237 lines
7.3 KiB
Python
237 lines
7.3 KiB
Python
|
import numpy as np
|
||
|
|
|
||
|
|
try:
|
||
|
|
from scipy.sparse.linalg import spsolve
|
||
|
|
from scipy.sparse import coo_matrix, eye
|
||
|
|
except ImportError:
|
||
|
|
pass
|
||
|
|
|
||
|
|
from . import triangles
|
||
|
|
|
||
|
|
|
||
|
|
def filter_laplacian(mesh,
|
||
|
|
lamb=0.5,
|
||
|
|
iterations=10,
|
||
|
|
implicit_time_integration=False,
|
||
|
|
volume_constraint=True,
|
||
|
|
laplacian_operator=None):
|
||
|
|
"""
|
||
|
|
Smooth a mesh in-place using laplacian smoothing.
|
||
|
|
Articles
|
||
|
|
1 - "Improved Laplacian Smoothing of Noisy Surface Meshes"
|
||
|
|
J. Vollmer, R. Mencl, and H. Muller
|
||
|
|
2 - "Implicit Fairing of Irregular Meshes using Diffusion
|
||
|
|
and Curvature Flow". M. Desbrun, M. Meyer,
|
||
|
|
P. Schroder, A.H.B. Caltech
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
------------
|
||
|
|
mesh : trimesh.Trimesh
|
||
|
|
Mesh to be smoothed in place
|
||
|
|
lamb : float
|
||
|
|
Diffusion speed constant
|
||
|
|
If 0.0, no diffusion
|
||
|
|
If > 0.0, diffusion occurs
|
||
|
|
implicit_time_integration: boolean
|
||
|
|
if False: explicit time integration
|
||
|
|
-lamb <= 1.0 - Stability Limit (Article 1)
|
||
|
|
if True: implicit time integration
|
||
|
|
-lamb no limit (Article 2)
|
||
|
|
iterations : int
|
||
|
|
Number of passes to run filter
|
||
|
|
laplacian_operator : None or scipy.sparse.coo.coo_matrix
|
||
|
|
Sparse matrix laplacian operator
|
||
|
|
Will be autogenerated if None
|
||
|
|
"""
|
||
|
|
|
||
|
|
# if the laplacian operator was not passed create it here
|
||
|
|
if laplacian_operator is None:
|
||
|
|
laplacian_operator = laplacian_calculation(mesh)
|
||
|
|
|
||
|
|
# save initial volume
|
||
|
|
if volume_constraint:
|
||
|
|
vol_ini = mesh.volume
|
||
|
|
|
||
|
|
# get mesh vertices and faces as vanilla numpy array
|
||
|
|
vertices = mesh.vertices.copy().view(np.ndarray)
|
||
|
|
faces = mesh.faces.copy().view(np.ndarray)
|
||
|
|
|
||
|
|
# Set matrix for linear system of equations
|
||
|
|
if implicit_time_integration:
|
||
|
|
dlap = laplacian_operator.shape[0]
|
||
|
|
AA = eye(dlap) + lamb * (eye(dlap) - laplacian_operator)
|
||
|
|
|
||
|
|
# Number of passes
|
||
|
|
for _index in range(iterations):
|
||
|
|
# Classic Explicit Time Integration - Article 1
|
||
|
|
if not implicit_time_integration:
|
||
|
|
dot = laplacian_operator.dot(vertices) - vertices
|
||
|
|
vertices += lamb * dot
|
||
|
|
|
||
|
|
# Implicit Time Integration - Article 2
|
||
|
|
else:
|
||
|
|
vertices = spsolve(AA, vertices)
|
||
|
|
|
||
|
|
# volume constraint
|
||
|
|
if volume_constraint:
|
||
|
|
# find the volume with new vertex positions
|
||
|
|
vol_new = triangles.mass_properties(
|
||
|
|
vertices[faces], skip_inertia=True)["volume"]
|
||
|
|
# scale by volume ratio
|
||
|
|
vertices *= ((vol_ini / vol_new) ** (1.0 / 3.0))
|
||
|
|
|
||
|
|
# assign modified vertices back to mesh
|
||
|
|
mesh.vertices = vertices
|
||
|
|
return mesh
|
||
|
|
|
||
|
|
|
||
|
|
def filter_humphrey(mesh,
|
||
|
|
alpha=0.1,
|
||
|
|
beta=0.5,
|
||
|
|
iterations=10,
|
||
|
|
laplacian_operator=None):
|
||
|
|
"""
|
||
|
|
Smooth a mesh in-place using laplacian smoothing
|
||
|
|
and Humphrey filtering.
