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ardupilot/libraries/AP_Math/tools/geodesic_grid/geodesic_grid.py

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#!/usr/bin/env python
# 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/>.
from __future__ import print_function
import argparse
import numpy as np
import sys
import icosahedron as ico
import grid
def print_code_gen_notice():
print("/* This was generated with")
print(" * libraries/AP_Math/tools/geodesic_grid/geodesic_grid.py */")
def header_neighbor_umbrella(index):
t = ico.triangles[0]
a, b, c = t
triangle, edge = (
( t, ( a, b)),
( t, ( b, c)),
( t, ( c, a)),
(-t, (-a, -b)),
(-t, (-b, -c)),
(-t, (-c, -a)),
)[index]
return ico.neighbor_umbrella(triangle, edge), edge
parser = argparse.ArgumentParser(
description="""
Utility script for helping to understand concepts used by AP_GeodesicGrid as
well as for aiding its development.
When passing a vertex as argument to one of the options, the valid values for
the coordinates are 0, -1, 1, g and -g, where g is the golden ratio.
""",
)
parser.add_argument(
'-p', '--plot',
action='store_true',
help="""
Plot results when applicable.
""",
)
parser.add_argument(
'-b', '--plot-subtriangles',
action='store_true',
help="""
Plot subtriangles as well. This implies -p.
""",
)
parser.add_argument(
'--icosahedron',
action='store_true',
help='Get the icosahedron triangles.',
)
parser.add_argument(
'-t', '--triangle',
action='append',
type=int,
nargs='+',
metavar='INDEX',
help="""
Get the icosahedron triangle at INDEX.
""",
)
parser.add_argument(
'-s', '--section',
action='append',
type=int,
nargs='+',
help="""
Get the grid section SECTION. If --plot is passed, then --plot-subtriangles is
implied.
""",
)
parser.add_argument(
'-u', '--umbrella',
action='append',
nargs=3,
metavar=('X', 'Y', 'Z'),
help="""
Get the umbrella with pivot denoted by (X, Y, Z). The pivot must be one of the
icosahedron's vertices.
""",
)
parser.add_argument(
'-n', '--neighbor-umbrella',
action='append',
nargs='+',
metavar='INDEX',
help="""
Get the neighbor umbrella at INDEX as described by _neighbor_umbrellas in
AP_GeodesicGrid.h. The special value "all" for INDEX is also accepted, which
will make it ignore other indexes passed and get all neighbor umbrellas for
that member.
""",
)
parser.add_argument(
'--neighbor-umbrella-gen',
action='store_true',
help="""
Generate C++ code for the initialization of the member _neighbor_umbrellas
described in AP_GeodesicGrid.h.
""",
)
parser.add_argument(
'--inverses-gen',
action='store_true',
help="""
Generate C++ code for the initialization of members _inverses and _mid_inverses
declared in AP_GeodesicGrid.h.
