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Add OpenRV library.
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96
scripts/libraries/mtx.py
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96
scripts/libraries/mtx.py
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# The MIT License (MIT)
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#
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# Copyright (c) 2019 Nick Lee
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#
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# Permission is hereby granted, free of charge, to any person obtaining a copy of
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# this software and associated documentation files (the "Software"), to deal in
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# the Software without restriction, including without limitation the rights to
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# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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# the Software, and to permit persons to whom the Software is furnished to do so,
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# subject to the following conditions:
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#
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# The above copyright notice and this permission notice shall be included in all
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# copies or substantial portions of the Software.
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#
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
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# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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def _dot(a, b):
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s = 0
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for i in range(0, len(b)):
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s += a[i] * b[i]
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return s
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def mul(A, b):
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return [_dot(row, b) for row in A]
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def _height(A):
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return len(A)
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def _width(A):
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return len(A[0])
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def _max_magnitude_row(A, column):
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first_row = column
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max_row = first_row
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max_value = A[first_row][column]
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for i in range(first_row+1, _height(A)):
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if abs(A[i][column]) > abs(max_value):
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max_row = i
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max_value = A[i][column]
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return max_row
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def _subtract_rows_below(A, row, column, pivot_value):
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# Fill in factors where entries will become zero.
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for i in range(row+1, _height(A)):
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A[i][column] /= pivot_value
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for i in range(row+1, _height(A)):
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for j in range(column+1, _width(A)):
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A[i][j] -= (A[i][column] * A[row][j])
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def lu(A):
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P = None
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for pivot_column in range(0, _width(A)-1):
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pivot_row = pivot_column
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max_row = _max_magnitude_row(A, pivot_column)
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pivot_value = A[max_row][pivot_column]
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if max_row != pivot_row:
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A[pivot_row], A[max_row] = A[max_row], A[pivot_row]
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if P is None:
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P = list(range(0, _height(A)))
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P[pivot_row], P[max_row] = P[max_row], P[pivot_row]
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_subtract_rows_below(A, pivot_row, pivot_column, pivot_value)
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return P,A
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def _forward_substitute(A, b):
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for i in range(1, len(b)):
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for j in range(0, i):
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b[i] = b[i] - (b[j] * A[i][j])
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def _backward_substitute(A, b):
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size = len(b)
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b[-1] = b[-1] / A[-1][-1]
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for i in range(size-2, -1, -1):
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for j in range(i+1, size):
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b[i] = b[i] - (b[j] * A[i][j])
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b[i] = b[i] / A[i][i]
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def solve(PLU, b):
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P, LU = PLU
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x = b[:] if P is None else [b[i] for i in P] # permutation
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_forward_substitute(LU, x)
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_backward_substitute(LU, x)
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return x
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674
scripts/libraries/rv/LICENSE.txt
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674
scripts/libraries/rv/LICENSE.txt
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GNU GENERAL PUBLIC LICENSE
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Version 3, 29 June 2007
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Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
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|
Everyone is permitted to copy and distribute verbatim copies
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|
of this license document, but changing it is not allowed.
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|
|
||||||
|
Preamble
|
||||||
|
|
||||||
|
The GNU General Public License is a free, copyleft license for
|
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|
software and other kinds of works.
|
||||||
|
|
||||||
|
The licenses for most software and other practical works are designed
|
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|
to take away your freedom to share and change the works. By contrast,
|
||||||
|
the GNU General Public License is intended to guarantee your freedom to
|
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|
share and change all versions of a program--to make sure it remains free
|
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|
software for all its users. We, the Free Software Foundation, use the
|
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|
GNU General Public License for most of our software; it applies also to
|
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|
any other work released this way by its authors. You can apply it to
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|
your programs, too.
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|
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|
When we speak of free software, we are referring to freedom, not
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price. Our General Public Licenses are designed to make sure that you
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have the freedom to distribute copies of free software (and charge for
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them if you wish), that you receive source code or can get it if you
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want it, that you can change the software or use pieces of it in new
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free programs, and that you know you can do these things.
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|
To protect your rights, we need to prevent others from denying you
|
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|
these rights or asking you to surrender the rights. Therefore, you have
|
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|
certain responsibilities if you distribute copies of the software, or if
|
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you modify it: responsibilities to respect the freedom of others.
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For example, if you distribute copies of such a program, whether
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|
gratis or for a fee, you must pass on to the recipients the same
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|
freedoms that you received. You must make sure that they, too, receive
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or can get the source code. And you must show them these terms so they
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know their rights.
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Developers that use the GNU GPL protect your rights with two steps:
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(1) assert copyright on the software, and (2) offer you this License
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giving you legal permission to copy, distribute and/or modify it.
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For the developers' and authors' protection, the GPL clearly explains
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that there is no warranty for this free software. For both users' and
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authors' sake, the GPL requires that modified versions be marked as
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changed, so that their problems will not be attributed erroneously to
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authors of previous versions.
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Some devices are designed to deny users access to install or run
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modified versions of the software inside them, although the manufacturer
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can do so. This is fundamentally incompatible with the aim of
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protecting users' freedom to change the software. The systematic
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pattern of such abuse occurs in the area of products for individuals to
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use, which is precisely where it is most unacceptable. Therefore, we
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have designed this version of the GPL to prohibit the practice for those
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products. If such problems arise substantially in other domains, we
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stand ready to extend this provision to those domains in future versions
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of the GPL, as needed to protect the freedom of users.
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|
Finally, every program is threatened constantly by software patents.
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States should not allow patents to restrict development and use of
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software on general-purpose computers, but in those that do, we wish to
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avoid the special danger that patents applied to a free program could
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make it effectively proprietary. To prevent this, the GPL assures that
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patents cannot be used to render the program non-free.
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|
The precise terms and conditions for copying, distribution and
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|
modification follow.
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|
TERMS AND CONDITIONS
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|
0. Definitions.
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"This License" refers to version 3 of the GNU General Public License.
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|
"Copyright" also means copyright-like laws that apply to other kinds of
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works, such as semiconductor masks.
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"The Program" refers to any copyrightable work licensed under this
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License. Each licensee is addressed as "you". "Licensees" and
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"recipients" may be individuals or organizations.
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To "modify" a work means to copy from or adapt all or part of the work
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in a fashion requiring copyright permission, other than the making of an
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exact copy. The resulting work is called a "modified version" of the
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earlier work or a work "based on" the earlier work.
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A "covered work" means either the unmodified Program or a work based
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on the Program.
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To "propagate" a work means to do anything with it that, without
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permission, would make you directly or secondarily liable for
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infringement under applicable copyright law, except executing it on a
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computer or modifying a private copy. Propagation includes copying,
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distribution (with or without modification), making available to the
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public, and in some countries other activities as well.
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To "convey" a work means any kind of propagation that enables other
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parties to make or receive copies. Mere interaction with a user through
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An interactive user interface displays "Appropriate Legal Notices"
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to the extent that it includes a convenient and prominently visible
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tells the user that there is no warranty for the work (except to the
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extent that warranties are provided), that licensees may convey the
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work under this License, and how to view a copy of this License. If
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the interface presents a list of user commands or options, such as a
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menu, a prominent item in the list meets this criterion.
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1. Source Code.
