643 lines
17 KiB
Python
643 lines
17 KiB
Python
"""
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points.py
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-------------
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Functions dealing with (n, d) points.
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"""
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import copy
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import numpy as np
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from .parent import Geometry
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from .geometry import plane_transform
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from .constants import tol
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from .visual.color import VertexColor
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from . import util
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from . import caching
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from . import grouping
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from . import transformations
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def point_plane_distance(points,
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plane_normal,
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plane_origin=[0.0, 0.0, 0.0]):
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"""
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The minimum perpendicular distance of a point to a plane.
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Parameters
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-----------
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points : (n, 3) float
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Points in space
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plane_normal : (3,) float
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Unit normal vector
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plane_origin : (3,) float
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Plane origin in space
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Returns
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------------
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distances : (n,) float
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Distance from point to plane
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"""
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points = np.asanyarray(points, dtype=np.float64)
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w = points - plane_origin
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distances = np.dot(plane_normal, w.T) / np.linalg.norm(plane_normal)
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return distances
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def major_axis(points):
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"""
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Returns an approximate vector representing the major
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axis of the passed points.
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Parameters
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-------------
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points : (n, dimension) float
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Points in space
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Returns
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-------------
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axis : (dimension,) float
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Vector along approximate major axis
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"""
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U, S, V = np.linalg.svd(points)
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axis = util.unitize(np.dot(S, V))
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return axis
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def plane_fit(points):
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"""
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Fit a plane to points using SVD.
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Parameters
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---------
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points : (n, 3) float
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3D points in space
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Returns
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---------
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C : (3,) float
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Point on the plane
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N : (3,) float
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Unit normal vector of plane
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"""
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# make sure input is numpy array
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points = np.asanyarray(points, dtype=np.float64)
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# make the plane origin the mean of the points
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C = points.mean(axis=0)
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# points offset by the plane origin
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x = points - C
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# create a (3, 3) matrix
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M = np.dot(x.T, x)
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# run SVD
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N = np.linalg.svd(M)[0][:, -1]
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return C, N
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def radial_sort(points,
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origin,
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normal):
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"""
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Sorts a set of points radially (by angle) around an
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an axis specified by origin and normal vector.
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Parameters
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--------------
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points : (n, 3) float
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Points in space
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origin : (3,) float
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Origin to sort around
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normal : (3,) float
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Vector to sort around
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Returns
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--------------
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ordered : (n, 3) float
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Same as input points but reordered
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"""
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# create two axis perpendicular to each other and the normal,
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# and project the points onto them
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axis0 = [normal[0], normal[2], -normal[1]]
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axis1 = np.cross(normal, axis0)
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ptVec = points - origin
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pr0 = np.dot(ptVec, axis0)
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pr1 = np.dot(ptVec, axis1)
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# calculate the angles of the points on the axis
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angles = np.arctan2(pr0, pr1)
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# return the points sorted by angle
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return points[[np.argsort(angles)]]
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def project_to_plane(points,
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plane_normal=[0, 0, 1],
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plane_origin=[0, 0, 0],
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transform=None,
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return_transform=False,
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return_planar=True):
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"""
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Project (n, 3) points onto a plane.
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Parameters
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-----------
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points : (n, 3) float
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Points in space.
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plane_normal : (3,) float
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Unit normal vector of plane
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plane_origin : (3,)
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Origin point of plane
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transform : None or (4, 4) float
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Homogeneous transform, if specified, normal+origin are overridden
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return_transform : bool
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Returns the (4, 4) matrix used or not
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return_planar : bool
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Return (n, 2) points rather than (n, 3) points
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"""
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if np.all(np.abs(plane_normal) < tol.zero):
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raise NameError('Normal must be nonzero!')
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if transform is None:
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transform = plane_transform(plane_origin, plane_normal)
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transformed = transformations.transform_points(points, transform)
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transformed = transformed[:, 0:(3 - int(return_planar))]
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if return_transform:
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polygon_to_3D = np.linalg.inv(transform)
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return transformed, polygon_to_3D
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return transformed
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def remove_close(points, radius):
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"""
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Given an (n, m) array of points return a subset of
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points where no point is closer than radius.
