deeplearning/modulus/modulus-sym/_modules/modulus/sym/geometry/geometry.html
Source code for modulus.sym.geometry.geometry
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# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License");
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"""
Defines base class for all geometries
"""
import copy
import numpy as np
import itertools
import sympy
from typing import Callable, Union, List
from modulus.sym.utils.sympy import np_lambdify
from modulus.sym.constants import diff_str
from .parameterization import Parameterization, Bounds
from .helper import (
_concat_numpy_dict_list,
_sympy_sdf_to_sdf,
_sympy_criteria_to_criteria,
_sympy_func_to_func,
)
def csg_curve_naming(index):
return "PRIMITIVE_PARAM_" + str(index).zfill(5)
[docs]class Geometry:
"""
Base class for all geometries
"""
def __init__(
self,
curves,
sdf,
dims,
bounds,
parameterization=Parameterization(),
interior_epsilon=1e-6,
):
# store attributes
self.curves = curves
self.sdf = sdf
self._dims = dims
self.bounds = bounds
self.parameterization = parameterization
self.interior_epsilon = interior_epsilon # to check if in domain or outside
@property
def dims(self):
"""
Returns
-------
dims : List[srt]
output can be ['x'], ['x','y'], or ['x','y','z']
"""
return ["x", "y", "z"][: self._dims]
[docs] def scale(
self,
x: Union[float, sympy.Basic],
parameterization: Parameterization = Parameterization(),
):
"""
Scales geometry.
Parameters
----------
x : Union[float, sympy.Basic]
Scale factor. Can be a sympy expression if parameterizing.
parameterization : Parameterization
Parameterization if scale factor is parameterized.
"""
# create scaled sdf function
def _scale_sdf(sdf, dims, x):
if isinstance(x, (float, int)):
pass
elif isinstance(x, sympy.Basic):
x = _sympy_func_to_func(x)
else:
raise TypeError("Scaling by type " + str(type(x)) + "is not supported")
def scale_sdf(invar, params, compute_sdf_derivatives=False):
# compute scale if needed
if isinstance(x, (float, int)):
computed_scale = x
else:
computed_scale = x(params)
# scale input to sdf function
scaled_invar = {**invar}
for key in dims:
scaled_invar[key] = scaled_invar[key] / computed_scale
# compute sdf
computed_sdf = sdf(scaled_invar, params, compute_sdf_derivatives)
# scale output sdf values
if isinstance(x, (float, int)):
computed_sdf["sdf"] *= x
else:
computed_sdf["sdf"] *= x(params)
return computed_sdf
return scale_sdf
new_sdf = _scale_sdf(self.sdf, self.dims, x)
# add parameterization
new_parameterization = self.parameterization.union(parameterization)
# scale bounds
new_bounds = self.bounds.scale(x, parameterization)
# scale curves
new_curves = [c.scale(x, parameterization) for c in self.curves]
# return scaled geometry
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
[docs] def translate(
self,
xyz: List[Union[float, sympy.Basic]],
parameterization: Parameterization = Parameterization(),
):
"""
Translates geometry.
Parameters
----------
xyz : List[Union[float, sympy.Basic]]
Translation. Can be a sympy expression if parameterizing.
parameterization : Parameterization
Parameterization if translation is parameterized.
"""
# create translated sdf function
def _translate_sdf(sdf, dims, xyx):
compiled_xyz = []
for i, x in enumerate(xyz):
if isinstance(x, (float, int)):
compiled_xyz.append(x)
elif isinstance(x, sympy.Basic):
compiled_xyz.append(_sympy_func_to_func(x))
else:
raise TypeError(
"Translate by type " + str(type(x)) + "is not supported"
)
def translate_sdf(invar, params, compute_sdf_derivatives=False):
# compute translation if needed
computed_translation = []
for x in compiled_xyz:
if isinstance(x, (float, int)):
computed_translation.append(x)
else:
computed_translation.append(x(params))
# translate input to sdf function
translated_invar = {**invar}
for i, key in enumerate(dims):
translated_invar[key] = (
translated_invar[key] - computed_translation[i]
)
# compute sdf
computed_sdf = sdf(translated_invar, params, compute_sdf_derivatives)
return computed_sdf
return translate_sdf
new_sdf = _translate_sdf(self.sdf, self.dims, xyz)
# add parameterization
new_parameterization = self.parameterization.union(parameterization)
# translate bounds
new_bounds = self.bounds.translate(xyz, parameterization)
# translate curves
new_curves = [c.translate(xyz, parameterization) for c in self.curves]
# return translated geometry
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
[docs] def rotate(
self,
angle: Union[float, sympy.Basic],
axis: str = "z",
center: Union[None, List[float]] = None,
parameterization=Parameterization(),
):
"""
Rotates geometry.