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The "source code" for a work means the preferred form of the work
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A "Standard Interface" means an interface that either is an official
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standard defined by a recognized standards body, or, in the case of
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interfaces specified for a particular programming language, one that
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is widely used among developers working in that language.
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The "System Libraries" of an executable work include anything, other
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than the work as a whole, that (a) is included in the normal form of
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packaging a Major Component, but which is not part of that Major
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Component, and (b) serves only to enable use of the work with that
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implementation is available to the public in source code form. A
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"Major Component", in this context, means a major essential component
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the source code needed to generate, install, and (for an executable
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work) run the object code and to modify the work, including scripts to
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control those activities. However, it does not include the work's
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System Libraries, or general-purpose tools or generally available free
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includes interface definition files associated with source files for
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The Corresponding Source need not include anything that users
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can regenerate automatically from other parts of the Corresponding
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Source.
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The Corresponding Source for a work in source code form is that
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2. Basic Permissions.
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All rights granted under this License are granted for the term of
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copyright on the Program, and are irrevocable provided the stated
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conditions are met. This License explicitly affirms your unlimited
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permission to run the unmodified Program. The output from running a
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covered work is covered by this License only if the output, given its
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content, constitutes a covered work. This License acknowledges your
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rights of fair use or other equivalent, as provided by copyright law.
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You may make, run and propagate covered works that you do not
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convey, without conditions so long as your license otherwise remains
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in force. You may convey covered works to others for the sole purpose
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of having them make modifications exclusively for you, or provide you
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with facilities for running those works, provided that you comply with
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the terms of this License in conveying all material for which you do
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not control copyright. Those thus making or running the covered works
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for you must do so exclusively on your behalf, under your direction
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Conveying under any other circumstances is permitted solely under
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the conditions stated below. Sublicensing is not allowed; section 10
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makes it unnecessary.
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3. Protecting Users' Legal Rights From Anti-Circumvention Law.
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No covered work shall be deemed part of an effective technological
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When you convey a covered work, you waive any legal power to forbid
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4. Conveying Verbatim Copies.
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receive it, in any medium, provided that you conspicuously and
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You may charge any price or no price for each copy that you convey,
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and you may offer support or warranty protection for a fee.
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terms of section 4, provided that you also meet all of these conditions:
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a) The work must carry prominent notices stating that you modified
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it, and giving a relevant date.
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b) The work must carry prominent notices stating that it is
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released under this License and any conditions added under section
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c) You must license the entire work, as a whole, under this
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License to anyone who comes into possession of a copy. This
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License will therefore apply, along with any applicable section 7
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d) If the work has interactive user interfaces, each must display
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6. Conveying Non-Source Forms.
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You may convey a covered work in object code form under the terms
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a) Convey the object code in, or embodied in, a physical product
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b) Convey the object code in, or embodied in, a physical product
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|
product that is covered by this License, on a durable physical
|
||||||
|
medium customarily used for software interchange, for a price no
|
||||||
|
more than your reasonable cost of physically performing this
|
||||||
|
conveying of source, or (2) access to copy the
|
||||||
|
Corresponding Source from a network server at no charge.
|
||||||
|
|
||||||
|
c) Convey individual copies of the object code with a copy of the
|
||||||
|
written offer to provide the Corresponding Source. This
|
||||||
|
alternative is allowed only occasionally and noncommercially, and
|
||||||
|
only if you received the object code with such an offer, in accord
|
||||||
|
with subsection 6b.
|
||||||
|
|
||||||
|
d) Convey the object code by offering access from a designated
|
||||||
|
place (gratis or for a charge), and offer equivalent access to the
|
||||||
|
Corresponding Source in the same way through the same place at no
|
||||||
|
further charge. You need not require recipients to copy the
|
||||||
|
Corresponding Source along with the object code. If the place to
|
||||||
|
copy the object code is a network server, the Corresponding Source
|
||||||
|
may be on a different server (operated by you or a third party)
|
||||||
|
that supports equivalent copying facilities, provided you maintain
|
||||||
|
clear directions next to the object code saying where to find the
|
||||||
|
Corresponding Source. Regardless of what server hosts the
|
||||||
|
Corresponding Source, you remain obligated to ensure that it is
|
||||||
|
available for as long as needed to satisfy these requirements.
|
||||||
|
|
||||||
|
e) Convey the object code using peer-to-peer transmission, provided
|
||||||
|
you inform other peers where the object code and Corresponding
|
||||||
|
Source of the work are being offered to the general public at no
|
||||||
|
charge under subsection 6d.
|
||||||
|
|
||||||
|
A separable portion of the object code, whose source code is excluded
|
||||||
|
from the Corresponding Source as a System Library, need not be
|
||||||
|
included in conveying the object code work.
|
||||||
|
|
||||||
|
A "User Product" is either (1) a "consumer product", which means any
|
||||||
|
tangible personal property which is normally used for personal, family,
|
||||||
|
or household purposes, or (2) anything designed or sold for incorporation
|
||||||
|
into a dwelling. In determining whether a product is a consumer product,
|
||||||
|
doubtful cases shall be resolved in favor of coverage. For a particular
|
||||||
|
product received by a particular user, "normally used" refers to a
|
||||||
|
typical or common use of that class of product, regardless of the status
|
||||||
|
of the particular user or of the way in which the particular user
|
||||||
|
actually uses, or expects or is expected to use, the product. A product
|
||||||
|
is a consumer product regardless of whether the product has substantial
|
||||||
|
commercial, industrial or non-consumer uses, unless such uses represent
|
||||||
|
the only significant mode of use of the product.
|
||||||
|
|
||||||
|
"Installation Information" for a User Product means any methods,
|
||||||
|
procedures, authorization keys, or other information required to install
|
||||||
|
and execute modified versions of a covered work in that User Product from
|
||||||
|
a modified version of its Corresponding Source. The information must
|
||||||
|
suffice to ensure that the continued functioning of the modified object
|
||||||
|
code is in no case prevented or interfered with solely because
|
||||||
|
modification has been made.
|
||||||
|
|
||||||
|
If you convey an object code work under this section in, or with, or
|
||||||
|
specifically for use in, a User Product, and the conveying occurs as
|
||||||
|
part of a transaction in which the right of possession and use of the
|
||||||
|
User Product is transferred to the recipient in perpetuity or for a
|
||||||
|
fixed term (regardless of how the transaction is characterized), the
|
||||||
|
Corresponding Source conveyed under this section must be accompanied
|
||||||
|
by the Installation Information. But this requirement does not apply
|
||||||
|
if neither you nor any third party retains the ability to install
|
||||||
|
modified object code on the User Product (for example, the work has
|
||||||
|
been installed in ROM).
|
||||||
|
|
||||||
|
The requirement to provide Installation Information does not include a
|
||||||
|
requirement to continue to provide support service, warranty, or updates
|
||||||
|
for a work that has been modified or installed by the recipient, or for
|
||||||
|
the User Product in which it has been modified or installed. Access to a
|
||||||
|
network may be denied when the modification itself materially and
|
||||||
|
adversely affects the operation of the network or violates the rules and
|
||||||
|
protocols for communication across the network.
|
||||||
|
|
||||||
|
Corresponding Source conveyed, and Installation Information provided,
|
||||||
|
in accord with this section must be in a format that is publicly
|
||||||
|
documented (and with an implementation available to the public in
|
||||||
|
source code form), and must require no special password or key for
|
||||||
|
unpacking, reading or copying.
