def test_srf_de(PLOT=0):
p = 2
q = 1
U = np.asarray([0,0,0, 1,1,1], dtype=float)
V = np.asarray([0,0, 1,1], dtype=float)
n = len(U)-1-(p+1)
m = len(V)-1-(q+1)
Pw = np.zeros((n+1,m+1,4))
Pw[0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,:] = [1.0, 0.0, 0.0, 1.0]
Pw[1,:,:] *= np.sqrt(2)/2
nurbs = NURBS([U,V],Pw)
nrb = nurbs.copy().elevate(0,0).elevate(1,0)
(Uh, Vh), Qw = nrb.knots, nrb.control
nrb = nurbs.copy().elevate(0,1).elevate(1,0)
(Uh, Vh), Qw = nrb.knots, nrb.control
nrb = nurbs.copy().elevate(0,0).elevate(1,1)
(Uh, Vh), Qw = nrb.knots, nrb.control
r, s = 1, 2
nrb = nurbs.copy().elevate(0,r).elevate(1,s)
(Uh, Vh), Qw = nrb.knots, nrb.control
ph = p+r; qh = q+s;
u = np.linspace(Uh[0], Uh[-1], 31)
v = np.linspace(Vh[0], Vh[-1], 10)
Cw = bsp.Evaluate2(ph,Uh,qh,Vh,Qw,u,v)
Q = Qw[:,:,:2] / Qw[:,:,3, None]
C = Cw[:,:,:2] / Cw[:,:,3, None]
if not PLOT: return
plt.figure()
plt.title("Surface - Degree Elevation")
x = Q[:,:,0]
y = Q[:,:,1]
plt.plot(x,y,'sr')
x = C[:,:,0]
y = C[:,:,1]
plt.plot(x,y,'.b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
plt.plot(1.0*a,1.0*b,'-k')
plt.plot(0.5*a,0.5*b,'-k')
plt.axis("equal")
def test_srf_ki(PLOT=0):
p = 2
q = 1
U = np.asarray([0,0,0, 1,1,1], dtype=float)
V = np.asarray([0,0, 1,1], dtype=float)
n = len(U)-1-(p+1)
m = len(V)-1-(q+1)
Pw = np.zeros((n+1,m+1,4))
Pw[0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,:] = [1.0, 0.0, 0.0, 1.0]
Pw[1,:,:] *= np.sqrt(2)/2
nurbs = NURBS([U,V],Pw)
X = np.asarray([])
Y = np.asarray([])
nrb = nurbs.copy().refine(0,X).refine(1,Y)
(Ubar, Vbar), Qw = nrb.knots, nrb.control
assert np.allclose(U, Ubar)
assert np.allclose(V, Vbar)
assert np.allclose(Pw, Qw)
X = np.asarray([.25, 0.5])#;X = np.asarray([])
Y = np.asarray([0.5, .75])#;Y = np.asarray([])
nrb = nurbs.refine(0,X).refine(1,Y)
(Ubar, Vbar), Qw = nrb.knots, nrb.control
u = np.linspace(Ubar[0], Ubar[-1], 31)
v = np.linspace(Vbar[0], Vbar[-1], 10)
Cw = bsp.Evaluate2(p,Ubar,q,Vbar,Qw,u,v)
Q = Qw[:,:,:2] / Qw[:,:,3,None]
C = Cw[:,:,:2] / Cw[:,:,3,None]
if not PLOT: return
plt.figure()
plt.title("Surface - Knot Insertion")
x = Q[:,:,0]
y = Q[:,:,1]
plt.plot(x,y,'sr')
x = C[:,:,0]
y = C[:,:,1]
plt.plot(x,y,'.b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
plt.plot(1.0*a,1.0*b,'-k')
plt.plot(0.5*a,0.5*b,'-k')
plt.axis("equal")
def test_vol_de(PLOT=0):
px = 2
py = 1
pz = 1
Ux = np.asarray([0,0,0, 1,1,1], dtype=float)
Uy = np.asarray([0,0, 1,1], dtype=float)
Uz = np.asarray([0,0, 1,1], dtype=float)
nx = len(Ux)-1-(px+1)
ny = len(Uy)-1-(py+1)
nz = len(Uz)-1-(pz+1)
Pw = np.zeros((nx+1,ny+1,nz+1,4), dtype=float)
Pw[0,0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,0,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,0,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,0,:] = [1.0, 0.0, 0.0, 1.0]
Pw[0,0,1,:] = [0.0, 0.5, 1.0, 1.0]
Pw[1,0,1,:] = [0.5, 0.5, 1.0, 1.0]
Pw[2,0,1,:] = [0.5, 0.0, 1.0, 1.0]
Pw[0,1,1,:] = [0.0, 1.0, 1.0, 1.0]
Pw[1,1,1,:] = [1.0, 1.0, 1.0, 1.0]
Pw[2,1,1,:] = [1.0, 0.0, 1.0, 1.0]
Pw[1,:,:,:] *= np.sqrt(2)/2
nurbs = NURBS([Ux,Uy,Uz],Pw)