Parameters
----------
angle : Union[float, sympy.Basic]
Angle of rotate in radians. Can be a sympy expression if parameterizing.
axis : str
Axis of rotation. Default is `"z"`.
center : Union[None, List[Union[float, sympy.Basic]]] = None
If given then center the rotation around this point.
parameterization : Parameterization
Parameterization if translation is parameterized.
"""
# create rotated sdf function
def _rotate_sdf(sdf, dims, angle, axis, center):
if isinstance(angle, (float, int)):
pass
elif isinstance(angle, sympy.Basic):
angle = _sympy_func_to_func(angle)
else:
raise TypeError(
"Scaling by type " + str(type(angle)) + "is not supported"
)
def rotate_sdf(invar, params, compute_sdf_derivatives=False):
# compute translation if needed
if isinstance(angle, (float, int)):
computed_angle = angle
else:
computed_angle = angle(params)
# rotate input to sdf function
rotated_invar = {**invar}
if center is not None:
for i, key in enumerate(dims):
rotated_invar[key] = rotated_invar[key] - center[i]
_rotated_invar = {**rotated_invar}
rotated_dims = [key for key in dims if key != axis]
_rotated_invar[rotated_dims[0]] = (
np.cos(computed_angle) * rotated_invar[rotated_dims[0]]
+ np.sin(computed_angle) * rotated_invar[rotated_dims[1]]
)
_rotated_invar[rotated_dims[1]] = (
-np.sin(computed_angle) * rotated_invar[rotated_dims[0]]
+ np.cos(computed_angle) * rotated_invar[rotated_dims[1]]
)
if center is not None:
for i, key in enumerate(dims):
_rotated_invar[key] = _rotated_invar[key] + center[i]
# compute sdf
computed_sdf = sdf(_rotated_invar, params, compute_sdf_derivatives)
return computed_sdf
return rotate_sdf
new_sdf = _rotate_sdf(self.sdf, self.dims, angle, axis, center)
# add parameterization
new_parameterization = self.parameterization.union(parameterization)
# rotate bounds
if center is not None:
new_bounds = self.bounds.translate([-x for x in center])
new_bounds = new_bounds.rotate(angle, axis, parameterization)
new_bounds = new_bounds.translate(center)
else:
new_bounds = self.bounds.rotate(angle, axis, parameterization)
# rotate curves
new_curves = []
for c in self.curves:
if center is not None:
new_c = c.translate([-x for x in center])
new_c = new_c.rotate(angle, axis, parameterization)
new_c = new_c.translate(center)
else:
new_c = c.rotate(angle, axis, parameterization)
new_curves.append(new_c)
# return rotated geometry
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
[docs] def repeat(
self,
spacing: float,
repeat_lower: List[int],
repeat_higher: List[int],
center: Union[None, List[float]] = None,
):
"""
Finite Repetition of geometry.
Parameters
----------
spacing : float
Spacing between each repetition.
repeat_lower : List[int]
How many repetitions going in negative direction.
repeat_upper : List[int]
How many repetitions going in positive direction.
center : Union[None, List[Union[float, sympy.Basic]]] = None
If given then center the rotation around this point.
