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"""
Ray factory
classes that provide vertex and triangle information for rays on spheres
Example:
rays = Rays_Tetra(n_level = 4)
print(rays.vertices)
print(rays.faces)
"""
from __future__ import print_function, unicode_literals, absolute_import, division
import numpy as np
from scipy.spatial import ConvexHull
import copy
import warnings
class Rays_Base(object):
def __init__(self, **kwargs):
self.kwargs = kwargs
self._vertices, self._faces = self.setup_vertices_faces()
self._vertices = np.asarray(self._vertices, np.float32)
self._faces = np.asarray(self._faces, int)
self._faces = np.asanyarray(self._faces)
def setup_vertices_faces(self):
"""has to return
verts , faces
verts = ( (z_1,y_1,x_1), ... )
faces ( (0,1,2), (2,3,4), ... )
"""
raise NotImplementedError()
@property
def vertices(self):
"""read-only property"""
return self._vertices.copy()
@property
def faces(self):
"""read-only property"""
return self._faces.copy()
def __getitem__(self, i):
return self.vertices[i]
def __len__(self):
return len(self._vertices)
def __repr__(self):
def _conv(x):
if isinstance(x,(tuple, list, np.ndarray)):
return "_".join(_conv(_x) for _x in x)
if isinstance(x,float):
return "%.2f"%x
return str(x)
return "%s_%s" % (self.__class__.__name__, "_".join("%s_%s" % (k, _conv(v)) for k, v in sorted(self.kwargs.items())))
def to_json(self):
return {
"name": self.__class__.__name__,
"kwargs": self.kwargs
}
def dist_loss_weights(self, anisotropy = (1,1,1)):
"""returns the anisotropy corrected weights for each ray"""
anisotropy = np.array(anisotropy)
assert anisotropy.shape == (3,)
return np.linalg.norm(self.vertices*anisotropy, axis = -1)
def volume(self, dist=None):
"""volume of the starconvex polyhedron spanned by dist (if None, uses dist=1)
dist can be a nD array, but the last dimension has to be of length n_rays
"""
if dist is None: dist = np.ones_like(self.vertices)
dist = np.asarray(dist)
if not dist.shape[-1]==len(self.vertices):
raise ValueError("last dimension of dist should have length len(rays.vertices)")
# all the shuffling below is to allow dist to be an arbitrary sized array (with last dim n_rays)
# self.vertices -> (n_rays,3)
# dist -> (m,n,..., n_rays)
# dist -> (m,n,..., n_rays, 3)
dist = np.repeat(np.expand_dims(dist,-1), 3, axis = -1)
# verts -> (m,n,..., n_rays, 3)
verts = np.broadcast_to(self.vertices, dist.shape)
# dist, verts -> (n_rays, m,n, ..., 3)
dist = np.moveaxis(dist,-2,0)
verts = np.moveaxis(verts,-2,0)
# vs -> (n_faces, 3, m, n, ..., 3)
vs = (dist*verts)[self.faces]
# vs -> (n_faces, m, n, ..., 3, 3)
vs = np.moveaxis(vs, 1,-2)
# vs -> (n_faces * m * n, 3, 3)
vs = vs.reshape((len(self.faces)*int(np.prod(dist.shape[1:-1])),3,3))
d = np.linalg.det(list(vs)).reshape((len(self.faces),)+dist.shape[1:-1])
return -1./6*np.sum(d, axis = 0)
def surface(self, dist=None):