|
||||||
|
|
||||||
|
7. Additional Terms.
|
||||||
|
|
||||||
|
"Additional permissions" are terms that supplement the terms of this
|
||||||
|
License by making exceptions from one or more of its conditions.
|
||||||
|
Additional permissions that are applicable to the entire Program shall
|
||||||
|
be treated as though they were included in this License, to the extent
|
||||||
|
that they are valid under applicable law. If additional permissions
|
||||||
|
apply only to part of the Program, that part may be used separately
|
||||||
|
under those permissions, but the entire Program remains governed by
|
||||||
|
this License without regard to the additional permissions.
|
||||||
|
|
||||||
|
When you convey a copy of a covered work, you may at your option
|
||||||
|
remove any additional permissions from that copy, or from any part of
|
||||||
|
it. (Additional permissions may be written to require their own
|
||||||
|
removal in certain cases when you modify the work.) You may place
|
||||||
|
additional permissions on material, added by you to a covered work,
|
||||||
|
for which you have or can give appropriate copyright permission.
|
||||||
|
|
||||||
|
Notwithstanding any other provision of this License, for material you
|
||||||
|
add to a covered work, you may (if authorized by the copyright holders of
|
||||||
|
that material) supplement the terms of this License with terms:
|
||||||
|
|
||||||
|
a) Disclaiming warranty or limiting liability differently from the
|
||||||
|
terms of sections 15 and 16 of this License; or
|
||||||
|
|
||||||
|
b) Requiring preservation of specified reasonable legal notices or
|
||||||
|
author attributions in that material or in the Appropriate Legal
|
||||||
|
Notices displayed by works containing it; or
|
||||||
|
|
||||||
|
c) Prohibiting misrepresentation of the origin of that material, or
|
||||||
|
requiring that modified versions of such material be marked in
|
||||||
|
reasonable ways as different from the original version; or
|
||||||
|
|
||||||
|
d) Limiting the use for publicity purposes of names of licensors or
|
||||||
|
authors of the material; or
|
||||||
|
|
||||||
|
e) Declining to grant rights under trademark law for use of some
|
||||||
|
trade names, trademarks, or service marks; or
|
||||||
|
|
||||||
|
f) Requiring indemnification of licensors and authors of that
|
||||||
|
material by anyone who conveys the material (or modified versions of
|
||||||
|
it) with contractual assumptions of liability to the recipient, for
|
||||||
|
any liability that these contractual assumptions directly impose on
|
||||||
|
those licensors and authors.
|
||||||
|
|
||||||
|
All other non-permissive additional terms are considered "further
|
||||||
|
restrictions" within the meaning of section 10. If the Program as you
|
||||||
|
received it, or any part of it, contains a notice stating that it is
|
||||||
|
governed by this License along with a term that is a further
|
||||||
|
restriction, you may remove that term. If a license document contains
|
||||||
|
a further restriction but permits relicensing or conveying under this
|
||||||
|
License, you may add to a covered work material governed by the terms
|
||||||
|
of that license document, provided that the further restriction does
|
||||||
|
not survive such relicensing or conveying.
|
||||||
|
|
||||||
|
If you add terms to a covered work in accord with this section, you
|
||||||
|
must place, in the relevant source files, a statement of the
|
||||||
|
additional terms that apply to those files, or a notice indicating
|
||||||
|
where to find the applicable terms.
|
||||||
|
|
||||||
|
Additional terms, permissive or non-permissive, may be stated in the
|
||||||
|
form of a separately written license, or stated as exceptions;
|
||||||
|
the above requirements apply either way.
|
||||||
|
|
||||||
|
8. Termination.
|
||||||
|
|
||||||
|
You may not propagate or modify a covered work except as expressly
|
||||||
|
provided under this License. Any attempt otherwise to propagate or
|
||||||
|
modify it is void, and will automatically terminate your rights under
|
||||||
|
this License (including any patent licenses granted under the third
|
||||||
|
paragraph of section 11).
|
||||||
|
|
||||||
|
However, if you cease all violation of this License, then your
|
||||||
|
license from a particular copyright holder is reinstated (a)
|
||||||
|
provisionally, unless and until the copyright holder explicitly and
|
||||||
|
finally terminates your license, and (b) permanently, if the copyright
|
||||||
|
holder fails to notify you of the violation by some reasonable means
|
||||||
|
prior to 60 days after the cessation.
|
||||||
|
|
||||||
|
Moreover, your license from a particular copyright holder is
|
||||||
|
reinstated permanently if the copyright holder notifies you of the
|
||||||
|
violation by some reasonable means, this is the first time you have
|
||||||
|
received notice of violation of this License (for any work) from that
|
||||||
|
copyright holder, and you cure the violation prior to 30 days after
|
||||||
|
your receipt of the notice.
|
||||||
|
|
||||||
|
Termination of your rights under this section does not terminate the
|
||||||
|
licenses of parties who have received copies or rights from you under
|
||||||
|
this License. If your rights have been terminated and not permanently
|
||||||
|
reinstated, you do not qualify to receive new licenses for the same
|
||||||
|
material under section 10.
|
||||||
|
|
||||||
|
9. Acceptance Not Required for Having Copies.
|
||||||
|
|
||||||
|
You are not required to accept this License in order to receive or
|
||||||
|
run a copy of the Program. Ancillary propagation of a covered work
|
||||||
|
occurring solely as a consequence of using peer-to-peer transmission
|
||||||
|
to receive a copy likewise does not require acceptance. However,
|
||||||
|
nothing other than this License grants you permission to propagate or
|
||||||
|
modify any covered work. These actions infringe copyright if you do
|
||||||
|
not accept this License. Therefore, by modifying or propagating a
|
||||||
|
covered work, you indicate your acceptance of this License to do so.
|
||||||
|
|
||||||
|
10. Automatic Licensing of Downstream Recipients.
|
||||||
|
|
||||||
|
Each time you convey a covered work, the recipient automatically
|
||||||
|
receives a license from the original licensors, to run, modify and
|
||||||
|
propagate that work, subject to this License. You are not responsible
|
||||||
|
for enforcing compliance by third parties with this License.
|
||||||
|
|
||||||
|
An "entity transaction" is a transaction transferring control of an
|
||||||
|
organization, or substantially all assets of one, or subdividing an
|
||||||
|
organization, or merging organizations. If propagation of a covered
|
||||||
|
work results from an entity transaction, each party to that
|
||||||
|
transaction who receives a copy of the work also receives whatever
|
||||||
|
licenses to the work the party's predecessor in interest had or could
|
||||||
|
give under the previous paragraph, plus a right to possession of the
|
||||||
|
Corresponding Source of the work from the predecessor in interest, if
|
||||||
|
the predecessor has it or can get it with reasonable efforts.
|
||||||
|
|
||||||
|
You may not impose any further restrictions on the exercise of the
|
||||||
|
rights granted or affirmed under this License. For example, you may
|
||||||
|
not impose a license fee, royalty, or other charge for exercise of
|
||||||
|
rights granted under this License, and you may not initiate litigation
|
||||||
|
(including a cross-claim or counterclaim in a lawsuit) alleging that
|
||||||
|
any patent claim is infringed by making, using, selling, offering for
|
||||||
|
sale, or importing the Program or any portion of it.
