"""
points.py
-------------
Functions dealing with (n, d) points.
"""
import copy
import numpy as np
from .parent import Geometry3D
from .geometry import plane_transform
from .constants import tol
from .visual.color import VertexColor
from . import util
from . import caching
from . import grouping
from . import transformations
def point_plane_distance(points,
plane_normal,
plane_origin=None):
"""
The minimum perpendicular distance of a point to a plane.
Parameters
-----------
points : (n, 3) float
Points in space
plane_normal : (3,) float
Unit normal vector
plane_origin : (3,) float
Plane origin in space
Returns
------------
distances : (n,) float
Distance from point to plane
"""
points = np.asanyarray(points, dtype=np.float64)
if plane_origin is None:
w = points
else:
w = points - plane_origin
distances = np.dot(plane_normal, w.T) / np.linalg.norm(plane_normal)
return distances
def major_axis(points):
"""
Returns an approximate vector representing the major
axis of the passed points.
Parameters
-------------
points : (n, dimension) float
Points in space
Returns
-------------
axis : (dimension,) float
Vector along approximate major axis
"""
U, S, V = np.linalg.svd(points)
axis = util.unitize(np.dot(S, V))
return axis
def plane_fit(points):
"""
Fit a plane to points using SVD.
Parameters
---------
points : (n, 3) float or (p, n, 3,) float
3D points in space
Second option allows to simultaneously compute
p centroids and normals
Returns
---------
C : (3,) float or (p, 3,) float
Point on the plane
N : (3,) float or (p, 3,) float
Unit normal vector of plane
"""
# make sure input is numpy array
points = np.asanyarray(points, dtype=np.float64)
assert points.ndim == 2 or points.ndim == 3
# with only one point set, np.dot is faster
if points.ndim == 2:
# make the plane origin the mean of the points
C = points.mean(axis=0)
# points offset by the plane origin
x = points - C[None, :]
# create a (3, 3) matrix
M = np.dot(x.T, x)
else:
# make the plane origin the mean of the points
C = points.mean(axis=1)
# points offset by the plane origin
x = points - C[:, None, :]
# create a (p, 3, 3) matrix
M = np.einsum('pnd, pnm->pdm', x, x)
# run SVD
N = np.linalg.svd(M)[0][..., -1]
# return the centroid(s) and normal(s)
return C, N
def radial_sort(points,
origin,
normal,
start=None):
"""
Sorts a set of points radially (by angle) around an
axis specified by origin and normal vector.
Parameters
--------------
points : (n, 3) float
Points in space
origin : (3,) float
Origin to sort around
normal : (3,) float
Vector to sort around
start : (3,) float
Vector to specify start position in counter-clockwise
order viewing in direction of normal, MUST not be
parallel with normal
Returns
--------------
ordered : (n, 3) float
Same as input points but reordered
"""
# create two axis perpendicular to each other and
# the normal and project the points onto them
if start is None:
axis0 = [normal[0], normal[2], -normal[1]]
axis1 = np.cross(normal, axis0)
else:
normal, start = util.unitize([normal, start])
if np.abs(1 - np.abs(np.dot(normal, start))) < tol.zero:
raise ValueError('start must not parallel with normal')
axis0 = np.cross(start, normal)
axis1 = np.cross(axis0, normal)
vectors = points - origin
# calculate the angles of the points on the axis
angles = np.arctan2(np.dot(vectors, axis0),
np.dot(vectors, axis1))
# return the points sorted by angle
return points[angles.argsort()[::-1]]
def project_to_plane(points,
plane_normal,
plane_origin,
transform=None,
return_transform=False,
return_planar=True):
"""
Project (n, 3) points onto a plane.
