symcad.core.HelperMethods

 1#!/usr/bin/env python3
 2# Copyright (C) 2022, Will Hedgecock
 3#
 4# This program is free software: you can redistribute it and/or modify
 5# it under the terms of the GNU General Public License as published by
 6# the Free Software Foundation, either version 3 of the License, or
 7# (at your option) any later version.
 8#
 9# This program is distributed in the hope that it will be useful,
10# but WITHOUT ANY WARRANTY; without even the implied warranty of
11# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
12# GNU General Public License for more details.
13#
14# You should have received a copy of the GNU General Public License
15# along with this program.  If not, see <http://www.gnu.org/licenses/>.
16
17from __future__ import annotations
18from typing import List, Tuple, Union
19from sympy import Expr
20import math
21
22def spherical_points(*, num_points: int,
23                        radius: Union[float, Expr],
24                        center_x: Union[float, Expr],
25                        center_y: Union[float, Expr],
26                        center_z: Union[float, Expr]) -> List[Tuple[float, float, float]]:
27   points = []
28   for i in range(1, num_points + 1):
29      h = -1.0 + 2.0 * (i - 1) / (num_points - 1)
30      theta = math.acos(h)
31      phi = 0 if i == 1 or i == num_points else phi + (3.6 / math.sqrt(num_points * (1.0 - h**2)))
32      points.append((center_x + (math.sin(phi) * math.sin(theta) * radius),
33                     center_y + (math.cos(phi) * math.sin(theta) * radius),
34                     center_z - (math.cos(theta) * radius)))
35      phi %= (2.0 * math.pi)
36   return points