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Parameters
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------------
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points : (n, dimension) float
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Points in space
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radius : float
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Minimum radius between result points
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Returns
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------------
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culled : (m, dimension) float
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Points in space
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mask : (n,) bool
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Which points from the original points were returned
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"""
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from scipy.spatial import cKDTree
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tree = cKDTree(points)
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# get the index of every pair of points closer than our radius
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pairs = tree.query_pairs(radius, output_type='ndarray')
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# how often each vertex index appears in a pair
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# this is essentially a cheaply computed "vertex degree"
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# in the graph that we could construct for connected points
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count = np.bincount(pairs.ravel(), minlength=len(points))
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# for every pair we know we have to remove one of them
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# which of the two options we pick can have a large impact
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# on how much over-culling we end up doing
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column = count[pairs].argmax(axis=1)
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# take the value in each row with the highest degree
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# there is probably better numpy slicing you could do here
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highest = pairs.ravel()[column + 2 * np.arange(len(column))]
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# mask the vertices by index
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mask = np.ones(len(points), dtype=np.bool)
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mask[highest] = False
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if tol.strict:
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# verify we actually did what we said we'd do
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test = cKDTree(points[mask])
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assert len(test.query_pairs(radius)) == 0
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return points[mask], mask
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def k_means(points, k, **kwargs):
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"""
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Find k centroids that attempt to minimize the k- means problem:
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https://en.wikipedia.org/wiki/Metric_k-center
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Parameters
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----------
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points: (n, d) float
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Points in space
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k : int
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Number of centroids to compute
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**kwargs : dict
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Passed directly to scipy.cluster.vq.kmeans
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Returns
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----------
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centroids : (k, d) float
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Points in some space
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labels: (n) int
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Indexes for which points belong to which centroid
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"""
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from scipy.cluster.vq import kmeans
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from scipy.spatial import cKDTree
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points = np.asanyarray(points, dtype=np.float64)
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points_std = points.std(axis=0)
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whitened = points / points_std
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centroids_whitened, distortion = kmeans(whitened, k, **kwargs)
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centroids = centroids_whitened * points_std
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# find which centroid each point is closest to
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tree = cKDTree(centroids)
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labels = tree.query(points, k=1)[1]
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return centroids, labels
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def tsp(points, start=0):
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"""
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Find an ordering of points where each is visited and
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the next point is the closest in euclidean distance,
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and if there are multiple points with equal distance
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go to an arbitrary one.
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Assumes every point is visitable from every other point,
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i.e. the travelling salesman problem on a fully connected
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graph. It is not a MINIMUM traversal; rather it is a
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"not totally goofy traversal, quickly." On random points
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this traversal is often ~20x shorter than random ordering,
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and executes on 1000 points in around 29ms on a 2014 i7.
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Parameters
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---------------
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points : (n, dimension) float
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ND points in space
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start : int
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The index of points we should start at
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Returns
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---------------
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traversal : (n,) int
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Ordered traversal visiting every point
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distances : (n - 1,) float
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The euclidean distance between points in traversal
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"""
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# points should be float
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points = np.asanyarray(points, dtype=np.float64)
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if len(points.shape) != 2:
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raise ValueError('points must be (n, dimension)!')
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# start should be an index
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start = int(start)
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# a mask of unvisited points by index
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unvisited = np.ones(len(points), dtype=np.bool)
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unvisited[start] = False
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# traversal of points by index
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traversal = np.zeros(len(points), dtype=np.int64) - 1
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traversal[0] = start
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# list of distances
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distances = np.zeros(len(points) - 1, dtype=np.float64)
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# a mask of indexes in order
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index_mask = np.arange(len(points), dtype=np.int64)
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# in the loop we want to call distances.sum(axis=1)
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# a lot and it's actually kind of slow for "reasons"
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# dot products with ones is equivalent and ~2x faster
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sum_ones = np.ones(points.shape[1])
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# loop through all points
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for i in range(len(points) - 1):
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# which point are we currently on
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current = points[traversal[i]]
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# do NlogN distance query
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# use dot instead of .sum(axis=1) or np.linalg.norm
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# as it is faster, also don't square root here
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dist = np.dot((points[unvisited] - current) ** 2,
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sum_ones)
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# minimum distance index
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min_index = dist.argmin()
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# successor is closest unvisited point
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successor = index_mask[unvisited][min_index]
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# update the mask
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unvisited[successor] = False
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# store the index to the traversal
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traversal[i + 1] = successor
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# store the distance
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distances[i] = dist[min_index]
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# we were comparing distance^2 so take square root
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distances **= 0.5
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return traversal, distances
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def plot_points(points, show=True):
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"""
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Plot an (n, 3) list of points using matplotlib
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Parameters
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-------------
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points : (n, 3) float
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Points in space
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show : bool
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If False, will not show until plt.show() is called
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"""
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D # NOQA
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points = np.asanyarray(points, dtype=np.float64)
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if len(points.shape) != 2:
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raise ValueError('Points must be (n, 2|3)!')
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if points.shape[1] == 3:
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d')
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ax.scatter(*points.T)
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elif points.shape[1] == 2:
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plt.scatter(*points.T)
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else:
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raise ValueError('points not 2D/3D: {}'.format(
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points.shape))
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if show:
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plt.show()
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class PointCloud(Geometry):
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"""
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Hold 3D points in an object which can be visualized
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in a scene.
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"""
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def __init__(self, vertices, colors=None, metadata=None, **kwargs):
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"""
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Load an array of points into a PointCloud object.
