u[i + p - r + 1] - u[i]
if abs(denominator) < 1e-6:
raise Exception(
f"Can't insert the knot t={u_bar} for {i}th time: u[i+p-r+1]={u[i+p-r+1]}, u[i]={u[i]}, denom={denominator}"
)
alpha = (u_bar - u[i]) / denominator
point = alpha * prev_control_points[i] + (
1.0 - alpha) * prev_control_points[i - 1]
#print(f"P[{r},{i}]: alpha {alpha}, pts {i}{prev_control_points[i]}, {i-1}{prev_control_points[i-1]} => {point}")
else:
point = prev_control_points[i - 1]
#print(f"P[{r},{i}] := {i-1}{prev_control_points[i-1]}")
control_points.append(point)
N += 1
control_points, weights = from_homogenous(np.array(control_points))
curve = SvNativeNurbsCurve(self.degree, new_knotvector, control_points,
weights)
return curve