Parameters
-----------
points : (n, 3) float
Points in space.
plane_normal : (3,) float
Unit normal vector of plane
plane_origin : (3,)
Origin point of plane
transform : None or (4, 4) float
Homogeneous transform, if specified, normal+origin are overridden
return_transform : bool
Returns the (4, 4) matrix used or not
return_planar : bool
Return (n, 2) points rather than (n, 3) points
"""
if np.all(np.abs(plane_normal) < tol.zero):
raise NameError('Normal must be nonzero!')
if transform is None:
transform = plane_transform(plane_origin, plane_normal)
transformed = transformations.transform_points(points, transform)
transformed = transformed[:, 0:(3 - int(return_planar))]
if return_transform:
polygon_to_3D = np.linalg.inv(transform)
return transformed, polygon_to_3D
return transformed
def remove_close(points, radius):
"""
Given an (n, m) array of points return a subset of
points where no point is closer than radius.
Parameters
------------
points : (n, dimension) float
Points in space
radius : float
Minimum radius between result points
Returns
------------
culled : (m, dimension) float
Points in space
mask : (n,) bool
Which points from the original points were returned
"""
from scipy.spatial import cKDTree
tree = cKDTree(points)
# get the index of every pair of points closer than our radius
pairs = tree.query_pairs(radius, output_type='ndarray')
# how often each vertex index appears in a pair
# this is essentially a cheaply computed "vertex degree"
# in the graph that we could construct for connected points
count = np.bincount(pairs.ravel(), minlength=len(points))
# for every pair we know we have to remove one of them
# which of the two options we pick can have a large impact
# on how much over-culling we end up doing
column = count[pairs].argmax(axis=1)
# take the value in each row with the highest degree
# there is probably better numpy slicing you could do here
highest = pairs.ravel()[column + 2 * np.arange(len(column))]
# mask the vertices by index
mask = np.ones(len(points), dtype=bool)
mask[highest] = False
if tol.strict:
# verify we actually did what we said we'd do
test = cKDTree(points[mask])
assert len(test.query_pairs(radius)) == 0
return points[mask], mask
def k_means(points, k, **kwargs):
"""
Find k centroids that attempt to minimize the k- means problem:
https://en.wikipedia.org/wiki/Metric_k-center
Parameters
----------
points: (n, d) float
Points in space
k : int
Number of centroids to compute
**kwargs : dict
Passed directly to scipy.cluster.vq.kmeans
Returns
----------
centroids : (k, d) float
Points in some space
labels: (n) int
Indexes for which points belong to which centroid
"""
from scipy.cluster.vq import kmeans
from scipy.spatial import cKDTree
points = np.asanyarray(points, dtype=np.float64)
points_std = points.std(axis=0)
points_std[points_std < tol.zero] = 1
whitened = points / points_std
centroids_whitened, distortion = kmeans(whitened, k, **kwargs)
centroids = centroids_whitened * points_std
# find which centroid each point is closest to
tree = cKDTree(centroids)
labels = tree.query(points, k=1)[1]
return centroids, labels
def tsp(points, start=0):
"""
Find an ordering of points where each is visited and
the next point is the closest in euclidean distance,
and if there are multiple points with equal distance
go to an arbitrary one.
Assumes every point is visitable from every other point,
i.e. the travelling salesman problem on a fully connected
graph. It is not a MINIMUM traversal; rather it is a
"not totally goofy traversal, quickly." On random points
this traversal is often ~20x shorter than random ordering,
and executes on 1000 points in around 29ms on a 2014 i7.
Parameters
---------------
points : (n, dimension) float
ND points in space
start : int
The index of points we should start at
Returns
---------------
traversal : (n,) int
Ordered traversal visiting every point
distances : (n - 1,) float
The euclidean distance between points in traversal
"""
# points should be float
points = np.asanyarray(points, dtype=np.float64)
if len(points.shape) != 2:
raise ValueError('points must be (n, dimension)!')