|
||||||
|
|
||||||
|
11. Patents.
|
||||||
|
|
||||||
|
A "contributor" is a copyright holder who authorizes use under this
|
||||||
|
License of the Program or a work on which the Program is based. The
|
||||||
|
work thus licensed is called the contributor's "contributor version".
|
||||||
|
|
||||||
|
A contributor's "essential patent claims" are all patent claims
|
||||||
|
owned or controlled by the contributor, whether already acquired or
|
||||||
|
hereafter acquired, that would be infringed by some manner, permitted
|
||||||
|
by this License, of making, using, or selling its contributor version,
|
||||||
|
but do not include claims that would be infringed only as a
|
||||||
|
consequence of further modification of the contributor version. For
|
||||||
|
purposes of this definition, "control" includes the right to grant
|
||||||
|
patent sublicenses in a manner consistent with the requirements of
|
||||||
|
this License.
|
||||||
|
|
||||||
|
Each contributor grants you a non-exclusive, worldwide, royalty-free
|
||||||
|
patent license under the contributor's essential patent claims, to
|
||||||
|
make, use, sell, offer for sale, import and otherwise run, modify and
|
||||||
|
propagate the contents of its contributor version.
|
||||||
|
|
||||||
|
In the following three paragraphs, a "patent license" is any express
|
||||||
|
agreement or commitment, however denominated, not to enforce a patent
|
||||||
|
(such as an express permission to practice a patent or covenant not to
|
||||||
|
sue for patent infringement). To "grant" such a patent license to a
|
||||||
|
party means to make such an agreement or commitment not to enforce a
|
||||||
|
patent against the party.
|
||||||
|
|
||||||
|
If you convey a covered work, knowingly relying on a patent license,
|
||||||
|
and the Corresponding Source of the work is not available for anyone
|
||||||
|
to copy, free of charge and under the terms of this License, through a
|
||||||
|
publicly available network server or other readily accessible means,
|
||||||
|
then you must either (1) cause the Corresponding Source to be so
|
||||||
|
available, or (2) arrange to deprive yourself of the benefit of the
|
||||||
|
patent license for this particular work, or (3) arrange, in a manner
|
||||||
|
consistent with the requirements of this License, to extend the patent
|
||||||
|
license to downstream recipients. "Knowingly relying" means you have
|
||||||
|
actual knowledge that, but for the patent license, your conveying the
|
||||||
|
covered work in a country, or your recipient's use of the covered work
|
||||||
|
in a country, would infringe one or more identifiable patents in that
|
||||||
|
country that you have reason to believe are valid.
|
||||||
|
|
||||||
|
If, pursuant to or in connection with a single transaction or
|
||||||
|
arrangement, you convey, or propagate by procuring conveyance of, a
|
||||||
|
covered work, and grant a patent license to some of the parties
|
||||||
|
receiving the covered work authorizing them to use, propagate, modify
|
||||||
|
or convey a specific copy of the covered work, then the patent license
|
||||||
|
you grant is automatically extended to all recipients of the covered
|
||||||
|
work and works based on it.
|
||||||
|
|
||||||
|
A patent license is "discriminatory" if it does not include within
|
||||||
|
the scope of its coverage, prohibits the exercise of, or is
|
||||||
|
conditioned on the non-exercise of one or more of the rights that are
|
||||||
|
specifically granted under this License. You may not convey a covered
|
||||||
|
work if you are a party to an arrangement with a third party that is
|
||||||
|
in the business of distributing software, under which you make payment
|
||||||
|
to the third party based on the extent of your activity of conveying
|
||||||
|
the work, and under which the third party grants, to any of the
|
||||||
|
parties who would receive the covered work from you, a discriminatory
|
||||||
|
patent license (a) in connection with copies of the covered work
|
||||||
|
conveyed by you (or copies made from those copies), or (b) primarily
|
||||||
|
for and in connection with specific products or compilations that
|
||||||
|
contain the covered work, unless you entered into that arrangement,
|
||||||
|
or that patent license was granted, prior to 28 March 2007.
|
||||||
|
|
||||||
|
Nothing in this License shall be construed as excluding or limiting
|
||||||
|
any implied license or other defenses to infringement that may
|
||||||
|
otherwise be available to you under applicable patent law.
|
||||||
|
|
||||||
|
12. No Surrender of Others' Freedom.
|
||||||
|
|
||||||
|
If conditions are imposed on you (whether by court order, agreement or
|
||||||
|
otherwise) that contradict the conditions of this License, they do not
|
||||||
|
excuse you from the conditions of this License. If you cannot convey a
|
||||||
|
covered work so as to satisfy simultaneously your obligations under this
|
||||||
|
License and any other pertinent obligations, then as a consequence you may
|
||||||
|
not convey it at all. For example, if you agree to terms that obligate you
|
||||||
|
to collect a royalty for further conveying from those to whom you convey
|
||||||
|
the Program, the only way you could satisfy both those terms and this
|
||||||
|
License would be to refrain entirely from conveying the Program.
|
||||||
|
|
||||||
|
13. Use with the GNU Affero General Public License.
|
||||||
|
|
||||||
|
Notwithstanding any other provision of this License, you have
|
||||||
|
permission to link or combine any covered work with a work licensed
|
||||||
|
under version 3 of the GNU Affero General Public License into a single
|
||||||
|
combined work, and to convey the resulting work. The terms of this
|
||||||
|
License will continue to apply to the part which is the covered work,
|
||||||
|
but the special requirements of the GNU Affero General Public License,
|
||||||
|
section 13, concerning interaction through a network will apply to the
|
||||||
|
combination as such.
|
||||||
|
|
||||||
|
14. Revised Versions of this License.
|
||||||
|
|
||||||
|
The Free Software Foundation may publish revised and/or new versions of
|
||||||
|
the GNU General Public License from time to time. Such new versions will
|
||||||
|
be similar in spirit to the present version, but may differ in detail to
|
||||||
|
address new problems or concerns.
|
||||||
|
|
||||||
|
Each version is given a distinguishing version number. If the
|
||||||
|
Program specifies that a certain numbered version of the GNU General
|
||||||
|
Public License "or any later version" applies to it, you have the
|
||||||
|
option of following the terms and conditions either of that numbered
|
||||||
|
version or of any later version published by the Free Software
|
||||||
|
Foundation. If the Program does not specify a version number of the
|
||||||
|
GNU General Public License, you may choose any version ever published
|
||||||
|
by the Free Software Foundation.
|
||||||
|
|
||||||
|
If the Program specifies that a proxy can decide which future
|
||||||
|
versions of the GNU General Public License can be used, that proxy's
|
||||||
|
public statement of acceptance of a version permanently authorizes you
|
||||||
|
to choose that version for the Program.
|
||||||
|
|
||||||
|
Later license versions may give you additional or different
|
||||||
|
permissions. However, no additional obligations are imposed on any
|
||||||
|
author or copyright holder as a result of your choosing to follow a
|
||||||
|
later version.
|
||||||
|
|
||||||
|
15. Disclaimer of Warranty.
|
||||||
|
|
||||||
|
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
|
||||||
|
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
|
||||||
|
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
|
||||||
|
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
|
||||||
|
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||||
|
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
|
||||||
|
IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
|
||||||
|
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
|
||||||
|
|
||||||
|
16. Limitation of Liability.
|
||||||
|
|
||||||
|
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||||
|
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
|
||||||
|
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
|
||||||
|
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
|
||||||
|
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
|
||||||
|
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
|
||||||
|
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
|
||||||
|
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
|
||||||
|
SUCH DAMAGES.
