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import numpy as np
import numpy.ma as ma
import pycuda.driver as cuda
from pycuda import gpuarray
def interleave(arr, bits):
"""
Interleave the bits of quantized three-dimensional points in space.
Example
>>> interleave(np.identity(3, dtype=np.int))
array([4, 2, 1], dtype=uint64)
"""
if len(arr.shape) != 2 or arr.shape[1] != 3:
raise Exception('shape mismatch')
z = np.zeros(arr.shape[0], dtype=np.uint32)
for i in range(bits):
z |= (arr[:,2] & 1 << i) << (2*i) | \
(arr[:,1] & 1 << i) << (2*i+1) | \
(arr[:,0] & 1 << i) << (2*i+2)
return z
def morton_order(mesh, bits):
"""
Return a list of zvalues for triangles in `mesh` by interleaving the
bits of the quantized center coordinates of each triangle. Each coordinate
axis is quantized into 2**bits bins.
"""
lower_bound = np.array([np.min(mesh[:,:,0]),
np.min(mesh[:,:,1]),
np.min(mesh[:,:,2])])
upper_bound = np.array([np.max(mesh[:,:,0]),
np.max(mesh[:,:,1]),
np.max(mesh[:,:,2])])
if bits <= 0 or bits > 12:
raise Exception('number of bits must be in the range (0,12].')
max_value = 2**bits - 1
def quantize(x):
return np.uint32((x-lower_bound)*max_value/(upper_bound-lower_bound))
mean_positions = quantize(np.mean(mesh, axis=1))
return interleave(mean_positions, bits)
class Solid(object):
"""
Object which stores a closed triangle mesh associated with a physically
distinct object.
Args:
- mesh, array
A closed triangle mesh.
- material1, Material
The material inside within the mesh.
- material2, Material
The material outside the mesh.
- surface1, Surface,
The surface on the inside of the mesh.
- surface2, Surface,
The surface on the outside of the mesh.
.. warning::
It is possible to define logically inconsistent geometries unless
you are careful. For example, solid A may define its inside material
as water but contain solid B which defines its outside material as air.
In this case, a photon traveling out of solid B will reflect/refract
assuming it's going into air, but upon reaching solid A's boundary will
calculate attenuation factors assuming it just traveled through water.
"""
def __init__(self, mesh, material1, material2, \
surface1=None, surface2=None):
if len(mesh.shape) != 3 or mesh.shape[1] != 3 or mesh.shape[2] != 3:
raise Exception('shape mismatch; mesh must be a triangle mesh')
self.mesh = mesh
self.material1 = material1
self.material2 = material2
self.surface1 = surface1
self.surface2 = surface2
def __len__(self):
return self.mesh.shape[0]
class Geometry(object):
"""Object which stores the global mesh for a geometry."""
def __init__(self):
self.solids = []
self.materials = []
self.surfaces = []
def add_solid(self, solid):
"""Add a solid to the geometry."""
self.solids.append(solid)
if solid.material1 not in self.materials:
self.materials.append(solid.material1)
if solid.material2 not in self.materials:
self.materials.append(solid.material2)
if solid.surface1 not in self.surfaces:
self.surfaces.append(solid.surface1)
if solid.surface2 not in self.surfaces:
self.surfaces.append(solid.surface1)
def build(self, bits=8):
"""Build the bounding volume hierarchy of the geometry."""
mesh = np.concatenate([solid.mesh for solid in self.solids])
# lookup solid/material/surface index from triangle index
solid_index = \
np.concatenate([np.tile(self.solids.index(solid), \
len(solid)) for solid in self.solids])
material1_index = \
np.concatenate([np.tile(self.materials.index(solid.material1), \
len(solid)) for solid in self.solids])
material2_index = \
np.concatenate([np.tile(self.materials.index(solid.material2), \
len(solid)) for solid in self.solids])
surface1_index = \
np.concatenate([np.tile(self.surfaces.index(solid.surface1), \
len(solid)) for solid in self.solids])
surface2_index = \
np.concatenate([np.tile(self.surfaces.index(solid.surface2), \
len(solid)) for solid in self.solids])
zvalues_mesh = morton_order(mesh, bits)
reorder = np.argsort(zvalues_mesh)
zvalues_mesh = zvalues_mesh[reorder]
if (np.diff(zvalues_mesh) < 0).any():
raise Exception('zvalues_mesh out of order')
self.mesh = mesh[reorder]
self.solid_index = solid_index[reorder]
self.material1_index = material1_index[reorder]