"""
# create repeated sdf function
def _repeat_sdf(
sdf, dims, spacing, repeat_lower, repeat_higher, center
): # TODO make spacing, repeat_lower, and repeat_higher parameterizable
def repeat_sdf(invar, params, compute_sdf_derivatives=False):
# clamp position values
clamped_invar = {**invar}
if center is not None:
for i, key in enumerate(dims):
clamped_invar[key] = clamped_invar[key] - center[i]
for d, rl, rh in zip(dims, repeat_lower, repeat_higher):
clamped_invar[d] = clamped_invar[d] - spacing * np.minimum(
np.maximum(np.around(clamped_invar[d] / spacing), rl), rh
)
if center is not None:
for i, key in enumerate(dims):
clamped_invar[key] = clamped_invar[key] + center[i]
# compute sdf
computed_sdf = sdf(clamped_invar, params, compute_sdf_derivatives)
return computed_sdf
return repeat_sdf
new_sdf = _repeat_sdf(
self.sdf, self.dims, spacing, repeat_lower, repeat_higher, center
)
# repeat bounds and curves
new_bounds = self.bounds.copy()
new_curves = []
for t in itertools.product(
*[list(range(rl, rh + 1)) for rl, rh in zip(repeat_lower, repeat_higher)]
):
new_bounds = new_bounds.union(
self.bounds.translate([spacing * a for a in t])
)
new_curves += [c.translate([spacing * a for a in t]) for c in self.curves]
# return repeated geometry
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
self.parameterization.copy(),
interior_epsilon=self.interior_epsilon,
)def copy(self):
return copy.deepcopy(self)
def boundary_criteria(self, invar, criteria=None, params={}):
# check if moving in or out of normal direction changes SDF
invar_normal_plus = {**invar}
invar_normal_minus = {**invar}
for key in self.dims:
invar_normal_plus[key] = (
invar_normal_plus[key]
+ self.interior_epsilon * invar_normal_plus["normal_" + key]
)
invar_normal_minus[key] = (
invar_normal_minus[key]
- self.interior_epsilon * invar_normal_minus["normal_" + key]
)
sdf_normal_plus = self.sdf(
invar_normal_plus, params, compute_sdf_derivatives=False
)["sdf"]
sdf_normal_minus = self.sdf(
invar_normal_minus, params, compute_sdf_derivatives=False
)["sdf"]
on_boundary = np.greater_equal(0, sdf_normal_plus * sdf_normal_minus)
# check if points satisfy the criteria function
if criteria is not None:
# convert sympy criteria if needed
satify_criteria = criteria(invar, params)
# update on_boundary
on_boundary = np.logical_and(on_boundary, satify_criteria)
return on_boundary
[docs] def sample_boundary(
self,
nr_points: int,
criteria: Union[sympy.Basic, None] = None,
parameterization: Union[Parameterization, None] = None,
quasirandom: bool = False,
):
"""
Samples the surface or perimeter of the geometry.
Parameters
----------
nr_points : int
number of points to sample on boundary.
criteria : Union[sympy.Basic, None]
Only sample points that satisfy this criteria.
parameterization : Union[Parameterization, None], optional
If the geometry is parameterized then you can provide ranges
for the parameters with this. By default the sampling will be
done with the internal parameterization.
quasirandom : bool
If true then sample the points using the Halton sequences.
Default is False.
Returns
-------
points : Dict[str, np.ndarray]
Dictionary contain a point cloud sampled uniformly.
For example in 2D it would be
```
points = {'x': np.ndarray (N, 1),
'y': np.ndarray (N, 1),
'normal_x': np.ndarray (N, 1),
'normal_y': np.ndarray (N, 1),
'area': np.ndarray (N, 1)}
```
The `area` value can be used for Monte Carlo integration
like the following,
`total_area = np.sum(points['area'])`
"""
# compile criteria from sympy if needed
if criteria is not None:
if isinstance(criteria, sympy.Basic):
criteria = _sympy_criteria_to_criteria(criteria)
elif isinstance(criteria, Callable):
pass
else:
raise TypeError(
"criteria type is not supported: " + str(type(criteria))
)
# use internal parameterization if not given
if parameterization is None:
parameterization = self.parameterization
elif isinstance(parameterization, dict):
parameterization = Parameterization(parameterization)
# create boundary criteria closure
def _boundary_criteria(criteria):
def boundary_criteria(invar, params):
return self.boundary_criteria(invar, criteria=criteria, params=params)
return boundary_criteria
closed_boundary_criteria = _boundary_criteria(criteria)
# compute required points on each curve
curve_areas = np.array(
[
curve.approx_area(parameterization, criteria=closed_boundary_criteria)
for curve in self.curves
]
)
assert np.sum(curve_areas) > 0, "Geometry has no surface"
curve_probabilities = curve_areas / np.linalg.norm(curve_areas, ord=1)
curve_index = np.arange(len(self.curves))
points_per_curve = np.random.choice(
curve_index, nr_points, p=curve_probabilities
)
points_per_curve, _ = np.histogram(
points_per_curve, np.arange(len(self.curves) + 1) - 0.5
)
# continually sample each curve until reached desired number of points
list_invar = []
list_params = []
for n, a, curve in zip(points_per_curve, curve_areas, self.curves):
if n > 0:
i, p = curve.sample(
n,
criteria=closed_boundary_criteria,
parameterization=parameterization,
)
i["area"] = np.full_like(i["area"], a / n)
list_invar.append(i)
list_params.append(p)
invar = _concat_numpy_dict_list(list_invar)
params = _concat_numpy_dict_list(list_params)
invar.update(params)
return invar
[docs] def sample_interior(
self,
nr_points: int,
bounds: Union[Bounds, None] = None,
criteria: Union[sympy.Basic, None] = None,
parameterization: Union[Parameterization, None] = None,
compute_sdf_derivatives: bool = False,
quasirandom: bool = False,
flip_interior: bool = False,
):
"""
Samples the interior of the geometry.