# start should be an index
start = int(start)
# a mask of unvisited points by index
unvisited = np.ones(len(points), dtype=bool)
unvisited[start] = False
# traversal of points by index
traversal = np.zeros(len(points), dtype=np.int64) - 1
traversal[0] = start
# list of distances
distances = np.zeros(len(points) - 1, dtype=np.float64)
# a mask of indexes in order
index_mask = np.arange(len(points), dtype=np.int64)
# in the loop we want to call distances.sum(axis=1)
# a lot and it's actually kind of slow for "reasons"
# dot products with ones is equivalent and ~2x faster
sum_ones = np.ones(points.shape[1])
# loop through all points
for i in range(len(points) - 1):
# which point are we currently on
current = points[traversal[i]]
# do NlogN distance query
# use dot instead of .sum(axis=1) or np.linalg.norm
# as it is faster, also don't square root here
dist = np.dot((points[unvisited] - current) ** 2,
sum_ones)
# minimum distance index
min_index = dist.argmin()
# successor is closest unvisited point
successor = index_mask[unvisited][min_index]
# update the mask
unvisited[successor] = False
# store the index to the traversal
traversal[i + 1] = successor
# store the distance
distances[i] = dist[min_index]
# we were comparing distance^2 so take square root
distances **= 0.5
return traversal, distances
def plot_points(points, show=True):
"""
Plot an (n, 3) list of points using matplotlib
Parameters
-------------
points : (n, 3) float
Points in space
show : bool
If False, will not show until plt.show() is called
"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D # NOQA
points = np.asanyarray(points, dtype=np.float64)
if len(points.shape) != 2:
raise ValueError('Points must be (n, 2|3)!')
if points.shape[1] == 3:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(*points.T)
elif points.shape[1] == 2:
plt.scatter(*points.T)
else:
raise ValueError('points not 2D/3D: {}'.format(
points.shape))
if show:
plt.show()
[docs]
class PointCloud(Geometry3D):
"""
Hold 3D points in an object which can be visualized
in a scene.
"""
[docs]
def __init__(self, vertices, colors=None, metadata=None, **kwargs):
"""
Load an array of points into a PointCloud object.
Parameters
-------------
vertices : (n, 3) float
Points in space
colors : (n, 4) uint8 or None
RGBA colors for each point
metadata : dict or None
Metadata about points
"""
self._data = caching.DataStore()
self._cache = caching.Cache(self._data.__hash__)
self.metadata = {}
if metadata is not None:
self.metadata.update(metadata)
# load vertices
self.vertices = vertices
if 'vertex_colors' in kwargs and colors is None:
colors = kwargs['vertex_colors']
# save visual data to vertex color object
self.visual = VertexColor(colors=colors, obj=self)
def __setitem__(self, *args, **kwargs):
return self.vertices.__setitem__(*args, **kwargs)
def __getitem__(self, *args, **kwargs):
return self.vertices.__getitem__(*args, **kwargs)
@property
def shape(self):
"""
Get the shape of the pointcloud
Returns
----------
shape : (2,) int
Shape of vertex array
"""
return self.vertices.shape
@property
def is_empty(self):
"""
Are there any vertices defined or not.
Returns
----------
empty : bool
True if no vertices defined
"""
return len(self.vertices) == 0
[docs]
def copy(self):
"""
Safely get a copy of the current point cloud.
Copied objects will have emptied caches to avoid memory
issues and so may be slow on initial operations until
caches are regenerated.
Current object will *not* have its cache cleared.
Returns
---------
copied : trimesh.PointCloud
Copy of current point cloud
"""
copied = PointCloud(vertices=None)
# copy vertex and face data
copied._data.data = copy.deepcopy(self._data.data)
# get metadata
copied.metadata = copy.deepcopy(self.metadata)
# make sure cache is set from here
copied._cache.clear()
return copied
[docs]
def hash(self):
"""
Get a hash of the current vertices.
Returns
----------
hash : str
Hash of self.vertices
"""
return self._data.__hash__()
[docs]
def crc(self):
"""
Get a CRC hash of the current vertices.
