deeplearning/modulus/modulus-sym-v130/_modules/modulus/sym/geometry/tessellation.html
Source code for modulus.sym.geometry.tessellation
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"""
Defines base class for all mesh type geometries
"""
import numpy as np
import csv
from stl import mesh as np_mesh
from sympy import Symbol
try:
import pysdf.sdf as pysdf
except:
print(
"Error importing pysdf. Make sure 'libsdf.so' is in LD_LIBRARY_PATH and pysdf is installed"
)
raise
from .geometry import Geometry
from .parameterization import Parameterization, Bounds, Parameter
from .curve import Curve
from modulus.sym.constants import diff_str
[docs]class Tessellation(Geometry):
"""
Constructive Tessellation Module that allows sampling on surface and interior
of a tessellated geometry.
Parameters
----------
mesh : Mesh (numpy-stl)
A mesh that defines the surface of the geometry.
airtight : bool
If the geometry is airtight or not. If false sample everywhere for interior.
parameterization : Parameterization
Parameterization of geometry.
"""
def __init__(self, mesh, airtight=True, parameterization=Parameterization()):
# make curves
def _sample(mesh):
def sample(
nr_points, parameterization=Parameterization(), quasirandom=False
):
# compute required points on per triangle
triangle_areas = _area_of_triangles(mesh.v0, mesh.v1, mesh.v2)
triangle_probabilities = triangle_areas / np.linalg.norm(
triangle_areas, ord=1
)
triangle_index = np.arange(triangle_probabilities.shape[0])
points_per_triangle = np.random.choice(
triangle_index, nr_points, p=triangle_probabilities
)
points_per_triangle, _ = np.histogram(
points_per_triangle,
np.arange(triangle_probabilities.shape[0] + 1) - 0.5,
)
# go through every triangle and sample it
invar = {
"x": [],
"y": [],
"z": [],
"normal_x": [],
"normal_y": [],
"normal_z": [],
"area": [],
}
for index, nr_p in enumerate(
points_per_triangle
): # TODO can be more efficent
x, y, z = _sample_triangle(
mesh.v0[index], mesh.v1[index], mesh.v2[index], nr_p
)
invar["x"].append(x)
invar["y"].append(y)
invar["z"].append(z)
normal_scale = np.linalg.norm(mesh.normals[index])
invar["normal_x"].append(
np.full(x.shape, mesh.normals[index, 0]) / normal_scale
)
invar["normal_y"].append(
np.full(x.shape, mesh.normals[index, 1]) / normal_scale
)
invar["normal_z"].append(
np.full(x.shape, mesh.normals[index, 2]) / normal_scale
)
invar["area"].append(
np.full(x.shape, triangle_areas[index] / x.shape[0])
)
invar["x"] = np.concatenate(invar["x"], axis=0)
invar["y"] = np.concatenate(invar["y"], axis=0)
invar["z"] = np.concatenate(invar["z"], axis=0)
invar["normal_x"] = np.concatenate(invar["normal_x"], axis=0)
invar["normal_y"] = np.concatenate(invar["normal_y"], axis=0)
invar["normal_z"] = np.concatenate(invar["normal_z"], axis=0)
invar["area"] = np.concatenate(invar["area"], axis=0)
# sample from the param ranges
params = parameterization.sample(nr_points, quasirandom=quasirandom)
return invar, params
return sample
curves = [Curve(_sample(mesh), dims=3, parameterization=parameterization)]
# make sdf function
def _sdf(triangles, airtight):
def sdf(invar, params, compute_sdf_derivatives=False):
# gather points
points = np.stack([invar["x"], invar["y"], invar["z"]], axis=1)
# normalize triangles and points
minx, maxx, miny, maxy, minz, maxz = _find_mins_maxs(points)
max_dis = max(max((maxx - minx), (maxy - miny)), (maxz - minz))
store_triangles = np.array(triangles, dtype=np.float64)
