436 lines
12 KiB
Python
436 lines
12 KiB
Python
import numpy as np
|
|
|
|
from .. import util
|
|
from ..constants import log
|
|
|
|
|
|
def fill_orthographic(dense):
|
|
shape = dense.shape
|
|
indices = np.stack(
|
|
np.meshgrid(*(np.arange(s) for s in shape), indexing='ij'),
|
|
axis=-1)
|
|
empty = np.logical_not(dense)
|
|
|
|
def fill_axis(axis):
|
|
base_local_indices = indices[..., axis]
|
|
local_indices = base_local_indices.copy()
|
|
local_indices[empty] = shape[axis]
|
|
mins = np.min(local_indices, axis=axis, keepdims=True)
|
|
local_indices = base_local_indices.copy()
|
|
local_indices[empty] = -1
|
|
maxs = np.max(local_indices, axis=axis, keepdims=True)
|
|
|
|
return np.logical_and(
|
|
base_local_indices >= mins,
|
|
base_local_indices <= maxs,
|
|
)
|
|
|
|
filled = fill_axis(axis=0)
|
|
for axis in range(1, len(shape)):
|
|
filled = np.logical_and(filled, fill_axis(axis))
|
|
return filled
|
|
|
|
|
|
def fill_base(sparse_indices):
|
|
"""
|
|
Given a sparse surface voxelization, fill in between columns.
|
|
|
|
Parameters
|
|
--------------
|
|
sparse_indices: (n, 3) int, location of filled cells
|
|
|
|
Returns
|
|
--------------
|
|
filled: (m, 3) int, location of filled cells
|
|
"""
|
|
# validate inputs
|
|
sparse_indices = np.asanyarray(sparse_indices, dtype=np.int64)
|
|
if not util.is_shape(sparse_indices, (-1, 3)):
|
|
raise ValueError('incorrect shape')
|
|
|
|
# create grid and mark inner voxels
|
|
max_value = sparse_indices.max() + 3
|
|
|
|
grid = np.zeros((max_value,
|
|
max_value,
|
|
max_value),
|
|
bool)
|
|
voxels_sparse = np.add(sparse_indices, 1)
|
|
|
|
grid[tuple(voxels_sparse.T)] = 1
|
|
|
|
for i in range(max_value):
|
|
check_dir2 = False
|
|
for j in range(0, max_value - 1):
|
|
idx = []
|
|
# find transitions first
|
|
# transition positions are from 0 to 1 and from 1 to 0
|
|
eq = np.equal(grid[i, j, :-1], grid[i, j, 1:])
|
|
idx = np.where(np.logical_not(eq))[0] + 1
|
|
c = len(idx)
|
|
check_dir2 = (c % 4) > 0 and c > 4
|
|
if c < 4:
|
|
continue
|
|
for s in range(0, c - c % 4, 4):
|
|
grid[i, j, idx[s]:idx[s + 3]] = 1
|
|
if not check_dir2:
|
|
continue
|
|
|
|
# check another direction for robustness
|
|
for k in range(0, max_value - 1):
|
|
idx = []
|
|
# find transitions first
|
|
eq = np.equal(grid[i, :-1, k], grid[i, 1:, k])
|
|
idx = np.where(np.logical_not(eq))[0] + 1
|
|
c = len(idx)
|
|
if c < 4:
|
|
continue
|
|
for s in range(0, c - c % 4, 4):
|
|
grid[i, idx[s]:idx[s + 3], k] = 1
|
|
|
|
# generate new voxels
|
|
filled = np.column_stack(np.where(grid))
|
|
filled -= 1
|
|
|
|
return filled
|
|
|
|
|
|
fill_voxelization = fill_base
|
|
|
|
|
|
def matrix_to_marching_cubes(matrix, pitch=1.0):
|
|
"""
|
|
Convert an (n, m, p) matrix into a mesh, using marching_cubes.