|
||||||
|
|
||||||
|
17. Interpretation of Sections 15 and 16.
|
||||||
|
|
||||||
|
If the disclaimer of warranty and limitation of liability provided
|
||||||
|
above cannot be given local legal effect according to their terms,
|
||||||
|
reviewing courts shall apply local law that most closely approximates
|
||||||
|
an absolute waiver of all civil liability in connection with the
|
||||||
|
Program, unless a warranty or assumption of liability accompanies a
|
||||||
|
copy of the Program in return for a fee.
|
||||||
|
|
||||||
|
END OF TERMS AND CONDITIONS
|
||||||
|
|
||||||
|
How to Apply These Terms to Your New Programs
|
||||||
|
|
||||||
|
If you develop a new program, and you want it to be of the greatest
|
||||||
|
possible use to the public, the best way to achieve this is to make it
|
||||||
|
free software which everyone can redistribute and change under these terms.
|
||||||
|
|
||||||
|
To do so, attach the following notices to the program. It is safest
|
||||||
|
to attach them to the start of each source file to most effectively
|
||||||
|
state the exclusion of warranty; and each file should have at least
|
||||||
|
the "copyright" line and a pointer to where the full notice is found.
|
||||||
|
|
||||||
|
<one line to give the program's name and a brief idea of what it does.>
|
||||||
|
Copyright (C) <year> <name of author>
|
||||||
|
|
||||||
|
This program 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 program 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 <https://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
Also add information on how to contact you by electronic and paper mail.
|
||||||
|
|
||||||
|
If the program does terminal interaction, make it output a short
|
||||||
|
notice like this when it starts in an interactive mode:
|
||||||
|
|
||||||
|
<program> Copyright (C) <year> <name of author>
|
||||||
|
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
|
||||||
|
This is free software, and you are welcome to redistribute it
|
||||||
|
under certain conditions; type `show c' for details.
|
||||||
|
|
||||||
|
The hypothetical commands `show w' and `show c' should show the appropriate
|
||||||
|
parts of the General Public License. Of course, your program's commands
|
||||||
|
might be different; for a GUI interface, you would use an "about box".
|
||||||
|
|
||||||
|
You should also get your employer (if you work as a programmer) or school,
|
||||||
|
if any, to sign a "copyright disclaimer" for the program, if necessary.
|
||||||
|
For more information on this, and how to apply and follow the GNU GPL, see
|
||||||
|
<https://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
The GNU General Public License does not permit incorporating your program
|
||||||
|
into proprietary programs. If your program is a subroutine library, you
|
||||||
|
may consider it more useful to permit linking proprietary applications with
|
||||||
|
the library. If this is what you want to do, use the GNU Lesser General
|
||||||
|
Public License instead of this License. But first, please read
|
||||||
|
<https://www.gnu.org/licenses/why-not-lgpl.html>.
|
||||||
173
scripts/libraries/rv/README.md
Normal file
173
scripts/libraries/rv/README.md
Normal file
@ -0,0 +1,173 @@
|
|||||||
|
# OpenRV - Robot Vision routines for OpenMV
|
||||||
|
|
||||||
|
[OpenMV](https://openmv.io) is a small camera board for machine vision. I use it
|
||||||
|
to direct my robot. [The software
|
||||||
|
library](http://docs.openmv.io/library/index.html) is adequate, but lacks some
|
||||||
|
algorithms I need. Out comes this project, in which I implement a few missing
|
||||||
|
pieces myself. I hope it could save time for someone who tries to do the same.
|
||||||
|
|
||||||
|
**Everything is tested on OpenMV Cam H7**
|
||||||
|
|
||||||
|
## Prerequisites
|
||||||
|
|
||||||
|
Vector and matrix are mainstay in machine vision. Finding no satisfactory
|
||||||
|
libraries, I have again implemented my own.
|
||||||
|
|
||||||
|
#### Vector Operations on MicroPython
|
||||||
|
|
||||||
|
- [Project](https://gitlab.com/nickoala/micropython-vec)
|
||||||
|
- [Package](https://pypi.org/project/micropython-vec/)
|
||||||
|
|
||||||
|
#### Fast Matrix Multiplication and Linear Solver on MicroPython
|
||||||
|
|
||||||
|
- [Project](https://gitlab.com/nickoala/micropython-mtx)
|
||||||
|
- [Package](https://pypi.org/project/micropython-mtx/)
|
||||||
|
|
||||||
|
Along with this project's `rv` package, the OpenMV camera's SD card should
|
||||||
|
contain:
|
||||||
|
|
||||||
|
```
|
||||||
|
/
|
||||||
|
├── mtx.py
|
||||||
|
├── rv
|
||||||
|
│ ├── __init__.py
|
||||||
|
│ ├── moments.py
|
||||||
|
│ ├── planar.py
|
||||||
|
│ └── quickshiftpp.py
|
||||||
|
└── vec
|
||||||
|
├── distance.py
|
||||||
|
└── __init__.py
|
||||||
|
```
|
||||||
|
|
||||||
|
**In addition, you need some theoretical backgrounds to use vision algorithms
|
||||||
|
effectively. This page does not give you those backgrounds. Study them
|
||||||
|
yourself.**
|
||||||
|
|
||||||
|
## Hu moments
|
||||||
|
|
||||||
|
[Hu moments](https://docs.opencv.org/2.4/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html#humoments)
|
||||||
|
[is a shape descriptor](https://www.pyimagesearch.com/2014/10/27/opencv-shape-descriptor-hu-moments-example/)
|
||||||
|
[invariant to translation, scale, and rotation](https://www.learnopencv.com/shape-matching-using-hu-moments-c-python/).
|
||||||
|
That means it can recognize the same shape no matter its location, size, and orientation in the picture.
|
||||||
|
|
||||||
|
#### Usage
|
||||||
|
|
||||||
|
The last element of Hu moments is somewhat of an oddball. It indicates
|
||||||
|
reflection rather than the general shape. For matching, the last element should
|
||||||
|
be dropped.
|
||||||
|
|
||||||
|
Use the function `vec.distance.euclidean()` to see how close two vectors are.
|
||||||
|
|
||||||
|
```python
|
||||||
|
import rv.moments
|
||||||
|
import vec.distance
|
||||||
|
import image
|
||||||
|
|
||||||
|
a = image.Image('/images/a.pgm')
|
||||||
|
b = image.Image('/images/b.pgm')
|
||||||
|
|
||||||
|
ha = rv.moments.hu(a)
|
||||||
|
hb = rv.moments.hu(b)
|
||||||
|
|
||||||
|
print(vec.distance.euclidean(ha[:-1], hb[:-1]))
|
||||||
|
```
|
||||||
|
|
||||||
|
**Remark:** Although accepting gray-level images, this implementation treats
|
||||||
|
pixels as either 0 or 1. Pixels having a non-zero brightness are treated as 1.
|
||||||
|
This speeds up calculation.
