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AP_Math: add geodesic_grid toolset
That was used to aid development AP_GeodesicGrid and understanding its concepts.
This commit is contained in:
Gustavo Jose de Sousa
Lucas De Marchi
parent
9d34b3b996
commit
b3068baa11
6
libraries/AP_Math/tools/geodesic_grid/README.md
Normal file
6
libraries/AP_Math/tools/geodesic_grid/README.md
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# Geodesic Grid Tool #
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This folder a toolset for helping understanding the concepts used by
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[`AP_GeodesicGrid`](../../AP_GeodesicGrid.cpp) as well as for aiding its
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development. The main script is named `geodesic_grid.py`. Use `geodesic_grid.py
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--help` to know how to use it.
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291
libraries/AP_Math/tools/geodesic_grid/geodesic_grid.py
Executable file
291
libraries/AP_Math/tools/geodesic_grid/geodesic_grid.py
Executable file
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#!/usr/bin/python
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# Copyright (C) 2016 Intel Corporation. All rights reserved.
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#
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# This file is free software: you can redistribute it and/or modify it
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# under the terms of the GNU General Public License as published by the
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# Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This file is distributed in the hope that it will be useful, but
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# WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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# See the GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License along
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# with this program. If not, see <http://www.gnu.org/licenses/>.
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from __future__ import print_function
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import argparse
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import numpy as np
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import sys
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import icosahedron as ico
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def print_code_gen_notice():
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print("/* This was generated with")
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print(" * libraries/AP_Math/tools/geodesic_grid/geodesic_grid.py */")
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def header_neighbor_umbrella(index):
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t = ico.triangles[0]
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a, b, c = t
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triangle, edge = (
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( t, ( a, b)),
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( t, ( b, c)),
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( t, ( c, a)),
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(-t, (-a, -b)),
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(-t, (-b, -c)),
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(-t, (-c, -a)),
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)[index]
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return ico.neighbor_umbrella(triangle, edge), edge
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parser = argparse.ArgumentParser(
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description="""
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Utility script for helping to understand concepts used by AP_GeodesicGrid as
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well as for aiding its development.
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When passing a vertex as argument to one of the options, the valid values for
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the coordinates are 0, -1, 1, g and -g, where g is the golden ratio.
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""",
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)
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parser.add_argument(
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'-p', '--plot',
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action='store_true',
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help="""
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Plot results when applicable.
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""",
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)
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parser.add_argument(
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'-s', '--plot-subtriangles',
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action='store_true',
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help="""
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Plot subtriangles as well. This implies -p.
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""",
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)
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parser.add_argument(
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'--icosahedron',
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action='store_true',
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help='Get the icosahedron triangles.',
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)
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parser.add_argument(
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'-t', '--triangle',
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action='append',
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type=int,
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nargs='+',
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metavar='INDEX',
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help="""
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Get the icosahedron triangle at INDEX.
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""",
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)
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parser.add_argument(
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'-u', '--umbrella',
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action='append',
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nargs=3,
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metavar=('X', 'Y', 'Z'),
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help="""
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Get the umbrella with pivot denoted by (X, Y, Z). The pivot must be one of the
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icosahedron's vertices.
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""",
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)
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parser.add_argument(
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'-n', '--neighbor-umbrella',
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action='append',
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nargs='+',
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metavar='INDEX',
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help="""
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Get the neighbor umbrella at INDEX as described by _neighbor_umbrellas in
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AP_GeodesicGrid.h. The special value "all" for INDEX is also accepted, which
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will make it ignore other indexes passed and get all neighbor umbrellas for
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that member.
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""",
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)
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parser.add_argument(
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'--neighbor-umbrella-gen',
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action='store_true',
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help="""
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Generate C++ code for the initialization of the member _neighbor_umbrellas
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described in AP_GeodesicGrid.h.
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""",
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)
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parser.add_argument(
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'--inverses-gen',
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action='store_true',
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help="""
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Generate C++ code for the initialization of members _inverses and _mid_inverses
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declared in AP_GeodesicGrid.h.