Parameters
----------
nr_points : int
number of points to sample.
bounds : Union[Bounds, None]
Bounds to sample points from. For example,
`bounds = Bounds({Parameter('x'): (0, 1), Parameter('y'): (0, 1)})`.
By default the internal bounds will be used.
criteria : Union[sympy.Basic, None]
Only sample points that satisfy this criteria.
parameterization: Union[Parameterization, None]
If the geometry is parameterized then you can provide ranges
for the parameters with this.
compute_sdf_derivatives : bool
Compute sdf derivatives if true.
quasirandom : bool
If true then sample the points using the Halton sequences.
Default is False.
flip_interior : bool
If true, then instead of sampling inside the geometry, the
points are sampled in the region defined between bounds and geometry.
Returns
-------
points : Dict[str, np.ndarray]
Dictionary contain a point cloud sampled uniformly.
For example in 2D it would be
```
points = {'x': np.ndarray (N, 1),
'y': np.ndarray (N, 1),
'sdf': np.ndarray (N, 1),
'area': np.ndarray (N, 1)}
```
The `area` value can be used for Monte Carlo integration
like the following,
`total_area = np.sum(points['area'])`
"""
# compile criteria from sympy if needed
if criteria is not None:
if isinstance(criteria, sympy.Basic):
criteria = _sympy_criteria_to_criteria(criteria)
elif isinstance(criteria, Callable):
pass
else:
raise TypeError(
"criteria type is not supported: " + str(type(criteria))
)
# use internal bounds if not given
if bounds is None:
bounds = self.bounds
elif isinstance(bounds, dict):
bounds = Bounds(bounds)
# use internal parameterization if not given
if parameterization is None:
parameterization = self.parameterization
elif isinstance(parameterization, dict):
parameterization = Parameterization(parameterization)
# continually sample until reached desired number of points
invar = {}
params = {}
total_tried = 0
nr_try = 0
while True:
# sample invar and params
local_invar = bounds.sample(nr_points, parameterization, quasirandom)
local_params = parameterization.sample(nr_points, quasirandom)
# evaluate SDF function on points
local_invar.update(
self.sdf(
local_invar,
local_params,
compute_sdf_derivatives=compute_sdf_derivatives,
)
)
# remove points inside/outside of domain
if flip_interior:
criteria_index = np.less(local_invar["sdf"], 0)
else:
criteria_index = np.greater(local_invar["sdf"], 0)
if criteria is not None:
criteria_index = np.logical_and(
criteria_index, criteria(local_invar, local_params)
)
for key in local_invar.keys():
local_invar[key] = local_invar[key][criteria_index[:, 0], :]
for key in local_params.keys():
local_params[key] = local_params[key][criteria_index[:, 0], :]
# add sampled points to list
for key in local_invar.keys():
if key not in invar.keys(): # TODO this can be condensed
invar[key] = local_invar[key]
else:
invar[key] = np.concatenate([invar[key], local_invar[key]], axis=0)
for key in local_params.keys():
if key not in params.keys(): # TODO this can be condensed
params[key] = local_params[key]
else:
params[key] = np.concatenate(
[params[key], local_params[key]], axis=0
)
# check if finished
total_sampled = next(iter(invar.values())).shape[0]
total_tried += nr_points
nr_try += 1
if total_sampled >= nr_points:
for key, value in invar.items():
invar[key] = value[:nr_points]
for key, value in params.items():
params[key] = value[:nr_points]
break
# report error if could not sample
if nr_try > 100 and total_sampled < 1:
raise RuntimeError(
"Could not sample interior of geometry. Check to make sure non-zero volume"
)