|
|
|
|
Parameters
|
|
-----------
|
|
matrix : (n, m, p) bool
|
|
Occupancy array
|
|
|
|
Returns
|
|
----------
|
|
mesh : trimesh.Trimesh
|
|
Mesh generated by meshing voxels using
|
|
the marching cubes algorithm in skimage
|
|
"""
|
|
from skimage import measure
|
|
from ..base import Trimesh
|
|
|
|
matrix = np.asanyarray(matrix, dtype=np.bool)
|
|
|
|
rev_matrix = np.logical_not(matrix) # Takes set about 0.
|
|
# Add in padding so marching cubes can function properly with
|
|
# voxels on edge of AABB
|
|
pad_width = 1
|
|
rev_matrix = np.pad(rev_matrix,
|
|
pad_width=(pad_width),
|
|
mode='constant',
|
|
constant_values=(1))
|
|
|
|
# pick between old and new API
|
|
if hasattr(measure, 'marching_cubes_lewiner'):
|
|
func = measure.marching_cubes_lewiner
|
|
else:
|
|
func = measure.marching_cubes
|
|
|
|
# Run marching cubes.
|
|
pitch = np.asanyarray(pitch)
|
|
if pitch.size == 1:
|
|
pitch = (pitch,) * 3
|
|
meshed = func(volume=rev_matrix,
|
|
level=.5, # it is a boolean voxel grid
|
|
spacing=pitch)
|
|
|
|
# allow results from either marching cubes function in skimage
|
|
# binaries available for python 3.3 and 3.4 appear to use the classic
|
|
# method
|
|
if len(meshed) == 2:
|
|
log.warning('using old marching cubes, may not be watertight!')
|
|
vertices, faces = meshed
|
|
normals = None
|
|
elif len(meshed) == 4:
|
|
vertices, faces, normals, vals = meshed
|
|
|
|
# Return to the origin, add in the pad_width
|
|
vertices = np.subtract(vertices, pad_width * pitch)
|
|
# create the mesh
|
|
mesh = Trimesh(vertices=vertices,
|
|
faces=faces,
|
|
vertex_normals=normals)
|
|
return mesh
|
|
|
|
|
|
def sparse_to_matrix(sparse):
|
|
"""
|
|
Take a sparse (n,3) list of integer indexes of filled cells,
|
|
turn it into a dense (m,o,p) matrix.
|
|
|
|
Parameters
|
|
-----------
|
|
sparse : (n, 3) int
|
|
Index of filled cells
|
|
|
|
Returns
|
|
------------
|
|
dense : (m, o, p) bool
|
|
Matrix of filled cells
|
|
"""
|
|
|
|
sparse = np.asanyarray(sparse, dtype=np.int)
|
|
if not util.is_shape(sparse, (-1, 3)):
|
|
raise ValueError('sparse must be (n,3)!')
|
|
|
|
shape = sparse.max(axis=0) + 1
|
|
matrix = np.zeros(np.product(shape), dtype=np.bool)
|
|
multiplier = np.array([np.product(shape[1:]), shape[2], 1])
|
|
|
|
index = (sparse * multiplier).sum(axis=1)
|
|
matrix[index] = True
|
|
|
|
dense = matrix.reshape(shape)
|
|
return dense
|
|
|
|
|
|
def points_to_marching_cubes(points, pitch=1.0):
|
|
"""
|
|
Mesh points by assuming they fill a voxel box, and then
|
|
running marching cubes on them
|
|
|
|
Parameters
|
|
------------
|
|
points : (n, 3) float
|
|
Points in 3D space
|
|
|
|
Returns
|
|
-------------
|
|
mesh : trimesh.Trimesh
|
|
Points meshed using marching cubes
|
|
"""
|
|
# make sure inputs are as expected
|
|
points = np.asanyarray(points, dtype=np.float64)
|
|
pitch = np.asanyarray(pitch, dtype=float)
|
|
|
|
# find the minimum value of points for origin
|
|
origin = points.min(axis=0)
|
|
# convert points to occupied voxel cells
|
|
index = ((points - origin) / pitch).round().astype(np.int64)
|
|
|
|
# convert voxel indices to a matrix
|
|
matrix = sparse_to_matrix(index)
|
|
|
|
# run marching cubes on the matrix to generate a mesh
|
|
mesh = matrix_to_marching_cubes(matrix, pitch=pitch)
|
|
mesh.vertices += origin
|
|
|
|
return mesh
|
|
|
|
|
|
def multibox(centers, pitch=1.0, colors=None):
|
|
"""
|
|
Return a Trimesh object with a box at every center.