"""surface area of the starconvex polyhedron spanned by dist (if None, uses dist=1)"""
dist = np.asarray(dist)
if not dist.shape[-1]==len(self.vertices):
raise ValueError("last dimension of dist should have length len(rays.vertices)")
# self.vertices -> (n_rays,3)
# dist -> (m,n,..., n_rays)
# all the shuffling below is to allow dist to be an arbitrary sized array (with last dim n_rays)
# dist -> (m,n,..., n_rays, 3)
dist = np.repeat(np.expand_dims(dist,-1), 3, axis = -1)
# verts -> (m,n,..., n_rays, 3)
verts = np.broadcast_to(self.vertices, dist.shape)
# dist, verts -> (n_rays, m,n, ..., 3)
dist = np.moveaxis(dist,-2,0)
verts = np.moveaxis(verts,-2,0)
# vs -> (n_faces, 3, m, n, ..., 3)
vs = (dist*verts)[self.faces]
# vs -> (n_faces, m, n, ..., 3, 3)
vs = np.moveaxis(vs, 1,-2)
# vs -> (n_faces * m * n, 3, 3)
vs = vs.reshape((len(self.faces)*int(np.prod(dist.shape[1:-1])),3,3))
pa = vs[...,1,:]-vs[...,0,:]
pb = vs[...,2,:]-vs[...,0,:]
d = .5*np.linalg.norm(np.cross(list(pa), list(pb)), axis = -1)
d = d.reshape((len(self.faces),)+dist.shape[1:-1])
return np.sum(d, axis = 0)
def copy(self, scale=(1,1,1)):
""" returns a copy whose vertices are scaled by given factor"""
scale = np.asarray(scale)
assert scale.shape == (3,)
res = copy.deepcopy(self)
res._vertices *= scale[np.newaxis]
return res
def rays_from_json(d):
return eval(d["name"])(**d["kwargs"])
################################################################
class Rays_Explicit(Rays_Base):
def __init__(self, vertices0, faces0):
self.vertices0, self.faces0 = vertices0, faces0
super().__init__(vertices0=list(vertices0), faces0=list(faces0))
def setup_vertices_faces(self):
return self.vertices0, self.faces0
class Rays_Cartesian(Rays_Base):
def __init__(self, n_rays_x=11, n_rays_z=5):
super().__init__(n_rays_x=n_rays_x, n_rays_z=n_rays_z)
def setup_vertices_faces(self):
"""has to return list of ( (z_1,y_1,x_1), ... ) _"""
n_rays_x, n_rays_z = self.kwargs["n_rays_x"], self.kwargs["n_rays_z"]
dphi = np.float32(2. * np.pi / n_rays_x)
dtheta = np.float32(np.pi / n_rays_z)
verts = []
for mz in range(n_rays_z):
for mx in range(n_rays_x):
phi = mx * dphi
theta = mz * dtheta
if mz == 0:
theta = 1e-12
if mz == n_rays_z - 1:
theta = np.pi - 1e-12
dx = np.cos(phi) * np.sin(theta)
dy = np.sin(phi) * np.sin(theta)
dz = np.cos(theta)
if mz == 0 or mz == n_rays_z - 1:
dx += 1e-12
dy += 1e-12
verts.append([dz, dy, dx])
verts = np.array(verts)
def _ind(mz, mx):
return mz * n_rays_x + mx
faces = []
for mz in range(n_rays_z - 1):
for mx in range(n_rays_x):
faces.append([_ind(mz, mx), _ind(mz + 1, (mx + 1) % n_rays_x), _ind(mz, (mx + 1) % n_rays_x)])
faces.append([_ind(mz, mx), _ind(mz + 1, mx), _ind(mz + 1, (mx + 1) % n_rays_x)])
faces = np.array(faces)
return verts, faces
class Rays_SubDivide(Rays_Base):
"""
Subdivision polyehdra
n_level = 1 -> base polyhedra
n_level = 2 -> 1x subdivision
n_level = 3 -> 2x subdivision
...
