def surface_normals(r,phi,theta,grid,gtype='spher'):
"""
Numerically compute surface normals of a grid (in absence of analytical alternative).
Also computes the surface elements, making L{surface_elements} obsolete.
"""
if gtype=='spher':
raise NotImplementedError
elif gtype=='delaunay':
raise NotImplementedError
elif gtype=='triangular':
#-- compute the angle between the surface normal and the radius vector
x,y,z = vectors.spher2cart_coord(r,phi,theta)
centers = np.zeros((len(grid.convex_hull),3))
normals = np.zeros((len(grid.convex_hull),3))
sizes = np.zeros(len(grid.convex_hull))
#vertx,verty,vertz = points.T
#-- compute centers,normals and sizes
for i,indices in enumerate(grid.convex_hull):
#-- center is triangle's barycenter
centers[i] = [x[indices].sum()/3,y[indices].sum()/3,z[indices].sum()/3]
#-- size is size of triangle
a = sqrt((x[indices[0]]-x[indices[1]])**2 + (y[indices[0]]-y[indices[1]])**2 + (z[indices[0]]-z[indices[1]])**2)
b = sqrt((x[indices[0]]-x[indices[2]])**2 + (y[indices[0]]-y[indices[2]])**2 + (z[indices[0]]-z[indices[2]])**2)
c = sqrt((x[indices[1]]-x[indices[2]])**2 + (y[indices[1]]-y[indices[2]])**2 + (z[indices[1]]-z[indices[2]])**2)
s = 0.5*(a+b+c)
sizes[i] = sqrt( s*(s-a)*(s-b)*(s-c))
#-- normal is cross product of two sides
side1 = [x[indices[1]]-x[indices[0]],y[indices[1]]-y[indices[0]],z[indices[1]]-z[indices[0]]]
side2 = [x[indices[2]]-x[indices[0]],y[indices[2]]-y[indices[0]],z[indices[2]]-z[indices[0]]]
normals[i] = np.cross(side1,side2)
#-- make sure the normal is pointed outwards
normal_r,normal_phi,normal_theta = vectors.cart2spher(centers.T,normals.T)
normal_r = np.abs(normal_r)
centers_sph = vectors.cart2spher_coord(*centers.T)
normals = np.array(vectors.spher2cart(centers_sph,(normal_r,normal_phi,normal_theta)))
#-- normalise and compute angles
normals_T = normals.T
normals = normals_T / vectors.norm(normals_T)
#cos_gamma = vectors.cos_angle(a,normals)
print centers.shape,sizes.shape,normals.shape
return centers, sizes, normals#, cos_gamma
mlab.figure(size=(1000, 800))
mlab.gcf().scene.disable_render = True
if l == 0 or l == 1:
asl = 0.1
else:
asl = 0.01
old_center = None
for i, t in enumerate(np.linspace(0, 2 * pi, 100)):
print k, l, m, i
r, th, ph = surface(theta, phi, l, m, t, asl=asl, k=k)
center, size, normal = local.surface_normals(
r, ph, th, grid, gtype='triangular')
if i == 0:
colors = r
r_c, phi_c, theta_c = vectors.cart2spher_coord(
*center.T)
colors_ = r_c
mlab.clf()
mlab.points3d(center.T[0],
center.T[1],
center.T[2],
colors_,
scale_factor=0.05,
scale_mode='none',
colormap='RdBu',
vmin=colors_.min(),
vmax=colors_.max())
#mlab.quiver3d(center.T[0],center.T[1],center.T[2],normal.T[0],normal.T[1],normal.T[2],colormap='spectral',scale_mode='none')
mlab.colorbar()
def surface_normals(r, phi, theta, grid, gtype='spher'):
"""
Numerically compute surface normals of a grid (in absence of analytical alternative).
Also computes the surface elements, making L{surface_elements} obsolete.
"""
if gtype == 'spher':
raise NotImplementedError
elif gtype == 'delaunay':
raise NotImplementedError
elif gtype == 'triangular':
#-- compute the angle between the surface normal and the radius vector
x, y, z = vectors.spher2cart_coord(r, phi, theta)
centers = np.zeros((len(grid.convex_hull), 3))
normals = np.zeros((len(grid.convex_hull), 3))
sizes = np.zeros(len(grid.convex_hull))
#vertx,verty,vertz = points.T
#-- compute centers,normals and sizes
for i, indices in enumerate(grid.convex_hull):
#-- center is triangle's barycenter
centers[i] = [
x[indices].sum() / 3, y[indices].sum() / 3,
z[indices].sum() / 3
]
#-- size is size of triangle
a = sqrt((x[indices[0]] - x[indices[1]])**2 +
(y[indices[0]] - y[indices[1]])**2 +
(z[indices[0]] - z[indices[1]])**2)
b = sqrt((x[indices[0]] - x[indices[2]])**2 +
(y[indices[0]] - y[indices[2]])**2 +
(z[indices[0]] - z[indices[2]])**2)
c = sqrt((x[indices[1]] - x[indices[2]])**2 +
(y[indices[1]] - y[indices[2]])**2 +
(z[indices[1]] - z[indices[2]])**2)
s = 0.5 * (a + b + c)
sizes[i] = sqrt(s * (s - a) * (s - b) * (s - c))
#-- normal is cross product of two sides
side1 = [
x[indices[1]] - x[indices[0]], y[indices[1]] - y[indices[0]],
z[indices[1]] - z[indices[0]]
]
side2 = [
x[indices[2]] - x[indices[0]], y[indices[2]] - y[indices[0]],
z[indices[2]] - z[indices[0]]
]
normals[i] = np.cross(side1, side2)
#-- make sure the normal is pointed outwards
normal_r, normal_phi, normal_theta = vectors.cart2spher(
centers.T, normals.T)
normal_r = np.abs(normal_r)
centers_sph = vectors.cart2spher_coord(*centers.T)
normals = np.array(
vectors.spher2cart(centers_sph,
(normal_r, normal_phi, normal_theta)))
#-- normalise and compute angles
normals_T = normals.T
normals = normals_T / vectors.norm(normals_T)
#cos_gamma = vectors.cos_angle(a,normals)
print(centers.shape, sizes.shape, normals.shape)
return centers, sizes, normals #, cos_gamma
for m in range(0,l+1,1):
mlab.figure(size=(1000,800))
mlab.gcf().scene.disable_render = True
if l==0 or l==1:
asl = 0.1
else:
asl = 0.01
old_center=None
for i,t in enumerate(np.linspace(0,2*pi,100)):
print k,l,m,i
r,th,ph = surface(theta,phi,l,m,t,asl=asl,k=k)
center,size,normal = local.surface_normals(r,ph,th,grid,gtype='triangular')
if i==0:
colors = r
r_c,phi_c,theta_c = vectors.cart2spher_coord(*center.T)
colors_ = r_c
mlab.clf()
mlab.points3d(center.T[0],center.T[1],center.T[2],colors_,scale_factor=0.05,scale_mode='none',colormap='RdBu',vmin=colors_.min(),vmax=colors_.max())
#mlab.quiver3d(center.T[0],center.T[1],center.T[2],normal.T[0],normal.T[1],normal.T[2],colormap='spectral',scale_mode='none')
mlab.colorbar()
if i>=1:
vx,vy,vz = center.T[0]-old_center.T[0],\
center.T[1]-old_center.T[1],\
center.T[2]-old_center.T[2]
v = np.sqrt(vx**2+vy**2+vz**2)
mlab.quiver3d(center.T[0],center.T[1],center.T[2],\
vx,vy,vz,scalars=v,colormap='spectral',scale_mode='scalar')