Source code for modulus.eq.pdes.signed_distance_function
"""Screened Poisson Distance
Equation taken from,
https://www.researchgate.net/publication/266149392_Dynamic_Distance-Based_Shape_Features_for_Gait_Recognition,
Equation 6 in paper.
"""
from sympy import Symbol, Function, sqrt
from modulus.eq.pde import PDE
[docs]class ScreenedPoissonDistance(PDE):
"""
Screened Poisson Distance
Parameters
==========
distance : str
A user-defined variable for distance.
Default is "normal_distance".
tau : float
A small, positive parameter. Default is 0.1.
dim : int
Dimension of the Screened Poisson Distance (1, 2, or 3).
Default is 3.
Example
========
>>> s = ScreenedPoissonDistance(tau=0.1, dim=2)
>>> s.pprint()
screened_poisson_normal_distance: -normal_distance__x**2
+ 0.316227766016838*normal_distance__x__x - normal_distance__y**2
+ 0.316227766016838*normal_distance__y__y + 1
"""
name = "ScreenedPoissonDistance"
def __init__(self, distance="normal_distance", tau=0.1, dim=3):
# set params
self.distance = distance
self.dim = dim
# coordinates
x, y, z = Symbol("x"), Symbol("y"), Symbol("z")
# make input variables
input_variables = {"x": x, "y": y, "z": z}
if self.dim == 1:
input_variables.pop("y")
input_variables.pop("z")
elif self.dim == 2:
input_variables.pop("z")
# distance u
assert type(distance) == str, "distance needs to be string"
distance = Function(distance)(*input_variables)
# set equations
self.equations = {}
sdf_grad = (
1 - distance.diff(x) ** 2 - distance.diff(y) ** 2 - distance.diff(z) ** 2
)
poisson = sqrt(tau) * (
distance.diff(x, 2) + distance.diff(y, 2) + distance.diff(z, 2)
)
self.equations["screened_poisson_" + self.distance] = sdf_grad + poisson