store_triangles[:, :, 0] -= minx
store_triangles[:, :, 1] -= miny
store_triangles[:, :, 2] -= minz
store_triangles *= 1 / max_dis
store_triangles = store_triangles.flatten()
points[:, 0] -= minx
points[:, 1] -= miny
points[:, 2] -= minz
points *= 1 / max_dis
points = points.astype(np.float64).flatten()
# compute sdf values
outputs = {}
if airtight:
sdf_field, sdf_derivative = pysdf.signed_distance_field(
store_triangles, points, include_hit_points=True
)
sdf_field = -np.expand_dims(max_dis * sdf_field, axis=1)
else:
sdf_field = np.zeros_like(invar["x"])
outputs["sdf"] = sdf_field
# get sdf derivatives
if compute_sdf_derivatives:
sdf_derivative = -(sdf_derivative - points)
sdf_derivative = np.reshape(
sdf_derivative, (sdf_derivative.shape[0] // 3, 3)
)
sdf_derivative = sdf_derivative / np.linalg.norm(
sdf_derivative, axis=1, keepdims=True
)
outputs["sdf" + diff_str + "x"] = sdf_derivative[:, 0:1]
outputs["sdf" + diff_str + "y"] = sdf_derivative[:, 1:2]
outputs["sdf" + diff_str + "z"] = sdf_derivative[:, 2:3]
return outputs
return sdf
# compute bounds
bounds = Bounds(
{
Parameter("x"): (
float(np.min(mesh.vectors[:, :, 0])),
float(np.max(mesh.vectors[:, :, 0])),
),
Parameter("y"): (
float(np.min(mesh.vectors[:, :, 1])),
float(np.max(mesh.vectors[:, :, 1])),
),
Parameter("z"): (
float(np.min(mesh.vectors[:, :, 2])),
float(np.max(mesh.vectors[:, :, 2])),
),
},
parameterization=parameterization,
)
# initialize geometry
super(Tessellation, self).__init__(
curves,
_sdf(mesh.vectors, airtight),
dims=3,
bounds=bounds,
parameterization=parameterization,
)
[docs] @classmethod
def from_stl(
cls,
filename,
airtight=True,
parameterization=Parameterization(),
):
"""
makes mesh from STL file
Parameters
----------
filename : str
filename of mesh.
airtight : bool
If the geometry is airtight or not. If false sample everywhere for interior.
parameterization : Parameterization
Parameterization of geometry.
"""
# read in mesh
mesh = np_mesh.Mesh.from_file(filename)
return cls(mesh, airtight, parameterization)# helper for sampling triangle
def _sample_triangle(
v0, v1, v2, nr_points
): # ref https://math.stackexchange.com/questions/18686/uniform-random-point-in-triangle
r1 = np.random.uniform(0, 1, size=(nr_points, 1))
r2 = np.random.uniform(0, 1, size=(nr_points, 1))
s1 = np.sqrt(r1)
x = v0[0] * (1.0 - s1) + v1[0] * (1.0 - r2) * s1 + v2[0] * r2 * s1
y = v0[1] * (1.0 - s1) + v1[1] * (1.0 - r2) * s1 + v2[1] * r2 * s1
z = v0[2] * (1.0 - s1) + v1[2] * (1.0 - r2) * s1 + v2[2] * r2 * s1
return x, y, z
# area of array of triangles
def _area_of_triangles(
v0, v1, v2
): # ref https://math.stackexchange.com/questions/128991/how-to-calculate-the-area-of-a-3d-triangle
a = np.sqrt(
(v0[:, 0] - v1[:, 0]) ** 2
+ (v0[:, 1] - v1[:, 1]) ** 2
+ (v0[:, 2] - v1[:, 2]) ** 2
+ 1e-10
)
b = np.sqrt(
(v1[:, 0] - v2[:, 0]) ** 2
+ (v1[:, 1] - v2[:, 1]) ** 2
+ (v1[:, 2] - v2[:, 2]) ** 2
+ 1e-10
)
c = np.sqrt(
(v0[:, 0] - v2[:, 0]) ** 2
+ (v0[:, 1] - v2[:, 1]) ** 2
+ (v0[:, 2] - v2[:, 2]) ** 2
+ 1e-10
)
s = (a + b + c) / 2
area = np.sqrt(s * (s - a) * (s - b) * (s - c) + 1e-10)
return area
# helper for min max
def _find_mins_maxs(points):
minx = float(np.min(points[:, 0]))
miny = float(np.min(points[:, 1]))
minz = float(np.min(points[:, 2]))
maxx = float(np.max(points[:, 0]))
maxy = float(np.max(points[:, 1]))
maxz = float(np.max(points[:, 2]))
return minx, maxx, miny, maxy, minz, maxz