|
|
|
|
Doesn't do anything nice or fancy.
|
|
|
|
Parameters
|
|
-----------
|
|
centers : (n, 3) float
|
|
Center of boxes that are occupied
|
|
pitch : float
|
|
The edge length of a voxel
|
|
colors : (3,) or (4,) or (n,3) or (n, 4) float
|
|
Color of boxes
|
|
|
|
Returns
|
|
---------
|
|
rough : Trimesh
|
|
Mesh object representing inputs
|
|
"""
|
|
from .. import primitives
|
|
from ..base import Trimesh
|
|
|
|
# get centers as numpy array
|
|
centers = np.asanyarray(
|
|
centers, dtype=np.float64)
|
|
|
|
# get a basic box
|
|
b = primitives.Box()
|
|
# apply the pitch
|
|
b.apply_scale(float(pitch))
|
|
# tile into one box vertex per center
|
|
v = np.tile(
|
|
centers,
|
|
(1, len(b.vertices))).reshape((-1, 3))
|
|
# offset to centers
|
|
v += np.tile(b.vertices, (len(centers), 1))
|
|
|
|
f = np.tile(b.faces, (len(centers), 1))
|
|
f += np.tile(
|
|
np.arange(len(centers)) * len(b.vertices),
|
|
(len(b.faces), 1)).T.reshape((-1, 1))
|
|
|
|
face_colors = None
|
|
if colors is not None:
|
|
colors = np.asarray(colors)
|
|
if colors.ndim == 1:
|
|
colors = colors[None].repeat(len(centers), axis=0)
|
|
if colors.ndim == 2 and len(colors) == len(centers):
|
|
face_colors = colors.repeat(12, axis=0)
|
|
|
|
mesh = Trimesh(vertices=v,
|
|
faces=f,
|
|
face_colors=face_colors)
|
|
|
|
return mesh
|
|
|
|
|
|
def boolean_sparse(a, b, operation=np.logical_and):
|
|
"""
|
|
Find common rows between two arrays very quickly
|
|
using 3D boolean sparse matrices.
|
|
|
|
Parameters
|
|
-----------
|
|
a: (n, d) int, coordinates in space
|
|
b: (m, d) int, coordinates in space
|
|
operation: numpy operation function, ie:
|
|
np.logical_and
|
|
np.logical_or
|
|
|
|
Returns
|
|
-----------
|
|
coords: (q, d) int, coordinates in space
|
|
"""
|
|
# 3D sparse arrays, using wrapped scipy.sparse
|
|
# pip install sparse
|
|
import sparse
|
|
|
|
# find the bounding box of both arrays
|
|
extrema = np.array([a.min(axis=0),
|
|
a.max(axis=0),
|
|
b.min(axis=0),
|
|
b.max(axis=0)])
|
|
origin = extrema.min(axis=0) - 1
|
|
size = tuple(extrema.ptp(axis=0) + 2)
|
|
|
|
# put nearby voxel arrays into same shape sparse array
|
|
sp_a = sparse.COO((a - origin).T,
|
|
data=np.ones(len(a), dtype=np.bool),
|
|
shape=size)
|
|
sp_b = sparse.COO((b - origin).T,
|
|
data=np.ones(len(b), dtype=np.bool),
|
|
shape=size)
|
|
|
|
# apply the logical operation
|
|
# get a sparse matrix out
|
|
applied = operation(sp_a, sp_b)
|
|
# reconstruct the original coordinates
|
|
coords = np.column_stack(applied.coords) + origin
|
|
|
|
return coords
|
|
|
|
|
|
def strip_array(data):
|
|
shape = data.shape
|
|
ndims = len(shape)
|
|
padding = []
|
|
slices = []
|
|
for dim, size in enumerate(shape):
|
|
axis = tuple(range(dim)) + tuple(range(dim + 1, ndims))
|
|
filled = np.any(data, axis=axis)
|
|
indices, = np.nonzero(filled)
|
|
pad_left = indices[0]
|
|
pad_right = indices[-1]
|
|
padding.append([pad_left, pad_right])
|
|
slices.append(slice(pad_left, pad_right))
|
|
return data[tuple(slices)], np.array(padding, int)
|
|
|
|
|
|
def indices_to_points(indices, pitch=None, origin=None):
|
|
"""
|
|
Convert indices of an (n,m,p) matrix into a set of voxel center points.