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""")
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args = parser.parse_args()
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if args.plot_subtriangles:
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args.plot = True
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if args.plot:
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import plot
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polygons_to_plot = []
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if args.triangle:
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indexes = []
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for l in args.triangle:
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indexes += l
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for i in indexes:
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if 0 > i or i >= len(ico.triangles):
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print(
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'Triangle index must be in the range [0,%d)' % len(ico.triangles),
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file=sys.stderr,
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)
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sys.exit(1)
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print(ico.triangles[i])
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if args.plot:
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plot.polygon(ico.triangles[i])
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if args.umbrella:
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for pivot in args.umbrella:
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for i, x in enumerate(pivot):
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if x == 'g':
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x = ico.g
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elif x == '-g':
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x = -ico.g
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else:
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try:
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x = int(x)
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if x not in (0, -1, 1):
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raise ValueError()
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except ValueError:
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print(
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'umbrella: invalid pivot coordinate: %s' % str(x),
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file=sys.stderr,
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)
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sys.exit(1)
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pivot[i] = x
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pivot = ico.Vertex(*pivot)
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if pivot not in ico.vertices:
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print(
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'umbrella: invalid pivot:', pivot,
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file=sys.stderr,
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)
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sys.exit(1)
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u = ico.umbrella(pivot)
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print("Components of the umbrella of %s:" % str(pivot))
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for c in u.components:
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print(" %s" % str(c))
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if args.plot:
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plot.polygons(u.components)
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if args.neighbor_umbrella:
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indexes = []
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for l in args.neighbor_umbrella:
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indexes += l
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if 'all' in indexes:
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indexes = range(6)
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else:
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for i, arg in enumerate(indexes):
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try:
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arg = int(arg)
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if arg not in range(6):
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raise ValueError()
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except ValueError:
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print(
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'neighbor_umbrella: invalid index %s' % str(arg),
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file=sys.stderr,
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)
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sys.exit(1)
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indexes[i] = arg
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for i in indexes:
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u, order_edge = header_neighbor_umbrella(i)
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print("Header umbrella %d:" % i)
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print(" Pivot:", u.pivot)
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for i in range(5):
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print(" Vertex %d:" % i, u.vertex(i, order_edge))
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for i in range(5):
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print(" Component %d:" % i, u.component(i, order_edge))
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if args.plot:
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plot.polygons(u.components)
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if args.neighbor_umbrella_gen:
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print("Header neighbor umbrellas code generation:")
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print_code_gen_notice()
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print("const struct AP_GeodesicGrid::neighbor_umbrella")
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print("AP_GeodesicGrid::_neighbor_umbrellas[3]{")
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for i in range(6):
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u, order_edge = header_neighbor_umbrella(i)
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components = tuple(
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ico.triangles.index(u.component(i, order_edge)) for i in range(5)
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)
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def vi_cj(i, j):
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v = u.vertex(i, order_edge)
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t = u.component(j, order_edge)
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return t.index(v)
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vi_cj_values = tuple(
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vi_cj(a, b) for a, b in ((0, 0), (1, 1), (2, 1), (4, 4), (0, 4))
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)
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print(" {{%s}, %s}," % (
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", ".join("%2d" % i for i in components),
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", ".join(str(i) for i in vi_cj_values),
