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feat: better sampling on a sphere

This commit is contained in:
weipengOO98 2022-07-11 11:13:31 +08:00
parent b0a8e72557
commit 6d89a6908f
1 changed files with 16 additions and 6 deletions
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22
idrlnet/geo_utils/geo_obj.py
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@ -4,7 +4,7 @@ import math
from math import pi from math import pi
from typing import Union, List, Tuple from typing import Union, List, Tuple
import numpy as np import numpy as np
from sympy import symbols, Abs, sqrt, Max, Min, cos, sin, log, sign, Heaviside from sympy import symbols, Abs, sqrt, Max, Min, cos, sin, log, sign, Heaviside, asin
from sympy.vector import CoordSys3D from sympy.vector import CoordSys3D
from .geo import Edge, Geometry1D, Geometry2D, Geometry3D from .geo import Edge, Geometry1D, Geometry2D, Geometry3D
@ -662,11 +662,21 @@ class Box(Geometry3D):
class Sphere(Geometry3D): class Sphere(Geometry3D):
def __init__(self, center, radius): def __init__(self, center, radius):
x, y, z, v_1, v_2, u_1, u_2 = symbols("x y z v_1 v_2 u_1 u_2") x, y, z, v_1, v_2 = symbols("x y z v_1 v_2")
ranges = {v_1: (0, 1), v_2: (0, 1), u_1: (0, 1), u_2: (0, 1)} ranges = {v_1: (0, 1), v_2: (0, 1)}
r_1 = sqrt(-log(v_1)) * cos(2 * pi * u_1)
r_2 = sqrt(-log(v_1)) * sin(2 * pi * u_1) theta = 2 * pi * v_1
r_3 = sqrt(-log(v_2)) * cos(2 * pi * u_2) r = sqrt(v_2)
phi = 2 * asin(r) # latitude
r_1 = cos(theta) * sin(phi)
r_2 = sin(theta) * sin(phi)
r_3 = cos(phi)
# x, y, z, v_1, v_2, u_1, u_2 = symbols("x y z v_1 v_2 u_1 u_2")
# ranges = {v_1: (0, 1), v_2: (0, 1), u_1: (0, 1), u_2: (0, 1)}
# r_1 = sqrt(-log(v_1)) * cos(2 * pi * u_1)
# r_2 = sqrt(-log(v_1)) * sin(2 * pi * u_1)
# r_3 = sqrt(-log(v_2)) * cos(2 * pi * u_2)
norm = sqrt(r_1 ** 2 + r_2 ** 2 + r_3 ** 2) norm = sqrt(r_1 ** 2 + r_2 ** 2 + r_3 ** 2)
edge_1 = Edge( edge_1 = Edge(