# compute area value for monte carlo integration
volume = (total_sampled / total_tried) * bounds.volume(parameterization)
invar["area"] = np.full_like(next(iter(invar.values())), volume / nr_points)
# add params to invar
invar.update(params)
return invar@staticmethod
def _convert_criteria(criteria):
return criteria
def __add__(self, other):
def _add_sdf(sdf_1, sdf_2, dims):
def add_sdf(invar, params, compute_sdf_derivatives=False):
computed_sdf_1 = sdf_1(invar, params, compute_sdf_derivatives)
computed_sdf_2 = sdf_2(invar, params, compute_sdf_derivatives)
computed_sdf = {}
computed_sdf["sdf"] = np.maximum(
computed_sdf_1["sdf"], computed_sdf_2["sdf"]
)
if compute_sdf_derivatives:
for d in dims:
computed_sdf["sdf" + diff_str + d] = np.where(
computed_sdf_1["sdf"] > computed_sdf_2["sdf"],
computed_sdf_1["sdf" + diff_str + d],
computed_sdf_2["sdf" + diff_str + d],
)
return computed_sdf
return add_sdf
new_sdf = _add_sdf(self.sdf, other.sdf, self.dims)
new_parameterization = self.parameterization.union(other.parameterization)
new_bounds = self.bounds.union(other.bounds)
return Geometry(
self.curves + other.curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
def __sub__(self, other):
def _sub_sdf(sdf_1, sdf_2, dims):
def sub_sdf(invar, params, compute_sdf_derivatives=False):
computed_sdf_1 = sdf_1(invar, params, compute_sdf_derivatives)
computed_sdf_2 = sdf_2(invar, params, compute_sdf_derivatives)
computed_sdf = {}
computed_sdf["sdf"] = np.minimum(
computed_sdf_1["sdf"], -computed_sdf_2["sdf"]
)
if compute_sdf_derivatives:
for d in dims:
computed_sdf["sdf" + diff_str + d] = np.where(
computed_sdf_1["sdf"] < -computed_sdf_2["sdf"],
computed_sdf_1["sdf" + diff_str + d],
-computed_sdf_2["sdf" + diff_str + d],
)
return computed_sdf
return sub_sdf
new_sdf = _sub_sdf(self.sdf, other.sdf, self.dims)
new_parameterization = self.parameterization.union(other.parameterization)
new_bounds = self.bounds.union(other.bounds)
new_curves = self.curves + [c.invert_normal() for c in other.curves]
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
def __invert__(self):
def _invert_sdf(sdf, dims):
def invert_sdf(invar, params, compute_sdf_derivatives=False):
computed_sdf = sdf(invar, params, compute_sdf_derivatives)
computed_sdf["sdf"] = -computed_sdf["sdf"]
if compute_sdf_derivatives:
for d in dims:
computed_sdf["sdf" + diff_str + d] = -computed_sdf[
"sdf" + diff_str + d
]
return computed_sdf
return invert_sdf
new_sdf = _invert_sdf(self.sdf, self.dims)
new_parameterization = self.parameterization.copy()
new_bounds = self.bounds.copy()
new_curves = [c.invert_normal() for c in self.curves]
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)
def __and__(self, other):
def _and_sdf(sdf_1, sdf_2, dims):
def and_sdf(invar, params, compute_sdf_derivatives=False):
computed_sdf_1 = sdf_1(invar, params, compute_sdf_derivatives)
computed_sdf_2 = sdf_2(invar, params, compute_sdf_derivatives)
computed_sdf = {}
computed_sdf["sdf"] = np.minimum(
computed_sdf_1["sdf"], computed_sdf_2["sdf"]
)
if compute_sdf_derivatives:
for d in dims:
computed_sdf["sdf" + diff_str + d] = np.where(
computed_sdf_1["sdf"] < computed_sdf_2["sdf"],
computed_sdf_1["sdf" + diff_str + d],
computed_sdf_2["sdf" + diff_str + d],
)
return computed_sdf
return and_sdf
new_sdf = _and_sdf(self.sdf, other.sdf, self.dims)
new_parameterization = self.parameterization.union(other.parameterization)
new_bounds = self.bounds.union(other.bounds)
new_curves = self.curves + other.curves
return Geometry(
new_curves,
new_sdf,
len(self.dims),
new_bounds,
new_parameterization,
interior_epsilon=self.interior_epsilon,
)