"""
def __init__(self, n_level=4):
super().__init__(n_level=n_level)
def base_polyhedron(self):
raise NotImplementedError()
def setup_vertices_faces(self):
n_level = self.kwargs["n_level"]
verts0, faces0 = self.base_polyhedron()
return self._recursive_split(verts0, faces0, n_level)
def _recursive_split(self, verts, faces, n_level):
if n_level <= 1:
return verts, faces
else:
verts, faces = Rays_SubDivide.split(verts, faces)
return self._recursive_split(verts, faces, n_level - 1)
@classmethod
def split(self, verts0, faces0):
"""split a level"""
split_edges = dict()
verts = list(verts0[:])
faces = []
def _add(a, b):
""" returns index of middle point and adds vertex if not already added"""
edge = tuple(sorted((a, b)))
if not edge in split_edges:
v = .5 * (verts[a] + verts[b])
v *= 1. / np.linalg.norm(v)
verts.append(v)
split_edges[edge] = len(verts) - 1
return split_edges[edge]
for v1, v2, v3 in faces0:
ind1 = _add(v1, v2)
ind2 = _add(v2, v3)
ind3 = _add(v3, v1)
faces.append([v1, ind1, ind3])
faces.append([v2, ind2, ind1])
faces.append([v3, ind3, ind2])
faces.append([ind1, ind2, ind3])
return verts, faces
class Rays_Tetra(Rays_SubDivide):
"""
Subdivision of a tetrahedron
n_level = 1 -> normal tetrahedron (4 vertices)
n_level = 2 -> 1x subdivision (10 vertices)
n_level = 3 -> 2x subdivision (34 vertices)
...
"""
def base_polyhedron(self):
verts = np.array([
[np.sqrt(8. / 9), 0., -1. / 3],
[-np.sqrt(2. / 9), np.sqrt(2. / 3), -1. / 3],
[-np.sqrt(2. / 9), -np.sqrt(2. / 3), -1. / 3],
[0., 0., 1.]
])
faces = [[0, 1, 2],
[0, 3, 1],
[0, 2, 3],
[1, 3, 2]]
return verts, faces
class Rays_Octo(Rays_SubDivide):
"""
Subdivision of a tetrahedron
n_level = 1 -> normal Octahedron (6 vertices)
n_level = 2 -> 1x subdivision (18 vertices)
n_level = 3 -> 2x subdivision (66 vertices)
"""
def base_polyhedron(self):
verts = np.array([
[0, 0, 1],
[0, 1, 0],
[0, 0, -1],
[0, -1, 0],
[1, 0, 0],
[-1, 0, 0]])
faces = [[0, 1, 4],
[0, 5, 1],
[1, 2, 4],
[1, 5, 2],
[2, 3, 4],
[2, 5, 3],
[3, 0, 4],
[3, 5, 0],
]
return verts, faces
def reorder_faces(verts, faces):
"""reorder faces such that their orientation points outward"""
def _single(face):
return face[::-1] if np.linalg.det(verts[face])>0 else face
return tuple(map(_single, faces))
class Rays_GoldenSpiral(Rays_Base):
def __init__(self, n=70, anisotropy = None):
if n<4:
raise ValueError("At least 4 points have to be given!")
super().__init__(n=n, anisotropy = anisotropy if anisotropy is None else tuple(anisotropy))
def setup_vertices_faces(self):
n = self.kwargs["n"]
anisotropy = self.kwargs["anisotropy"]
if anisotropy is None:
anisotropy = np.ones(3)
else:
anisotropy = np.array(anisotropy)
# the smaller golden angle = 2pi * 0.3819...
g = (3. - np.sqrt(5.)) * np.pi
phi = g * np.arange(n)
# z = np.linspace(-1, 1, n + 2)[1:-1]
# rho = np.sqrt(1. - z ** 2)
# verts = np.stack([rho*np.cos(phi), rho*np.sin(phi),z]).T
#
z = np.linspace(-1, 1, n)
rho = np.sqrt(1. - z ** 2)
verts = np.stack([z, rho * np.sin(phi), rho * np.cos(phi)]).T
# warnings.warn("ray definition has changed! Old results are invalid!")
# correct for anisotropy
verts = verts/anisotropy
#verts /= np.linalg.norm(verts, axis=-1, keepdims=True)
hull = ConvexHull(verts)
faces = reorder_faces(verts,hull.simplices)
verts /= np.linalg.norm(verts, axis=-1, keepdims=True)
return verts, faces
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