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))
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print("};")
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if args.inverses_gen:
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print("Header inverses code generation:")
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print_code_gen_notice()
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print("const Matrix3f AP_GeodesicGrid::_inverses[10]{")
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for i in range(10):
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a, b, c = ico.triangles[i]
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m = np.matrix((
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(a.x, b.x, c.x),
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(a.y, b.y, c.y),
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(a.z, b.z, c.z),
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)).getI()
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print(" {{%9.6ff, %9.6ff, %9.6ff}," % (m[0,0], m[0,1], m[0,2]))
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print(" {%9.6ff, %9.6ff, %9.6ff}," % (m[1,0], m[1,1], m[1,2]))
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print(" {%9.6ff, %9.6ff, %9.6ff}}," % (m[2,0], m[2,1], m[2,2]))
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print("};")
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print()
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print_code_gen_notice()
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print("const Matrix3f AP_GeodesicGrid::_mid_inverses[10]{")
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for i in range(10):
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a, b, c = ico.triangles[i]
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ma, mb, mc = .5 * (a + b), .5 * (b + c), .5 * (c + a)
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m = np.matrix((
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(ma.x, mb.x, mc.x),
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(ma.y, mb.y, mc.y),
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(ma.z, mb.z, mc.z),
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)).getI()
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print(" {{%9.6ff, %9.6ff, %9.6ff}," % (m[0,0], m[0,1], m[0,2]))
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print(" {%9.6ff, %9.6ff, %9.6ff}," % (m[1,0], m[1,1], m[1,2]))
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print(" {%9.6ff, %9.6ff, %9.6ff}}," % (m[2,0], m[2,1], m[2,2]))
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print("};")
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if args.icosahedron:
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print('Icosahedron:')
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for i, t in enumerate(ico.triangles):
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print(' %s' % str(t))
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if args.plot:
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plot.polygons(ico.triangles)
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if args.plot:
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plot.show(subtriangles=args.plot_subtriangles)
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198
libraries/AP_Math/tools/geodesic_grid/icosahedron.py
Normal file
198
libraries/AP_Math/tools/geodesic_grid/icosahedron.py
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# Copyright (C) 2016 Intel Corporation. All rights reserved.
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#
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# This file is free software: you can redistribute it and/or modify it
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# under the terms of the GNU General Public License as published by the
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# Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This file is distributed in the hope that it will be useful, but
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# WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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# See the GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License along
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# with this program. If not, see <http://www.gnu.org/licenses/>.
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import math
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from scipy.constants import golden as g
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class Vertex(tuple):
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def __new__(cls, x, y, z):
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instance = tuple.__new__(cls, (x, y, z))
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instance.x = x
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instance.y = y
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instance.z = z
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return instance
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def __repr__(self):
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return "(" + ",".join(Vertex._print_map.get(x, str(x)) for x in self) + ")"
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def __str__(self):
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return self.__repr__()
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def __neg__(self):
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return Vertex(-self.x, -self.y, -self.z)
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def __add__(self, other):
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return Vertex(self.x + other.x, self.y + other.y, self.z + other.z)
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def __sub__(self, other):
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return Vertex(self.x - other.x, self.y - other.y, self.z - other.z)
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def __mul__(self, s):
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return Vertex(s * self.x, s * self.y, s * self.z)
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__rmul__ = __mul__
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def length(self):
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return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
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def normalized(self):
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return (1.0 / self.length()) * self
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class Triangle(tuple):
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def __new__(cls, a, b, c):
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instance = tuple.__new__(cls, (a, b, c))
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instance.a = a
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instance.b = b
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instance.c = c
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return instance
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def __neg__(self):
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return Triangle(-self.a, -self.b, -self.c)
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def __str__(self):
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if self in triangles:
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i = triangles.index(self)
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return "Triangle %2d: %s" % (i, self.__repr__())
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else:
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return self.__repr__()
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Vertex._print_map = {
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g: ' g', -g: '-g', 1: ' 1', -1: '-1', 0: ' 0',
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}
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vertices = tuple(
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Vertex(x, y, z) for x, y, z in (
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( g, 1, 0),
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( g,-1, 0),
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(-g, 1, 0),
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(-g,-1, 0),
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( 1, 0, g),
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(-1, 0, g),
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( 1, 0,-g),
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(-1, 0,-g),
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( 0, g, 1),
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( 0, g,-1),
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( 0,-g, 1),
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( 0,-g,-1),
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)
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)
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_first_half = (
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Triangle(Vertex(-g, 1, 0), Vertex(-1, 0,-g), Vertex(-g,-1, 0)),
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Triangle(Vertex(-1, 0,-g), Vertex(-g,-1, 0), Vertex( 0,-g,-1)),
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Triangle(Vertex(-g,-1, 0), Vertex( 0,-g,-1), Vertex( 0,-g, 1)),
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Triangle(Vertex(-1, 0,-g), Vertex( 0,-g,-1), Vertex( 1, 0,-g)),
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Triangle(Vertex( 0,-g,-1), Vertex( 0,-g, 1), Vertex( g,-1, 0)),
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Triangle(Vertex( 0,-g,-1), Vertex( 1, 0,-g), Vertex( g,-1, 0)),
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Triangle(Vertex( g,-1, 0), Vertex( 1, 0,-g), Vertex( g, 1, 0)),
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Triangle(Vertex( 1, 0,-g), Vertex( g, 1, 0), Vertex( 0, g,-1)),
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Triangle(Vertex( 1, 0,-g), Vertex( 0, g,-1), Vertex(-1, 0,-g)),
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Triangle(Vertex( 0, g,-1), Vertex(-g, 1, 0), Vertex(-1, 0,-g)),
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)
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_second_half = tuple(-t for t in _first_half)
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triangles = _first_half + _second_half
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_neighbor_triangle_data = {}
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def neighbor_triangle(t, edge):
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""" Return the neighbor triangle of t with respect to edge = (a, b) """
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e = frozenset(edge)
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if (t, e) in _neighbor_triangle_data:
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return _neighbor_triangle_data[(t, e)]
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a, b = edge
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if a not in t or b not in t:
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return None
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for w in triangles:
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if a in w and b in w and w != t:
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_neighbor_triangle_data[(t, e)] = w
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return w
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return None
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class _Umbrella:
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def __init__(self, pivot):
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self.pivot = pivot
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self.components = frozenset(t for t in triangles if pivot in t)
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all_vertices = set()
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for t in self.components:
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for v in t:
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if v != pivot:
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all_vertices.add(v)
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self.all_vertices = frozenset(all_vertices)
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self._vertex_data = {}
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self._component_data = {}
|
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def vertex(self, i, ordered_edge):
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""" Return the i-th vertex with respect to ordered_edge = (a, b) """
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a, b = ordered_edge
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if a not in self.all_vertices:
|
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return None
|
||||
if b not in self.all_vertices:
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return None
|
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|
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if i == 0:
|
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return a
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if i == 1:
|
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return b
|
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|
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if (i, a, b) in self._vertex_data:
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return self._vertex_data[(i, a, b)]
|
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|
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previous = self.vertex(i - 1, ordered_edge)
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comp = self.component(i - 2, ordered_edge)
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neighbor = neighbor_triangle(comp, (self.pivot, previous))
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for v in neighbor:
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if v not in (self.pivot, previous):
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self._vertex_data[(i, a, b)] = v
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return v
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return None
|
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def component(self, i, ordered_edge):
|
||||
""" Return the i-th component with respect to ordered_edge = (a, b) """
|
||||
a, b = ordered_edge
|
||||
if (i, a, b) in self._component_data:
|
||||
return self._component_data[(i, a, b)]
|
||||
|
||||
vi = self.vertex(i, ordered_edge)
|
||||
vj = self.vertex(i + 1, ordered_edge)
|
||||
|
||||
for t in self.components:
|
||||
if vi in t and vj in t:
|
||||
self._component_data[(i, a, b)] = t
|
||||
return t
|
||||
return None
|
||||
|
||||
_umbrelas = {}
|
||||
def umbrella(pivot):
|
||||
if pivot not in vertices:
|
||||
return None
|
||||
|
||||
if pivot not in _umbrelas:
|
||||
_umbrelas[pivot] = _Umbrella(pivot)
|
||||
return _umbrelas[pivot]
|
||||
|
||||
def neighbor_umbrella(t, edge):
|
||||
neighbor = neighbor_triangle(t, edge)
|
||||
if not neighbor:
|
||||
return None
|
||||
|
||||
for pivot in neighbor:
|
||||
if pivot in edge:
|
||||
continue
|
||||
return umbrella(pivot)