Returns
----------
crc : int
Hash of self.vertices
"""
return self._data.crc()
[docs]
def merge_vertices(self):
"""
Merge vertices closer than tol.merge (default: 1e-8)
"""
# run unique rows
unique, inverse = grouping.unique_rows(self.vertices)
# apply unique mask to vertices
self.vertices = self.vertices[unique]
# apply unique mask to colors
if (self.colors is not None and
len(self.colors) == len(inverse)):
self.colors = self.colors[unique]
@property
def bounds(self):
"""
The axis aligned bounds of the PointCloud
Returns
------------
bounds : (2, 3) float
Minimum, Maximum verteex
"""
return np.array([self.vertices.min(axis=0),
self.vertices.max(axis=0)])
@property
def extents(self):
"""
The size of the axis aligned bounds
Returns
------------
extents : (3,) float
Edge length of axis aligned bounding box
"""
return self.bounds.ptp(axis=0)
@property
def centroid(self):
"""
The mean vertex position
Returns
------------
centroid : (3,) float
Mean vertex position
"""
return self.vertices.mean(axis=0)
@property
def vertices(self):
"""
Vertices of the PointCloud
Returns
------------
vertices : (n, 3) float
Points in the PointCloud
"""
return self._data['vertices']
@vertices.setter
def vertices(self, data):
if data is None:
self._data['vertices'] = None
else:
# we want to copy data for new object
data = np.array(data, dtype=np.float64, copy=True)
if not util.is_shape(data, (-1, 3)):
raise ValueError('Point clouds must be (n, 3)!')
self._data['vertices'] = data
@property
def colors(self):
"""
Stored per- point color
Returns
----------
colors : (len(self.vertices), 4) np.uint8
Per- point RGBA color
"""
return self.visual.vertex_colors
@colors.setter
def colors(self, data):
self.visual.vertex_colors = data
@caching.cache_decorator
def kdtree(self):
"""
Return a scipy.spatial.cKDTree of the vertices of the mesh.
Not cached as this lead to observed memory issues and segfaults.
Returns
---------
tree : scipy.spatial.cKDTree
Contains mesh.vertices
"""
from scipy.spatial import cKDTree
tree = cKDTree(self.vertices.view(np.ndarray))
return tree
@caching.cache_decorator
def convex_hull(self):
"""
A convex hull of every point.
Returns
-------------
convex_hull : trimesh.Trimesh
A watertight mesh of the hull of the points
"""
from . import convex
return convex.convex_hull(self.vertices)
[docs]
def scene(self):
"""
A scene containing just the PointCloud
Returns
----------
scene : trimesh.Scene
Scene object containing this PointCloud
"""
from .scene.scene import Scene
return Scene(self)
[docs]
def show(self, **kwargs):
"""
Open a viewer window displaying the current PointCloud
"""
self.scene().show(**kwargs)
[docs]
def export(self, file_obj=None, file_type=None, **kwargs):
"""
Export the current pointcloud to a file object.
If file_obj is a filename, file will be written there.
Supported formats are xyz
Parameters
------------
file_obj: open writeable file object
str, file name where to save the pointcloud
None, if you would like this function to return the export blob
file_type: str
Which file type to export as.
If file name is passed this is not required
"""
from .exchange.export import export_mesh
return export_mesh(self,
file_obj=file_obj,
file_type=file_type,
**kwargs)
[docs]
def query(self, input_points, **kwargs):
"""
Find the the closest points and associated attributes from this PointCloud.
Parameters
------------
input_points : (n, 3) float
Input query points
kwargs : dict
Arguments for proximity.query_from_points
result : proximity.NearestQueryResult
Result of the query.
"""
from .proximity import query_from_points
return query_from_points(
self.vertices, input_points, self.kdtree, **kwargs)
def __add__(self, other):
if len(other.colors) == len(self.colors) == 0:
colors = None
else:
# preserve colors
# if one point cloud has no color property use black
other_colors = [[0, 0, 0, 255]] * \
len(other.vertices) if len(other.colors) == 0 else other.colors
self_colors = [[0, 0, 0, 255]] * \
len(self.vertices) if len(self.colors) == 0 else self.colors
colors = np.vstack((self_colors, other_colors))
return PointCloud(vertices=np.vstack(
(self.vertices, other.vertices)), colors=colors)