""")
args = parser.parse_args()
if args.plot_subtriangles:
args.plot = True
if args.plot:
import plot
polygons_to_plot = []
if args.triangle:
indexes = []
for l in args.triangle:
indexes += l
for i in indexes:
if 0 > i or i >= len(ico.triangles):
print(
'Triangle index must be in the range [0,%d)' % len(ico.triangles),
file=sys.stderr,
)
sys.exit(1)
print(ico.triangles[i])
if args.plot:
plot.polygon(ico.triangles[i])
if args.section:
sections = []
for l in args.section:
sections += l
for s in sections:
if 0 > s or s >= 4 * len(ico.triangles):
print(
'Section must be in the range [0,%d)' % 4 * len(ico.triangles),
file=sys.stderr,
)
sys.exit(1)
print(grid.section_triangle(s))
if args.plot:
args.plot_subtriangles = True
plot.sections(sections)
if args.umbrella:
for pivot in args.umbrella:
for i, x in enumerate(pivot):
if x == 'g':
x = ico.g
elif x == '-g':
x = -ico.g
else:
try:
x = int(x)
if x not in (0, -1, 1):
raise ValueError()
except ValueError:
print(
'umbrella: invalid pivot coordinate: %s' % str(x),
file=sys.stderr,
)
sys.exit(1)
pivot[i] = x
pivot = ico.Vertex(*pivot)
if pivot not in ico.vertices:
print(
'umbrella: invalid pivot:', pivot,
file=sys.stderr,
)
sys.exit(1)
u = ico.umbrella(pivot)
print("Components of the umbrella of %s:" % str(pivot))
for c in u.components:
print(" %s" % str(c))
if args.plot:
plot.polygons(u.components)
if args.neighbor_umbrella:
indexes = []
for l in args.neighbor_umbrella:
indexes += l
if 'all' in indexes:
indexes = range(6)
else:
for i, arg in enumerate(indexes):
try:
arg = int(arg)
if arg not in range(6):
raise ValueError()
except ValueError:
print(
'neighbor_umbrella: invalid index %s' % str(arg),
file=sys.stderr,
)
sys.exit(1)
indexes[i] = arg
for i in indexes:
u, order_edge = header_neighbor_umbrella(i)
print("Header umbrella %d:" % i)
print(" Pivot:", u.pivot)
for i in range(5):
print(" Vertex %d:" % i, u.vertex(i, order_edge))
for i in range(5):
print(" Component %d:" % i, u.component(i, order_edge))
if args.plot:
plot.polygons(u.components)
if args.neighbor_umbrella_gen:
print("Header neighbor umbrellas code generation:")
print_code_gen_notice()
print("const struct AP_GeodesicGrid::neighbor_umbrella")
print("AP_GeodesicGrid::_neighbor_umbrellas[3]{")
for i in range(6):
u, order_edge = header_neighbor_umbrella(i)
components = tuple(
ico.triangles.index(u.component(i, order_edge)) for i in range(5)
)
def vi_cj(i, j):
v = u.vertex(i, order_edge)
t = u.component(j, order_edge)
return t.index(v)
vi_cj_values = tuple(
vi_cj(a, b) for a, b in ((0, 0), (1, 1), (2, 1), (4, 4), (0, 4))
)
print(" {{%s}, %s}," % (
", ".join("%2d" % i for i in components),
", ".join(str(i) for i in vi_cj_values),
))
print("};")
if args.inverses_gen:
print("Header inverses code generation:")
print_code_gen_notice()
print("const Matrix3f AP_GeodesicGrid::_inverses[10]{")
for i in range(10):
a, b, c = ico.triangles[i]
m = np.matrix((
(a.x, b.x, c.x),
(a.y, b.y, c.y),
(a.z, b.z, c.z),
)).getI()
print(" {{%9.6ff, %9.6ff, %9.6ff}," % (m[0,0], m[0,1], m[0,2]))
print(" {%9.6ff, %9.6ff, %9.6ff}," % (m[1,0], m[1,1], m[1,2]))
print(" {%9.6ff, %9.6ff, %9.6ff}}," % (m[2,0], m[2,1], m[2,2]))
print("};")
print()
print_code_gen_notice()
print("const Matrix3f AP_GeodesicGrid::_mid_inverses[10]{")
for i in range(10):
a, b, c = ico.triangles[i]
ma, mb, mc = .5 * (a + b), .5 * (b + c), .5 * (c + a)
m = np.matrix((
(ma.x, mb.x, mc.x),
(ma.y, mb.y, mc.y),
(ma.z, mb.z, mc.z),
)).getI()
print(" {{%9.6ff, %9.6ff, %9.6ff}," % (m[0,0], m[0,1], m[0,2]))
print(" {%9.6ff, %9.6ff, %9.6ff}," % (m[1,0], m[1,1], m[1,2]))
print(" {%9.6ff, %9.6ff, %9.6ff}}," % (m[2,0], m[2,1], m[2,2]))
print("};")
if args.icosahedron:
print('Icosahedron:')
for i, t in enumerate(ico.triangles):
print(' %s' % str(t))
if args.plot:
plot.polygons(ico.triangles)
if args.plot:
plot.show(subtriangles=args.plot_subtriangles)
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