|
||||
104
libraries/AP_Math/tools/geodesic_grid/plot.py
Normal file
104
libraries/AP_Math/tools/geodesic_grid/plot.py
Normal file
@ -0,0 +1,104 @@
|
||||
# Copyright (C) 2016 Intel Corporation. All rights reserved.
|
||||
#
|
||||
# This file is free software: you can redistribute it and/or modify it
|
||||
# under the terms of the GNU General Public License as published by the
|
||||
# Free Software Foundation, either version 3 of the License, or
|
||||
# (at your option) any later version.
|
||||
#
|
||||
# This file is distributed in the hope that it will be useful, but
|
||||
# WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
|
||||
# See the GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib.patches as mpatches
|
||||
|
||||
from mpl_toolkits.mplot3d import Axes3D
|
||||
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
|
||||
|
||||
import icosahedron as ico
|
||||
|
||||
fig = plt.figure()
|
||||
ax = fig.add_subplot(111, projection='3d')
|
||||
ax.set_xlim3d(-2, 2)
|
||||
ax.set_ylim3d(-2, 2)
|
||||
ax.set_zlim3d(-2, 2)
|
||||
|
||||
ax.set_xlabel('x')
|
||||
ax.set_ylabel('y')
|
||||
ax.set_zlabel('z')
|
||||
|
||||
ax.invert_zaxis()
|
||||
ax.invert_xaxis()
|
||||
|
||||
ax.set_aspect('equal')
|
||||
|
||||
added_polygons = set()
|
||||
|
||||
def polygons(polygons):
|
||||
for p in polygons:
|
||||
polygon(p)
|
||||
|
||||
|
||||
def polygon(polygon):
|
||||
added_polygons.add(polygon)
|
||||
|
||||
def show(subtriangles=False):
|
||||
polygons = []
|
||||
facecolors = []
|
||||
|
||||
for p in added_polygons:
|
||||
try:
|
||||
i = ico.triangles.index(p)
|
||||
except ValueError:
|
||||
polygons.append(p)
|
||||
continue
|
||||
|
||||
if subtriangles:
|
||||
a, b, c = p
|
||||
|
||||
# project the middle points to the sphere
|
||||
alpha = a.length() / (2.0 * ico.g)
|
||||
ma, mb, mc = alpha * (a + b), alpha * (b + c), alpha * (c + a)
|
||||
|
||||
polygons.append(ico.Triangle(ma, mb, mc))
|
||||
facecolors.append('#CCCCCC')
|
||||
|
||||
polygons.append(ico.Triangle( a, ma, mc))
|
||||
facecolors.append('#CCE5FF')
|
||||
|
||||
polygons.append(ico.Triangle(ma, b, mb))
|
||||
facecolors.append('#E5FFCC')
|
||||
|
||||
polygons.append(ico.Triangle(mc, mb, c))
|
||||
facecolors.append('#FFCCCC')
|
||||
else:
|
||||
polygons.append(p)
|
||||
facecolors.append('#DDDDDD')
|
||||
|
||||
mx = my = mz = 0
|
||||
for x, y, z in p:
|
||||
mx += x
|
||||
my += y
|
||||
mz += z
|
||||
ax.text(mx / 2.6, my /2.6, mz / 2.6, i, color='#444444')
|
||||
|
||||
ax.add_collection3d(Poly3DCollection(
|
||||
polygons,
|
||||
facecolors=facecolors,
|
||||
edgecolors="#777777",
|
||||
))
|
||||
|
||||
if subtriangles:
|
||||
ax.legend(
|
||||
handles=(
|
||||
mpatches.Patch(color='#CCCCCC', label='Sub-triangle #0'),
|
||||
mpatches.Patch(color='#CCE5FF', label='Sub-triangle #1'),
|
||||
mpatches.Patch(color='#E5FFCC', label='Sub-triangle #2'),
|
||||
mpatches.Patch(color='#FFCCCC', label='Sub-triangle #3'),
|
||||
),
|
||||
)
|
||||
|
||||
plt.show()
|
||||
Loading…
Reference in New Issue
Block a user