|
||
|
|
|
||
|
|
Articles
|
||
|
|
"Improved Laplacian Smoothing of Noisy Surface Meshes"
|
||
|
|
J. Vollmer, R. Mencl, and H. Muller
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
------------
|
||
|
|
mesh : trimesh.Trimesh
|
||
|
|
Mesh to be smoothed in place
|
||
|
|
alpha : float
|
||
|
|
Controls shrinkage, range is 0.0 - 1.0
|
||
|
|
If 0.0, not considered
|
||
|
|
If 1.0, no smoothing
|
||
|
|
beta : float
|
||
|
|
Controls how aggressive smoothing is
|
||
|
|
If 0.0, no smoothing
|
||
|
|
If 1.0, full aggressiveness
|
||
|
|
iterations : int
|
||
|
|
Number of passes to run filter
|
||
|
|
laplacian_operator : None or scipy.sparse.coo.coo_matrix
|
||
|
|
Sparse matrix laplacian operator
|
||
|
|
Will be autogenerated if None
|
||
|
|
"""
|
||
|
|
# if the laplacian operator was not passed create it here
|
||
|
|
if laplacian_operator is None:
|
||
|
|
laplacian_operator = laplacian_calculation(mesh)
|
||
|
|
|
||
|
|
# get mesh vertices as vanilla numpy array
|
||
|
|
vertices = mesh.vertices.copy().view(np.ndarray)
|
||
|
|
# save original unmodified vertices
|
||
|
|
original = vertices.copy()
|
||
|
|
|
||
|
|
# run through iterations of filter
|
||
|
|
for _index in range(iterations):
|
||
|
|
vert_q = vertices.copy()
|
||
|
|
vertices = laplacian_operator.dot(vertices)
|
||
|
|
vert_b = vertices - (alpha * original + (1.0 - alpha) * vert_q)
|
||
|
|
vertices -= (beta * vert_b + (1.0 - beta) *
|
||
|
|
laplacian_operator.dot(vert_b))
|
||
|
|
|
||
|
|
# assign modified vertices back to mesh
|
||
|
|
mesh.vertices = vertices
|
||
|
|
return mesh
|
||
|
|
|
||
|
|
|
||
|
|
def filter_taubin(mesh,
|
||
|
|
lamb=0.5,
|
||
|
|
nu=0.5,
|
||
|
|
iterations=10,
|
||
|
|
laplacian_operator=None):
|
||
|
|
"""
|
||
|
|
Smooth a mesh in-place using laplacian smoothing
|
||
|
|
and taubin filtering.
|
||
|
|
|
||
|
|
Articles
|
||
|
|
"Improved Laplacian Smoothing of Noisy Surface Meshes"
|
||
|
|
J. Vollmer, R. Mencl, and H. Muller
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
------------
|
||
|
|
mesh : trimesh.Trimesh
|
||
|
|
Mesh to be smoothed in place.
|
||
|
|
lamb : float
|
||
|
|
Controls shrinkage, range is 0.0 - 1.0
|
||
|
|
nu : float
|
||
|
|
Controls dilation, range is 0.0 - 1.0
|
||
|
|
Nu shall be between 0.0 < 1.0/lambda - 1.0/nu < 0.1
|
||
|
|
iterations : int
|
||
|
|
Number of passes to run the filter
|
||
|
|
laplacian_operator : None or scipy.sparse.coo.coo_matrix
|
||
|
|
Sparse matrix laplacian operator
|
||
|
|
Will be autogenerated if None
|
||
|
|
"""
|
||
|
|
# if the laplacian operator was not passed create it here
|
||
|
|
if laplacian_operator is None:
|
||
|
|
laplacian_operator = laplacian_calculation(mesh)
|
||
|
|
|
||
|
|
# get mesh vertices as vanilla numpy array
|
||
|
|
vertices = mesh.vertices.copy().view(np.ndarray)
|
||
|
|
|
||
|
|
# run through multiple passes of the filter
|
||
|
|
for index in range(iterations):
|
||
|
|
# do a sparse dot product on the vertices
|
||
|
|
dot = laplacian_operator.dot(vertices) - vertices
|
||
|
|
# alternate shrinkage and dilation
|
||
|
|
if index % 2 == 0:
|
||
|
|
vertices += lamb * dot
|
||
|
|
else:
|
||
|
|
vertices -= nu * dot
|
||
|
|
|
||
|
|
# assign updated vertices back to mesh
|
||
|
|
mesh.vertices = vertices
|
||
|
|
return mesh
|
||
|
|
|
||
|
|
|
||
|
|
def laplacian_calculation(mesh, equal_weight=True):
|
||
|
|
"""
|
||
|
|
Calculate a sparse matrix for laplacian operations.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
-------------
|
||
|
|
mesh : trimesh.Trimesh
|
||
|
|
Input geometry
|
||
|
|
equal_weight : bool
|
||
|
|
If True, all neighbors will be considered equally
|
||
|
|
If False, all neighbors will be weighted by inverse distance
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
laplacian : scipy.sparse.coo.coo_matrix
|
||
|
|
Laplacian operator
|
||
|
|
"""
|
||
|
|
# get the vertex neighbors from the cache
|
||
|
|
neighbors = mesh.vertex_neighbors
|
||
|
|
# avoid hitting crc checks in loops
|
||
|
|
vertices = mesh.vertices.view(np.ndarray)
|
||
|
|
|
||
|
|
# stack neighbors to 1D arrays
|
||
|
|
col = np.concatenate(neighbors)
|
||
|
|
row = np.concatenate([[i] * len(n)
|
||
|
|
for i, n in enumerate(neighbors)])
|
||
|
|
|
||
|
|
if equal_weight:
|
||
|
|
# equal weights for each neighbor
|
||
|
|
data = np.concatenate([[1.0 / len(n)] * len(n)
|
||
|
|
for n in neighbors])
|
||
|
|
else:
|
||
|
|
# umbrella weights, distance-weighted
|
||
|
|
# use dot product of ones to replace array.sum(axis=1)
|
||
|
|
ones = np.ones(3)
|
||
|
|
# the distance from verticesex to neighbors
|
||
|
|
norms = [1.0 / np.sqrt(np.dot((vertices[i] - vertices[n]) ** 2, ones))
|
||
|
|
for i, n in enumerate(neighbors)]
|
||
|
|
# normalize group and stack into single array
|
||
|
|
data = np.concatenate([i / i.sum() for i in norms])
|
||
|
|
|
||
|
|
# create the sparse matrix
|
||
|
|
matrix = coo_matrix((data, (row, col)),
|
||
|
|
shape=[len(vertices)] * 2)
|
||
|
|
|
||
|
|
return matrix
|