NVIDIA Modulus Sym v1.2.0
Sym v1.2.0

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Source code for modulus.sym.geometry.geometry

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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, ): """ 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. 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 outside of domain 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, )

© Copyright 2023, NVIDIA Modulus Team. Last updated on Jan 25, 2024.