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Parameters
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-------------
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vertices : (n, 3) float
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Points in space
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colors : (n, 4) uint8 or None
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RGBA colors for each point
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metadata : dict or None
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Metadata about points
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"""
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self._data = caching.DataStore()
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self._cache = caching.Cache(self._data.md5)
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self.metadata = {}
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if metadata is not None:
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self.metadata.update(metadata)
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# load vertices
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self.vertices = vertices
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# save visual data to vertex color object
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self.visual = VertexColor(colors=colors, obj=self)
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def __setitem__(self, *args, **kwargs):
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return self.vertices.__setitem__(*args, **kwargs)
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def __getitem__(self, *args, **kwargs):
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return self.vertices.__getitem__(*args, **kwargs)
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@property
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def shape(self):
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"""
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Get the shape of the pointcloud
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Returns
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----------
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shape : (2,) int
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Shape of vertex array
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"""
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return self.vertices.shape
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@property
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def is_empty(self):
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"""
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Are there any vertices defined or not.
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Returns
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----------
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empty : bool
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True if no vertices defined
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"""
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return len(self.vertices) == 0
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def copy(self):
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"""
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Safely get a copy of the current point cloud.
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Copied objects will have emptied caches to avoid memory
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issues and so may be slow on initial operations until
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caches are regenerated.
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Current object will *not* have its cache cleared.
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Returns
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---------
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copied : trimesh.PointCloud
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Copy of current point cloud
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"""
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copied = PointCloud(vertices=None)
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# copy vertex and face data
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copied._data.data = copy.deepcopy(self._data.data)
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# get metadata
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copied.metadata = copy.deepcopy(self.metadata)
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# make sure cache is set from here
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copied._cache.clear()
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return copied
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def md5(self):
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"""
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Get an MD5 hash of the current vertices.
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Returns
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----------
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md5 : str
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Hash of self.vertices
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"""
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return self._data.md5()
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def crc(self):
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"""
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Get a CRC hash of the current vertices.
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Returns
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----------
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crc : int
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Hash of self.vertices
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"""
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return self._data.crc()
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def merge_vertices(self):
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"""
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Merge vertices closer than tol.merge (default: 1e-8)
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"""
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# run unique rows
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unique, inverse = grouping.unique_rows(self.vertices)
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# apply unique mask to vertices
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self.vertices = self.vertices[unique]
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# apply unique mask to colors
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if (self.colors is not None and
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len(self.colors) == len(inverse)):
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self.colors = self.colors[unique]
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def apply_transform(self, transform):
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"""
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Apply a homogeneous transformation to the PointCloud
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object in- place.
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Parameters
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--------------
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transform : (4, 4) float
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Homogeneous transformation to apply to PointCloud
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"""
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self.vertices = transformations.transform_points(self.vertices,
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matrix=transform)
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@property
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def bounds(self):
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"""
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The axis aligned bounds of the PointCloud
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Returns
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------------
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bounds : (2, 3) float
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Minimum, Maximum verteex
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"""
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return np.array([self.vertices.min(axis=0),
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self.vertices.max(axis=0)])
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@property
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def extents(self):
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"""
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The size of the axis aligned bounds
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Returns
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------------
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extents : (3,) float
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Edge length of axis aligned bounding box
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"""
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return self.bounds.ptp(axis=0)
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@property
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def centroid(self):
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"""
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The mean vertex position
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Returns
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------------
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centroid : (3,) float
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Mean vertex position
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"""
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return self.vertices.mean(axis=0)
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@property
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def vertices(self):
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"""
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Vertices of the PointCloud
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Returns
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------------
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vertices : (n, 3) float
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Points in the PointCloud
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"""
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return self._data['vertices']
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@vertices.setter
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def vertices(self, data):
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if data is None:
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self._data['vertices'] = None
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else:
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# we want to copy data for new object
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data = np.array(data, dtype=np.float64, copy=True)
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if not util.is_shape(data, (-1, 3)):
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raise ValueError('Point clouds must be (n, 3)!')
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self._data['vertices'] = data
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@property
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def colors(self):
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"""
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Stored per- point color
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Returns
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----------
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colors : (len(self.vertices), 4) np.uint8
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Per- point RGBA color
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"""
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return self.visual.vertex_colors
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@colors.setter
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def colors(self, data):
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self.visual.vertex_colors = data
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@caching.cache_decorator
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def convex_hull(self):
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"""
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A convex hull of every point.
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Returns
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-------------
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convex_hull : trimesh.Trimesh
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A watertight mesh of the hull of the points
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"""
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from . import convex
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return convex.convex_hull(self.vertices)
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def scene(self):
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"""
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A scene containing just the PointCloud
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Returns
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----------
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scene : trimesh.Scene
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|
Scene object containing this PointCloud
|
|
"""
|
|
from .scene.scene import Scene
|
|
return Scene(self)
|
|
|
|
def show(self, **kwargs):
|
|
"""
|
|
Open a viewer window displaying the current PointCloud
|
|
"""
|
|
self.scene().show(**kwargs)
|
|
|
|
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)
|