self.material2_index = material2_index[reorder]
self.surface1_index = surface1_index[reorder]
self.surface2_index = surface2_index[reorder]
unique_zvalues = np.unique(zvalues_mesh)
zvalues = np.empty(unique_zvalues.size, dtype=np.uint64)
self.lower_bounds = np.empty((unique_zvalues.size,3), dtype=np.float32)
self.upper_bounds = np.empty((unique_zvalues.size,3), dtype=np.float32)
self.node_map = np.empty(unique_zvalues.size, dtype=np.uint32)
self.node_length = np.empty(unique_zvalues.size, dtype=np.uint32)
for i, z in enumerate(unique_zvalues):
i1 = np.searchsorted(zvalues_mesh, z)
i2 = np.searchsorted(zvalues_mesh, z, side='right')
self.lower_bounds[i] = [np.min(self.mesh[i1:i2,:,0]),
np.min(self.mesh[i1:i2,:,1]),
np.min(self.mesh[i1:i2,:,2])]
self.upper_bounds[i] = [np.max(self.mesh[i1:i2,:,0]),
np.max(self.mesh[i1:i2,:,1]),
np.max(self.mesh[i1:i2,:,2])]
self.node_map[i] = i1
self.node_length[i] = i2-i1
zvalues[i] = z
self.first_node = unique_zvalues.size
begin_last_layer = 0
while True:
bit_shifted_zvalues = zvalues >> 1
unique_bit_shifted_zvalues = np.unique(bit_shifted_zvalues)
zvalues = np.empty(unique_bit_shifted_zvalues.size, dtype=np.uint64)
self.lower_bounds.resize(\
(self.lower_bounds.shape[0]+unique_bit_shifted_zvalues.size,3))
self.upper_bounds.resize(\
(self.upper_bounds.shape[0]+unique_bit_shifted_zvalues.size,3))
self.node_map.resize(\
self.node_map.size+unique_bit_shifted_zvalues.size)
self.node_length.resize(\
self.node_length.size+unique_bit_shifted_zvalues.size)
for i, z in enumerate(unique_bit_shifted_zvalues):
i1 = np.searchsorted(bit_shifted_zvalues, z) + \
begin_last_layer
i2 = np.searchsorted(bit_shifted_zvalues, z, side='right') + \
begin_last_layer
zvalues[i] = z
i += begin_last_layer + bit_shifted_zvalues.size
self.lower_bounds[i] = \
[np.min(self.lower_bounds[i1:i2,0]),
np.min(self.lower_bounds[i1:i2,1]),
np.min(self.lower_bounds[i1:i2,2])]
self.upper_bounds[i] = \
[np.max(self.upper_bounds[i1:i2,0]),
np.max(self.upper_bounds[i1:i2,1]),
np.max(self.upper_bounds[i1:i2,2])]
self.node_map[i] = i1
self.node_length[i] = i2-i1
begin_last_layer += bit_shifted_zvalues.size
if unique_bit_shifted_zvalues.size == 1:
break
def load(self, module):
"""
Load the bounding volume hierarchy onto the GPU module,
bind it to the appropriate textures, and return a list
of the texture references.
"""
mesh = np.empty(self.mesh.shape[0]*3, dtype=gpuarray.vec.float4)
mesh['x'] = self.mesh[:,:,0].flatten()
mesh['y'] = self.mesh[:,:,1].flatten()
mesh['z'] = self.mesh[:,:,2].flatten()
lower_bounds = np.empty(self.lower_bounds.shape[0], dtype=gpuarray.vec.float4)
lower_bounds['x'] = self.lower_bounds[:,0]
lower_bounds['y'] = self.lower_bounds[:,1]
lower_bounds['z'] = self.lower_bounds[:,2]
upper_bounds = np.empty(self.upper_bounds.shape[0], dtype=gpuarray.vec.float4)
upper_bounds['x'] = self.upper_bounds[:,0]
upper_bounds['y'] = self.upper_bounds[:,1]
upper_bounds['z'] = self.upper_bounds[:,2]
self.mesh_gpu = cuda.to_device(mesh)
self.lower_bounds_gpu = cuda.to_device(lower_bounds)
self.upper_bounds_gpu = cuda.to_device(upper_bounds)
self.node_map_gpu = cuda.to_device(self.node_map)
self.node_length_gpu = cuda.to_device(self.node_length)
mesh_tex = module.get_texref('mesh')
lower_bounds_tex = module.get_texref('lower_bounds')
upper_bounds_tex = module.get_texref('upper_bounds')
node_map_tex = module.get_texref('node_map')
node_length_tex = module.get_texref('node_length')
mesh_tex.set_address(self.mesh_gpu, mesh.nbytes)
lower_bounds_tex.set_address(self.lower_bounds_gpu, lower_bounds.nbytes)
upper_bounds_tex.set_address(self.upper_bounds_gpu, upper_bounds.nbytes)
node_map_tex.set_address(self.node_map_gpu, self.node_map.nbytes)
node_length_tex.set_address(self.node_length_gpu, self.node_length.nbytes)
mesh_tex.set_format(cuda.array_format.FLOAT, 4)
lower_bounds_tex.set_format(cuda.array_format.FLOAT, 4)
upper_bounds_tex.set_format(cuda.array_format.FLOAT, 4)
node_map_tex.set_format(cuda.array_format.UNSIGNED_INT32, 1)
node_length_tex.set_format(cuda.array_format.UNSIGNED_INT32, 1)
return [mesh_tex, lower_bounds_tex, upper_bounds_tex, node_map_tex, node_length_tex]
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