|
||||||
|
|
||||||
|
**More:** [test_moments.py](test/test_moments.py)
|
||||||
|
|
||||||
|
## Planar homography
|
||||||
|
|
||||||
|
Map points from one coordinate system to another. For example, a red ball sits
|
||||||
|
at (90, 50) on the image and you know it is on the floor (not floating in air),
|
||||||
|
planar homography can map the image point (90, 50) to a position on the floor,
|
||||||
|
telling you how far the red ball is in front of the robot and how much left or
|
||||||
|
right. In this case, points are essentially mapped from the *image coordinate
|
||||||
|
system* to the *floor coordinate system*.
|
||||||
|
|
||||||
|
Once you can map points, finding out the size of objects is straight-forward.
|
||||||
|
|
||||||
|
#### Usage
|
||||||
|
|
||||||
|
It works only when two coordinate systems (i.e. the two planes) are fixed
|
||||||
|
relative to each other. In other words, the camera's height and orientation
|
||||||
|
relative to the floor cannot change.
|
||||||
|
|
||||||
|
**[First, you have to calibrate for a homography matrix, which is a very long
|
||||||
|
story. I have devoted an entire directory to discuss the process. Take a look
|
||||||
|
there.](homography)**
|
||||||
|
|
||||||
|
Once you have the matrix, the rest is easy.
|
||||||
|
|
||||||
|
```python
|
||||||
|
import rv.planar
|
||||||
|
|
||||||
|
H = [[ 3.14916496e+01, -9.79038178e+02, 1.03951636e+05],
|
||||||
|
[ 7.57939015e+02, -3.31912533e+01, -5.86807545e+04],
|
||||||
|
[ 2.06572544e-01, 2.03579263e+00, 1.00000000e+00]]
|
||||||
|
|
||||||
|
p = rv.planar.Planar(H)
|
||||||
|
|
||||||
|
image_points = [[83, 109],
|
||||||
|
[70, 100],
|
||||||
|
[51, 92]]
|
||||||
|
|
||||||
|
print(p.project(image_points))
|
||||||
|
```
|
||||||
|
|
||||||
|
**More:** [test_planar.py](test/test_planar.py)
|
||||||
|
|
||||||
|
## Quickshift++
|
||||||
|
|
||||||
|
[The latest member](https://github.com/google/quickshift) [of the
|
||||||
|
Meanshift](http://www.chioka.in/meanshift-algorithm-for-the-rest-of-us-python/)
|
||||||
|
[family of clustering
|
||||||
|
algorithms](https://github.com/Nick-Ol/MedoidShift-and-QuickShift), Quickshift++
|
||||||
|
accepts a bunch of points and group them. I use it to "discover" the colors of
|
||||||
|
disks on the floor, before using colors to pick out the disks. This saves me
|
||||||
|
from hard-coding the colors beforehand, and makes the robot adaptive.
|
||||||
|
|
||||||
|
It is not optimized to handle a large number of points. OpenMV's limited memory
|
||||||
|
precludes handling a lot of points anyway. Don't expect to use it to segment an
|
||||||
|
entire image.
|
||||||
|
|
||||||
|
#### Usage
|
||||||
|
|
||||||
|
```python
|
||||||
|
import rv.quickshiftpp
|
||||||
|
|
||||||
|
points = [
|
||||||
|
# cluster 1
|
||||||
|
[1, 1],
|
||||||
|
[1.0, 1.2],
|
||||||
|
[0.9, 1.1],
|
||||||
|
[0.95, 0.99],
|
||||||
|
|
||||||
|
# cluster 2
|
||||||
|
[3.3, 3.0],
|
||||||
|
|
||||||
|
# cluster 3
|
||||||
|
[5.0, 8.2],
|
||||||
|
[5.5, 7.9],
|
||||||
|
[4.8, 8.1],
|
||||||
|
[5.1, 7.7],
|
||||||
|
]
|
||||||
|
|
||||||
|
print(rv.quickshiftpp.cluster(points,
|
||||||
|
k=2,
|
||||||
|
beta=0.2))
|
||||||
|
```
|
||||||
|
|
||||||
|
The parameter `k` determines how density is estimated. It uses *distance to the
|
||||||
|
k-th nearest neighbor* to estimate density around each point.
|
||||||
|
|
||||||
|
The parameter `beta` determines how much density is allowed to vary within
|
||||||
|
cluster cores. Here is not the place to explain what "cluster core" means. Some
|
||||||
|
theoretical understanding cannot be avoided.
|
||||||
|
|
||||||
|
In short, use `k` and `beta` to tune the clustering.
|
||||||
|
|
||||||
|
**More:** [test_quickshiftpp.py](test/test_quickshiftpp.py) and
|
||||||
|
[test_quickshiftpp_colors.py](test/test_quickshiftpp_colors.py)
|
||||||
1
scripts/libraries/rv/__init__.py
Normal file
1
scripts/libraries/rv/__init__.py
Normal file
@ -0,0 +1 @@
|
|||||||
|
|
||||||
86
scripts/libraries/rv/moments.py
Normal file
86
scripts/libraries/rv/moments.py
Normal file
@ -0,0 +1,86 @@
|
|||||||
|
import math
|
||||||
|
|
||||||
|
def _sum(img, roi, f):
|
||||||
|
x, y, w, h = roi or (0, 0, img.width(), img.height())
|
||||||
|
s = 0
|
||||||
|
for i in range(x, x + w):
|
||||||
|
for j in range(y, y + h):
|
||||||
|
if img.get_pixel(i,j) != 0:
|
||||||
|
s += f(i, j)
|
||||||
|
return s
|
||||||
|
|
||||||
|
def centroid(img, roi=None, return_intermediate=False):
|
||||||
|
m10 = _sum(img, roi, lambda x,y: x)
|
||||||
|
m01 = _sum(img, roi, lambda x,y: y)
|
||||||
|
m00 = _sum(img, roi, lambda x,y: 1)
|
||||||
|
|
||||||
|
c = [0, 0] if m00 == 0 else [float(m10 / m00), float(m01 / m00)]
|
||||||
|
|
||||||
|
return [m00, c] if return_intermediate else c
|
||||||
|
|
||||||
|
def central(img, roi=None, return_intermediate=False):
|
||||||
|
results = centroid(img, roi, return_intermediate=True)
|
||||||
|
cx, cy = results[-1]
|
||||||
|
|
||||||
|
u20 = _sum(img, roi, lambda x,y: (x-cx)**2)
|
||||||
|
u11 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy))
|
||||||
|
u02 = _sum(img, roi, lambda x,y: (y-cy)**2)
|
||||||
|
|
||||||
|
u30 = _sum(img, roi, lambda x,y: (x-cx)**3)
|
||||||
|
u21 = _sum(img, roi, lambda x,y: (x-cx)**2 * (y-cy))
|
||||||
|
u12 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy)**2)
|
||||||
|
u03 = _sum(img, roi, lambda x,y: (y-cy)**3)
|
||||||
|
|
||||||
|
us = [u20, u11, u02, u30, u21, u12, u03]