nrb = nurbs.copy().elevate(0,0).elevate(1,0).elevate(2,0)
(Vx, Vy, Vz), Qw = nrb.knots, nrb.control
assert np.allclose(Ux, Vx)
assert np.allclose(Uy, Vy)
assert np.allclose(Uz, Vz)
assert np.allclose(Pw, Qw)
tx, ty, tz = 1, 2, 2
nrb = nurbs.copy().elevate(0,tx).elevate(1,ty).elevate(2,tz)
(Vx, Vy, Vz), Qw = nrb.knots, nrb.control
qx = px + tx
qy = py + ty
qz = pz + tz
x = np.linspace(Vx[0], Vx[-1], 15)
y = np.linspace(Vy[0], Vy[-1], 5)
z = np.linspace(Vz[0], Vz[-1], 4)
Cw = bsp.Evaluate3(qx,Vx,qy,Vy,qz,Vz,Qw,x,y,z)
Q = Qw[:,:,:,:3] / Qw[:,:,:,3,None]
C = Cw[:,:,:,:3] / Cw[:,:,:,3,None]
if not PLOT: return
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
plt.title("Volume - Degree Elevation")
x = Q[:,:,:,0].flatten()
y = Q[:,:,:,1].flatten()
z = Q[:,:,:,2].flatten()
ax.scatter(x,y,z, c='r')
x = C[:,:,:,0].flatten()
y = C[:,:,:,1].flatten()
z = C[:,:,:,2].flatten()
ax.scatter(x,y,z, c='b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
ax.plot(1.0*a,1.0*b,0,'-k')
ax.plot(1.0*a,1.0*b,1,'-k')
ax.plot(0.5*a,0.5*b,0,'-k')
ax.plot(0.5*a,0.5*b,1,'-k')
plt.axis("equal")
def test_vol_ki(PLOT=0):
px = 2
py = 1
pz = 1
Ux = np.asarray([0,0,0, 1,1,1], dtype=float)
Uy = np.asarray([0,0, 1,1], dtype=float)
Uz = np.asarray([0,0, 1,1], dtype=float)
nx = len(Ux)-1-(px+1)
ny = len(Uy)-1-(py+1)
nz = len(Uz)-1-(pz+1)
Pw = np.zeros((nx+1,ny+1,nz+1,4), dtype=float)
Pw[0,0,0,:] = [0.0, 0.5, 0.0, 1.0]
Pw[1,0,0,:] = [0.5, 0.5, 0.0, 1.0]
Pw[2,0,0,:] = [0.5, 0.0, 0.0, 1.0]
Pw[0,1,0,:] = [0.0, 1.0, 0.0, 1.0]
Pw[1,1,0,:] = [1.0, 1.0, 0.0, 1.0]
Pw[2,1,0,:] = [1.0, 0.0, 0.0, 1.0]
Pw[0,0,1,:] = [0.0, 0.5, 1.0, 1.0]
Pw[1,0,1,:] = [0.5, 0.5, 1.0, 1.0]
Pw[2,0,1,:] = [0.5, 0.0, 1.0, 1.0]
Pw[0,1,1,:] = [0.0, 1.0, 1.0, 1.0]
Pw[1,1,1,:] = [1.0, 1.0, 1.0, 1.0]
Pw[2,1,1,:] = [1.0, 0.0, 1.0, 1.0]
Pw[1,:,:,:] *= np.sqrt(2)/2
nurbs = NURBS([Ux,Uy,Uz],Pw)
X = np.asarray([], dtype=float)
Y = np.asarray([], dtype=float)
Z = np.asarray([], dtype=float)
nrb = nurbs.copy().refine(0,X).refine(1,Y).refine(2,Z)
(Vx, Vy, Vz), Qw = nrb.knots, nrb.control
assert np.allclose(Ux, Vx)
assert np.allclose(Uy, Vy)
assert np.allclose(Uz, Vz)
assert np.allclose(Pw, Qw)
X = np.asarray([0.25, 0.50])
Y = np.asarray([0.50, 0.75])
Z = np.asarray([0.25, 0.75])
nrb = nurbs.copy().refine(0,X).refine(1,Y).refine(2,Z)
(Vx, Vy, Vz), Qw = nrb.knots, nrb.control
x = np.linspace(Vx[0], Vx[-1], 15)
y = np.linspace(Vy[0], Vy[-1], 5)
z = np.linspace(Vy[0], Vy[-1], 4)
Cw = bsp.Evaluate3(px,Vx,py,Vy,pz,Vz,Qw,x,y,z)
Q = Qw[:,:,:,:3] / Qw[:,:,:,3,None]
C = Cw[:,:,:,:3] / Cw[:,:,:,3,None]
if not PLOT: return
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
plt.title("Volume - Knot Insertion")
x = Q[:,:,:,0].flatten()
y = Q[:,:,:,1].flatten()
z = Q[:,:,:,2].flatten()
ax.scatter(x,y,z, c='r')
x = C[:,:,:,0].flatten()
y = C[:,:,:,1].flatten()
z = C[:,:,:,2].flatten()
ax.scatter(x,y,z, c='b')
t = np.linspace(0,np.pi/2,100)
a = np.cos(t)
b = np.sin(t)
ax.plot(1.0*a,1.0*b,0,'-k')
ax.plot(1.0*a,1.0*b,1,'-k')
ax.plot(0.5*a,0.5*b,0,'-k')
ax.plot(0.5*a,0.5*b,1,'-k')
plt.axis("equal")