|
|
|
|
Parameters
|
|
----------
|
|
indices: (q, 3) int, index of voxel matrix (n,m,p)
|
|
pitch: float, what pitch was the voxel matrix computed with
|
|
origin: (3,) float, what is the origin of the voxel matrix
|
|
|
|
Returns
|
|
----------
|
|
points: (q, 3) float, list of points
|
|
"""
|
|
indices = np.asanyarray(indices)
|
|
if indices.shape[1:] != (3,):
|
|
from IPython import embed
|
|
embed()
|
|
raise ValueError('shape of indices must be (q, 3)')
|
|
|
|
points = np.array(indices, dtype=np.float64)
|
|
if pitch is not None:
|
|
points *= float(pitch)
|
|
if origin is not None:
|
|
origin = np.asanyarray(origin)
|
|
if origin.shape != (3,):
|
|
raise ValueError('shape of origin must be (3,)')
|
|
points += origin
|
|
|
|
return points
|
|
|
|
|
|
def matrix_to_points(matrix, pitch=None, origin=None):
|
|
"""
|
|
Convert an (n,m,p) matrix into a set of points for each voxel center.
|
|
|
|
Parameters
|
|
-----------
|
|
matrix: (n,m,p) bool, voxel matrix
|
|
pitch: float, what pitch was the voxel matrix computed with
|
|
origin: (3,) float, what is the origin of the voxel matrix
|
|
|
|
Returns
|
|
----------
|
|
points: (q, 3) list of points
|
|
"""
|
|
indices = np.column_stack(np.nonzero(matrix))
|
|
points = indices_to_points(indices=indices,
|
|
pitch=pitch,
|
|
origin=origin)
|
|
return points
|
|
|
|
|
|
def points_to_indices(points, pitch=None, origin=None):
|
|
"""
|
|
Convert center points of an (n,m,p) matrix into its indices.
|
|
|
|
Parameters
|
|
----------
|
|
points : (q, 3) float
|
|
Center points of voxel matrix (n,m,p)
|
|
pitch : float
|
|
What pitch was the voxel matrix computed with
|
|
origin : (3,) float
|
|
What is the origin of the voxel matrix
|
|
|
|
Returns
|
|
----------
|
|
indices : (q, 3) int
|
|
List of indices
|
|
"""
|
|
points = np.array(points, dtype=np.float64)
|
|
if points.shape != (points.shape[0], 3):
|
|
raise ValueError('shape of points must be (q, 3)')
|
|
|
|
if origin is not None:
|
|
origin = np.asanyarray(origin)
|
|
if origin.shape != (3,):
|
|
raise ValueError('shape of origin must be (3,)')
|
|
points -= origin
|
|
if pitch is not None:
|
|
points /= pitch
|
|
|
|
origin = np.asanyarray(origin, dtype=np.float64)
|
|
pitch = float(pitch)
|
|
|
|
indices = np.round(points).astype(int)
|
|
return indices
|