196 lines
6.9 KiB
Python
196 lines
6.9 KiB
Python
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"""
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comparison.py
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----------------
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Provide methods for quickly hashing and comparing meshes.
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"""
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import numpy as np
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from . import util
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from .constants import tol
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# how many significant figures to use for each field of the identifier
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id_sigfig = np.array([5, # area
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10, # euler number
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5, # area/volume ratio
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2, # convex/mesh area ratio
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2, # convex area/volume ratio
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3]) # max radius squared / area
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def identifier_simple(mesh):
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"""
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Return a basic identifier for a mesh, consisting of properties
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that have been hand tuned to be somewhat robust to rigid
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transformations and different tesselations.
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Parameters
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------------
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mesh : trimesh.Trimesh
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Source geometry
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Returns
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----------
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identifier : (6,) float
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Identifying values of the mesh
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"""
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# verify the cache once
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mesh._cache.verify()
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# don't check hashes during identifier as we aren't
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# changing any data values of the mesh inside block
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# if we did change values in cache block things would break
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with mesh._cache:
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# pre-allocate identifier so indexes of values can't move around
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# like they might if we used hstack or something else
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identifier = np.zeros(6, dtype=np.float64)
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# avoid thrashing the cache unnecessarily
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mesh_area = mesh.area
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# start with properties that are valid regardless of watertightness
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# note that we're going to try to make all parameters relative
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# to area so other values don't get blown up at weird scales
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identifier[0] = mesh_area
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# avoid divide-by-zero later
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if mesh_area < tol.merge:
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mesh_area = 1.0
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# topological constant and the only thing we can really
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# trust in this fallen world
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identifier[1] = mesh.euler_number
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# if we have a watertight mesh include volume and inertia
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if mesh.is_volume:
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# side length of a cube ratio
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# 1.0 for cubes, different values for other things
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identifier[2] = (((mesh_area / 6.0) ** (1.0 / 2.0)) /
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(mesh.volume ** (1.0 / 3.0)))
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# save vertices for radius calculation
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vertices = mesh.vertices - mesh.center_mass
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# we are going to special case radially symmetric meshes
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# to replace their surface area with ratio of their
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# surface area to a primitive sphere or cylinder surface area
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# this is because tessellated curved surfaces are really rough
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# to reliably hash as they are very sensitive to floating point
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# and tessellation error. By making area proportionate to a fit
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# primitive area we are able to reliably hash at more sigfigs
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if mesh.symmetry == 'radial':
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# cylinder height
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h = np.dot(vertices, mesh.symmetry_axis).ptp()
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# section radius summed per row then overall max
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R2 = np.dot((np.dot(vertices, mesh.symmetry_section.T)
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** 2), [1, 1]).max()
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# area of a cylinder primitive
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area = (2 * np.pi * (R2**.5) * h) + (2 * np.pi * R2)
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# replace area in this case with area ratio
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identifier[0] = mesh_area / area
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elif mesh.symmetry == 'spherical':
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# handle a spherically symmetric mesh
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R2 = np.dot((vertices ** 2), [1, 1, 1]).max()
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area = 4 * np.pi * R2
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identifier[0] = mesh_area / area
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else:
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# if we don't have a watertight mesh add information about the
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# convex hull which is slow to compute and unreliable
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try:
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# get the hull area and volume
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hull = mesh.convex_hull
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hull_area = hull.area
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hull_volume = hull.volume
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except BaseException:
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# in-plane or single point geometry has no hull
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hull_area = 6.0
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hull_volume = 1.0
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# just what we're looking for in a hash but hey
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identifier[3] = mesh_area / hull_area
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# cube side length ratio for the hull
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identifier[4] = (((hull_area / 6.0) ** (1.0 / 2.0)) /
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(hull_volume ** (1.0 / 3.0)))
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# calculate maximum mesh radius
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vertices = mesh.vertices - mesh.centroid
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# add in max radius^2 to area ratio
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R2 = np.dot((vertices ** 2), [1, 1, 1]).max()
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identifier[5] = R2 / mesh_area
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return identifier
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def identifier_hash(identifier, sigfig=None):
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"""
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Hash an identifier array to a specified number of
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significant figures.
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Parameters
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------------
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identifier : (n,) float
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Vector of properties
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sigfig : (n,) int
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Number of sigfigs per property
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Returns
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----------
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md5 : str
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MD5 hash of identifier
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"""
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if sigfig is None:
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sigfig = id_sigfig
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# convert identifier to integers and order of magnitude
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as_int, multiplier = util.sigfig_int(identifier, sigfig)
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# make all scales positive
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if (multiplier < 0).any():
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multiplier += np.abs(multiplier.min())
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hashable = (as_int * (10 ** multiplier)).astype(np.int64)
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md5 = util.md5_object(hashable)
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return md5
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def face_ordering(mesh):
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"""
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Return the size-order of every face in the input mesh.
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Triangles can be considered by the length order:
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[small edge, medium edge, large edge] (SML)
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[small edge, large edge, medium edge] (SLM)
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This function returns [-1, 0, 1], depending on whether
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the triangle is SML or SLM, and 0 if M == L.
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The reason this is useful as it as a rare property that is
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invariant to translation and rotation but changes when a
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mesh is reflected or inverted. It is NOT invariant to
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different tesselations of the same surface.
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Parameters
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-------------
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mesh : trimesh.Trimesh
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Source geometry to calculate ordering on
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Returns
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--------------
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order : (len(mesh.faces), ) int
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Is each face SML (-1), SLM (+1), or M==L (0)
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"""
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# the length of each edge in faces
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norms = mesh.edges_unique_length[
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mesh.edges_unique_inverse].reshape((-1, 3))
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# the per- row index of the shortest edge
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small = norms.argmin(axis=1)
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# the ordered index for the medium and large edge norm
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# arranged to reference flattened norms for indexing
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MLidx = np.column_stack((small + 1, small + 2)) % 3
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MLidx += (np.arange(len(small)) * 3).reshape((-1, 1))
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# subtract the two largest edge lengths from each other
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diff = np.subtract(*norms.reshape(-1)[MLidx.T])
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# mark by sign but keep zero values zero
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order = np.zeros(len(norms), dtype=np.int64)
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order[diff < tol.merge] = -1
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order[diff > tol.merge] = 1
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return order
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