|
||||||
|
|
||||||
|
return (results + [us]) if return_intermediate else us
|
||||||
|
|
||||||
|
def normalized_central(img, roi=None, return_intermediate=False):
|
||||||
|
results = central(img, roi, return_intermediate=True)
|
||||||
|
m00, _, [u20, u11, u02, u30, u21, u12, u03] = results
|
||||||
|
|
||||||
|
if m00 == 0:
|
||||||
|
ns = [0, 0, 0, 0, 0, 0, 0]
|
||||||
|
else:
|
||||||
|
m2 = m00**2
|
||||||
|
m3 = m00**2.5
|
||||||
|
n20, n11, n02 = u20/m2, u11/m2, u02/m2
|
||||||
|
n30, n21, n12, n03 = u30/m3, u21/m3, u12/m3, u03/m3
|
||||||
|
|
||||||
|
ns = [n20, n11, n02, n30, n21, n12, n03]
|
||||||
|
|
||||||
|
return (results + [ns]) if return_intermediate else ns
|
||||||
|
|
||||||
|
def hu(img, roi=None, return_intermediate=False):
|
||||||
|
results = normalized_central(img, roi, return_intermediate=True)
|
||||||
|
n20, n11, n02, n30, n21, n12, n03 = results[-1]
|
||||||
|
|
||||||
|
h0 = n20 + n02
|
||||||
|
|
||||||
|
h1 = (n20 - n02)**2 + 4 * n11 * n11
|
||||||
|
|
||||||
|
_n30_3n12 = n30 - 3 * n12
|
||||||
|
_3n21_n03 = 3 * n21 - n03
|
||||||
|
|
||||||
|
h2 = _n30_3n12**2 + _3n21_n03**2
|
||||||
|
|
||||||
|
n3012 = n30 + n12
|
||||||
|
n3012_2 = n3012 * n3012
|
||||||
|
|
||||||
|
n2103 = n21 + n03
|
||||||
|
n2103_2 = n2103 * n2103
|
||||||
|
|
||||||
|
h3 = n3012_2 + n2103_2
|
||||||
|
|
||||||
|
h4 = (_n30_3n12 * n3012 * ( n3012_2 - 3 * n2103_2 )
|
||||||
|
+ _3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 ))
|
||||||
|
|
||||||
|
h5 = ( n20 - n02 ) * ( n3012_2 - n2103_2 ) + 4 * n11 * n3012 * n2103
|
||||||
|
|
||||||
|
h6 = (_3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 )
|
||||||
|
- _n30_3n12 * n2103 * ( 3 * n3012_2 - n2103_2 ))
|
||||||
|
|
||||||
|
hs = [0 if h == 0 else math.copysign(math.log10(math.fabs(h)), h)
|
||||||
|
for h in [h0, h1, h2, h3, h4, h5, h6]]
|
||||||
|
|
||||||
|
return (results + [hs]) if return_intermediate else hs
|
||||||
20
scripts/libraries/rv/planar.py
Normal file
20
scripts/libraries/rv/planar.py
Normal file
@ -0,0 +1,20 @@
|
|||||||
|
import mtx, vec
|
||||||
|
|
||||||
|
class Planar(object):
|
||||||
|
def __init__(self, H, offset=[0,0]):
|
||||||
|
self.H = H
|
||||||
|
self.H_ = None # LU factorization of H
|
||||||
|
self.offset = offset
|
||||||
|
|
||||||
|
def project(self, points, reverse=False):
|
||||||
|
if reverse:
|
||||||
|
if self.H_ is None:
|
||||||
|
self.H_ = mtx.lu([r[:] for r in self.H])
|
||||||
|
|
||||||
|
qs = [mtx.solve(self.H_,
|
||||||
|
vec.sub(p, self.offset)+[1]) for p in points]
|
||||||
|
return [vec.div(q[:-1], q[-1]) for q in qs]
|
||||||
|
else:
|
||||||
|
qs = [mtx.mul(self.H, p+[1]) for p in points]
|
||||||
|
return [vec.add(self.offset,
|
||||||
|
vec.div(q[:-1], q[-1])) for q in qs]
|
||||||
162
scripts/libraries/rv/quickshiftpp.py
Normal file
162
scripts/libraries/rv/quickshiftpp.py
Normal file
@ -0,0 +1,162 @@
|
|||||||
|
import vec.distance
|
||||||
|
|
||||||
|
def distance_to_kth_nearest_neighbor(points, i, k):
|
||||||
|
fix = points[i]
|
||||||
|
d = [vec.distance.euclidean(fix, p) for p in points]
|
||||||
|
d.sort()
|
||||||
|
return d[k]
|
||||||
|
# Smallest distance is always to the point itself.
|
||||||
|
# First element can be ignored.
|
||||||
|
# Distance to k-th nearest neighbor is at index == k.
|
||||||
|
|
||||||
|
def calculate_threshold(r, d, beta):
|
||||||
|
return r / (1 - beta)**(1 / d)
|
||||||
|
|
||||||
|
def find_threshold_position(threshold, ascending):
|
||||||
|
lower = 0
|
||||||
|
upper = len(ascending) - 1
|
||||||
|
|
||||||
|
if ascending[upper][0] <= threshold:
|
||||||
|
return upper
|
||||||
|
|
||||||
|
# binary search
|
||||||
|
while upper - lower > 1:
|
||||||
|
i = (upper + lower) // 2
|
||||||
|
r = ascending[i][0]
|
||||||
|
|
||||||
|
if r == threshold:
|
||||||
|
# push `i` to last element equal to threshold
|
||||||
|
while i+1 < len(ascending) and ascending[i+1][0] == threshold:
|
||||||
|
i += 1
|
||||||
|
return i
|
||||||
|
elif r < threshold:
|
||||||
|
lower = i
|
||||||
|
else:
|
||||||
|
upper = i
|
||||||
|
|
||||||
|
if ascending[upper][0] <= threshold:
|
||||||
|
return upper
|
||||||
|
else:
|
||||||
|
return lower
|
||||||
|
|
||||||
|
def in_which(x, sets):
|
||||||
|
for s in sets:
|
||||||
|
if x in s:
|
||||||
|
return s
|
||||||
|
return None
|
||||||
|
|
||||||
|
def form_cluster_core(core_set,
|
||||||
|
existing_cores,
|
||||||
|
points,
|
||||||
|
sorted_radii,
|
||||||
|
seed_position,
|
||||||
|
threshold_position):
|
||||||
|
|
||||||
|
def include(current_position):
|
||||||
|
current_radius, current_index = sorted_radii[current_position]
|
||||||
|
|
||||||
|
core_set.add(current_index)
|
||||||
|
|
||||||
|
for other_position in range(0, threshold_position + 1):
|
||||||
|
other_radius, other_index = sorted_radii[other_position]
|
||||||
|
|
||||||
|
if other_index == current_index or other_index in core_set:
|
||||||
|
continue
|
||||||
|
|
||||||
|
distance = vec.distance.euclidean(
|
||||||
|
points[current_index], points[other_index])
|
||||||
|
|
||||||
|
if distance <= min(current_radius, other_radius):
|
||||||
|
# Connect current point to the other point
|
||||||
|
|
||||||
|
if in_which(other_index, existing_cores) is not None:
|
||||||
|
# The other point is already in another core.
|
||||||
|
# Current set will not be disjoint from existing cores.
|
||||||
|
# Current set cannot form a new core.
|
||||||
|
return False
|
||||||
|
else:
|
||||||
|
# Continue making connections, starting from new point.
|
||||||
|
clean = include(other_position)
|
||||||
|
if not clean:
|
||||||
|
return False
|
||||||
|
return True
|
||||||
|
|
||||||
|
return include(seed_position)
|
||||||
|
|
||||||
|
def assign_cluster(clusters,
|
||||||
|
points,
|
||||||
|
sorted_radii,
|
||||||
|
position):
|
||||||
|
|
||||||
|
def find_cluster_to_belong(current_position):
|
||||||
|
_, current_index = sorted_radii[current_position]
|
||||||
|
|
||||||
|
cluster_set = in_which(current_index, clusters)
|
||||||
|
if cluster_set is not None:
|
||||||
|
# already belong to a cluster
|
||||||
|
return cluster_set
|
||||||
|
|
||||||
|
nearest_neighbor_distance = None
|
||||||
|
nearest_neighbor_position = None
|
||||||
|
|
||||||
|
# find nearest neighbor
|
||||||
|
for i in range(0, current_position):
|
||||||
|
_, other_index = sorted_radii[i]
|
||||||
|
|
||||||
|
distance = vec.distance.euclidean(
|
||||||
|
points[current_index], points[other_index])
|
||||||
|
|
||||||
|
if nearest_neighbor_distance is None \
|
||||||
|
or distance < nearest_neighbor_distance:
|
||||||
|
nearest_neighbor_distance = distance
|
||||||
|
nearest_neighbor_position = i
|
||||||
|
|
||||||
|
# join nearest neighbor's cluster
|
||||||
|
cluster_set = find_cluster_to_belong(nearest_neighbor_position)
|
||||||
|
cluster_set.add(current_index)
|
||||||
|
return cluster_set
|
||||||
|
|
||||||
|
find_cluster_to_belong(position)
|
||||||
|
|
||||||
|
def cluster(points,
|
||||||
|
k,
|
||||||
|
beta,
|
||||||
|
return_modes=False):
|
||||||
|
dimension = len(points[0])
|
||||||
|
|
||||||
|
sorted_radii = [(distance_to_kth_nearest_neighbor(points, i, k=k), i)
|
||||||
|
for i in range(0, len(points))]
|
||||||
|
sorted_radii.sort()
|
||||||
|
# smallest radius first, i.e. highest density first.
|
||||||
|
|
||||||
|
modes = []
|
||||||
|
clusters = []
|
||||||
|
proposed_core = set()
|
||||||
|
|
||||||
|
for position in range(0, len(sorted_radii)):
|
||||||
|
radius, index = sorted_radii[position]
|
||||||
|
|
||||||
|
threshold = calculate_threshold(radius, dimension, beta)
|
||||||
|
threshold_position = find_threshold_position(threshold, sorted_radii)
|
||||||
|
|
||||||
|
if form_cluster_core(proposed_core,
|
||||||
|
clusters,
|
||||||
|
points,
|
||||||
|
sorted_radii,
|
||||||
|
seed_position=position,
|
||||||
|
threshold_position=threshold_position):
|
||||||
|
clusters.append(proposed_core)
|
||||||
|
proposed_core = set()
|
||||||
|
|
||||||
|
if return_modes:
|
||||||
|
modes.append(index)
|
||||||
|
else:
|
||||||
|
proposed_core.clear()
|
||||||
|
|
||||||
|
for position in range(0, len(sorted_radii)):
|
||||||
|
assign_cluster(clusters,
|
||||||
|
points,
|
||||||
|
sorted_radii,
|
||||||
|
position=position)
|
||||||
|
|
||||||
|
return (clusters, modes) if return_modes else clusters
|
||||||
20
scripts/libraries/vec/LICENSE.md
Normal file
20
scripts/libraries/vec/LICENSE.md
Normal file
@ -0,0 +1,20 @@
|
|||||||
|
The MIT License (MIT)
|
||||||
|
|
||||||
|
Copyright (c) 2019 Nick Lee
|
||||||
|
|
||||||
|
Permission is hereby granted, free of charge, to any person obtaining a copy of
|
||||||
|
this software and associated documentation files (the "Software"), to deal in
|
||||||
|
the Software without restriction, including without limitation the rights to
|
||||||
|
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
|
||||||
|
the Software, and to permit persons to whom the Software is furnished to do so,
|
||||||
|
subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in all
|
||||||
|
copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
|
||||||
|
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
|
||||||
|
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||||
|
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||||
28
scripts/libraries/vec/README.md
Normal file
28
scripts/libraries/vec/README.md
Normal file
@ -0,0 +1,28 @@
|
|||||||
|
# Vector Operations on MicroPython
|
||||||
|
|
||||||
|
Nothing fancy. Treating list as vector, this library performs common
|
||||||
|
operations. I personally use it on [OpenMV](https://openmv.io) for robot vision.
|
||||||
|
|
||||||
|
```python
|
||||||
|
import vec
|
||||||
|
|
||||||
|
a = [1, 2, 3]
|
||||||
|
b = [4, 5, 6]
|
||||||
|
|
||||||
|
vec.add(a, b) # [5, 7, 9]
|
||||||
|
vec.sub(a, b) # [-3, -3, -3]
|
||||||
|
vec.dot(a, b) # 32
|
||||||
|
|
||||||
|
vec.mul(a, 2) # [2, 4, 6]
|
||||||
|
vec.div(a, 2) # [0.5, 1.0, 1.5]
|
||||||
|
```
|
||||||
|
|
||||||
|
```python
|
||||||
|
import vec.distance
|
||||||
|
|
||||||
|
a = [2, 3]
|
||||||
|
b = [5, 7]
|
||||||
|
|
||||||
|
vec.distance.manhattan(a, b) # 7
|
||||||
|
vec.distance.euclidean(a, b) # 5
|
||||||
|
```
|
||||||
17
scripts/libraries/vec/__init__.py
Normal file
17
scripts/libraries/vec/__init__.py
Normal file
@ -0,0 +1,17 @@
|
|||||||
|
def add(a, b):
|
||||||
|
return [a[i] + b[i] for i in range(0, min(len(a), len(b)))]
|
||||||
|
|
||||||
|
def sub(a, b):
|
||||||
|
return [a[i] - b[i] for i in range(0, min(len(a), len(b)))]
|
||||||
|
|
||||||
|
def mul(a, n):
|
||||||
|
return [a[i] * n for i in range(0, len(a))]
|
||||||
|
|
||||||
|
def div(a, n):
|
||||||
|
return [a[i] / n for i in range(0, len(a))]
|
||||||
|
|
||||||
|
def dot(a, b):
|
||||||
|
s = 0
|
||||||
|
for i in range(0, min(len(a), len(b))):
|
||||||
|
s += a[i] * b[i]
|
||||||
|
return s
|
||||||
13
scripts/libraries/vec/distance.py
Normal file
13
scripts/libraries/vec/distance.py
Normal file
@ -0,0 +1,13 @@
|
|||||||
|
import math
|
||||||
|
|
||||||
|
def manhattan(a, b):
|
||||||
|
s = 0
|
||||||
|
for i in range(0, min(len(a), len(b))):
|
||||||
|
s += abs(a[i] - b[i])
|
||||||
|
return s
|
||||||
|
|
||||||
|
def euclidean(a, b):
|
||||||
|
s = 0
|
||||||
|
for i in range(0, min(len(a), len(b))):
|
||||||
|
s += (a[i] - b[i])**2
|
||||||
|
return math.sqrt(s)
|
||||||
Loading…
Reference in New Issue
Block a user