def example3():
"""
Plot a B-Spline curve using a clamped and not clamped partition.
"""
V = np.array([[-0.,0.], [-0.,6.], [-1.,5.], [-3.,8.], [-1.,14.],[2.,14.],[4.,8.], [2.,5.], [1.,6.], [1.,0.]])
k = 4
pc = np.array([0., 0., 0., 0., 1./7., 2./7., 3./7., 4./7., 5./7., 6./7., 1., 1., 1., 1.])
pnc = np.array([-3./7., -2./7., -1./7., 0., 1./7., 2./7., 3./7., 4./7., 5./7., 6./7., 1., 8./7., 9./7., 10./7.])
fn.drawVertexes(V)
fn.drawVertexes(V,'o')
fn.drawVertexes(fn.bSpline(V, k, pc))
fn.drawVertexes(fn.bSpline(V, k, pnc))
def example5():
"""
Plot a 3 dimensional B-Spline curve.
"""
V = np.array([[0.,0.,0.], [0.,6.,1.], [-1.,5.,2.], [-3.,8.,3.], [-1.,14.,4.],[2.,14.,5.],[4.,8.,6.], [2.,5.,7.], [1.,6.,8.], [1.,0.,9.]])
k = 4
p = np.array([0.,0.,0.,0.,1./7.,2./7.,3./7.,4./7.,5./7.,6./7.,1.,1.,1.,1.])
fn.drawVertexes(V, 'o')
fn.drawVertexes(V)
fn.drawVertexes(fn.bSpline(V, k, p))
def exerB_3():
"""
Represent the B-Spline for a given control vertexes set
with a multeplicity.
"""
V = np.array([[0.,2.], [1.,0.], [2.,1.], [2.,1.], [3., 0.], [4., 2.]])
k = 3
p= np.array([0., 0., 0., 1./4., 1./2., 3./4., 1., 1., 1.])
fn.drawVertexes(V, 'o')
fn.drawVertexes(V)
fn.drawVertexes(fn.bSpline(V, k, p))
def exerB_4():
"""
Represent the B-Splines for a given control vertexes set
with a multeplicity and different nodal partitions,
one with a multeplicity and one without.
"""
V = np.array([[1.,0.], [0.,1.], [2.,1.5], [2.,1.5], [4., 1.], [3., 0.]])
k = 4
ps = [
np.array([0., 0., 0., 0., 1./4., 3./4., 1., 1., 1., 1.]),
np.array([0., 0., 0., 0., 1./2., 1./2., 1., 1., 1., 1.]),
]
fn.drawVertexes(V, 'o')
fn.drawVertexes(V)
for p in ps:
fn.drawVertexes(fn.bSpline(V, k, p))
def exerB_1():
"""
Given a fixed set of control vertexes, represent the B-Spline
curves for different nodal partitions and orders.
"""
V = np.array([[0.5,0.5], [0.4,1.], [1.,1.2], [0.9,0.], [2., 0.1], [1.5, 0.6]])
ks = [2, 3, 4, 5, 6]
ps = [
np.array([0., 0., 1./5., 2./5., 3./5., 4./5., 1., 1.]),
np.array([0., 0., 0., 1./4., 1./2., 3./4., 1., 1., 1.]),
np.array([0., 0., 0., 0., 1./3., 2./3., 1., 1., 1., 1.]),
np.array([0., 0., 0., 0., 0., 1./2., 1., 1., 1., 1., 1.]),
np.array([0., 0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 1.]),
]
for p,k in zip(ps, ks):
fn.drawVertexes(fn.bSpline(V, k, p))
fn.drawVertexes(V, 'o')
def exerB_2():
"""
Given a fixed set of control vertexes, represent the B-Spline
curves for different nodal partitions and orders.
"""
V = np.array([[0.,0.], [-0.4,-0.1], [-1.,0.2], [-0.1,1.], [1., 1.1], [1.1, 0.6], [1.2, 0.7], [1.3, 1.2], [2., 0.8], [2.5, 0.7]])
ks = [4, 4, 6, 6, 8]
ps = [
np.array([0., 0., 0., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.]),
np.array([0., 0., 0., 0., 1., 1., 2., 2., 3., 3., 4., 4., 4., 4.]),
np.array([0., 0., 0., 0., 0., 0., 1., 2., 3., 4., 5., 5., 5., 5., 5., 5.]),
np.array([0., 0., 0., 0., 0., 0., 1., 2., 3., 3., 4., 4., 4., 4., 4., 4.]),
np.array([0., 0., 0., 0., 0., 0., 0., 0., 1., 2., 3., 3., 3., 3., 3., 3., 3., 3.]),
]
for p,k in zip(ps, ks):
fn.drawVertexes(fn.bSpline(V, k, p))
fn.drawVertexes(V, 'o')
fn.drawVertexes(V)
def exerB_5():
"""
Determine different behavior for B-Splines with same
control vertexes but different multeplicity.
"""
Vs = [
np.array([[0.,1.], [1.,0.], [2.,1.], [3., 0.], [4., 1.]]),
np.array([[0.,1.], [1.,0.], [2.,1.], [2.,1.], [3., 0.], [4., 1.]]),
np.array([[0.,1.], [1.,0.], [2.,1.], [2.,1.], [2.,1.], [3., 0.], [4., 1.]])
]
ks = [4,4,4]
ps = [
np.array([0., 0., 0., 0.,1./2., 1., 1., 1., 1.]),
np.array([0., 0., 0., 0., 1./4., 3./4.,1., 1., 1., 1.]),
np.array([0., 0., 0., 0., 1./2., 1./2., 1./2.,1., 1., 1., 1.])
]
fn.drawVertexes(Vs[0], 'o')
fn.drawVertexes(Vs[0])
for V,k,p in zip(Vs,ks,ps):
fn.drawVertexes(fn.bSpline(V, k, p))