Compare commits
46 commits
882989af8f
...
ed2af1a072
Author | SHA1 | Date | |
---|---|---|---|
Simon Bruder | ed2af1a072 | ||
Simon Bruder | 0fb02e2024 | ||
Simon Bruder | ca0f1d4e1e | ||
Simon Bruder | 8d8c3de73f | ||
Simon Bruder | 088ec46226 | ||
Simon Bruder | 3b871a2caf | ||
Simon Bruder | c2a9ada979 | ||
Simon Bruder | 034772ea63 | ||
Simon Bruder | 0690c3dc5b | ||
Simon Bruder | fa9a61ce73 | ||
Simon Bruder | 1c66b87377 | ||
Simon Bruder | 3000083db9 | ||
Simon Bruder | 15f0ddb379 | ||
Simon Bruder | dc82014f5d | ||
Simon Bruder | cc2fe216b5 | ||
Simon Bruder | 7329995358 | ||
Simon Bruder | 81026474ce | ||
Simon Bruder | b0ec6adb9d | ||
Simon Bruder | 1d3896d437 | ||
Simon Bruder | 3dcabb8da9 | ||
Simon Bruder | e3a81a7354 | ||
Simon Bruder | f7b3c276a3 | ||
Simon Bruder | b208531838 | ||
Simon Bruder | 60cbffbf8a | ||
Simon Bruder | 517aa9e276 | ||
Simon Bruder | c74c074624 | ||
Simon Bruder | 282063b8b2 | ||
Simon Bruder | e3a3509295 | ||
Simon Bruder | d090df1297 | ||
Simon Bruder | 524f1046d0 | ||
Simon Bruder | 9d8cf220bb | ||
Simon Bruder | cabee0416b | ||
Simon Bruder | 60a8abfe34 | ||
Simon Bruder | 63431b6824 | ||
Simon Bruder | 8a07422a51 | ||
Simon Bruder | 9db38c33f5 | ||
Simon Bruder | f7e5769f8d | ||
Simon Bruder | 5ce178b914 | ||
Simon Bruder | db4d489ae8 | ||
Simon Bruder | 5c8784c9f4 | ||
Simon Bruder | e138a4d58c | ||
Simon Bruder | a4e9c4abda | ||
Simon Bruder | d81daf6b10 | ||
Simon Bruder | fd230375ee | ||
Simon Bruder | abb6291c56 | ||
Simon Bruder | 47e5d9c522 |
65
README.md
Normal file
65
README.md
Normal file
|
@ -0,0 +1,65 @@
|
|||
# Programming tasks for ECG
|
||||
|
||||
This repository includes my solutions to the tasks
|
||||
for the module [*Einführung in die Computergraphik* (Introduction to computer graphics)](https://tu-dresden.de/ing/informatik/smt/cgv/studium/lehrveranstaltungen/ss2023/ecg)
|
||||
in the summer semester 2023 at the [TU Dresden](https://tu-dresden.de/).
|
||||
|
||||
Each exercise includes a separate `readme.txt`
|
||||
that describes things specific to how I implemented the task.
|
||||
However, those documents are in German, which is a requirement.
|
||||
|
||||
**Note**:
|
||||
Due to copyright restrictions,
|
||||
I am not allowed to publish many of my solutions.
|
||||
The repository `ecg-prog-filtered` only includes files solely written by me.
|
||||
It is filtered with the [`filter.sh`](./filter.sh) script.
|
||||
Please **don’t** rely on the history of this repository,
|
||||
as rewriting is part of how it can exist.
|
||||
See [Licence](#Licence) for more information on the licencing.
|
||||
|
||||
If you want access to all of my solutions,
|
||||
please write me an email (or contact me in another way),
|
||||
I’ll see what I can do.
|
||||
|
||||
## Usage
|
||||
|
||||
### Build
|
||||
|
||||
To build a specific exercise,
|
||||
you can use [Nix](https://nixos.org/) with flake support:
|
||||
|
||||
```bash
|
||||
nix build -L .#u01
|
||||
```
|
||||
|
||||
You can also manually invoke CMake.
|
||||
This requires you to have all dependencies installed.
|
||||
Because this is not my preferred way, there is no canonical list of dependencies,
|
||||
but you can find them in `flake.nix`.
|
||||
|
||||
### Development
|
||||
|
||||
You can use `nix develop` or [`direnv`](https://direnv.net/).
|
||||
|
||||
To create a `compile_commands.json` for `ccls` (or similar),
|
||||
create a `build` directory inside the exercise directory,
|
||||
and from that, execute:
|
||||
|
||||
```bash
|
||||
cmake .. -DCMAKE_BUILD_TYPE=Debug -DCMAKE_EXPORT_COMPILE_COMMANDS=YES
|
||||
ln -sf build/compile_commands.json ..
|
||||
```
|
||||
|
||||
## Licence
|
||||
|
||||
[GPL-3.0-or-later](https://spdx.org/licenses/GPL-3.0-or-later.html)
|
||||
or [LGPL-3.0-or-later](https://spdx.org/licenses/LGPL-3.0-or-later.html)
|
||||
or “Copyright (C) CGV TU Dresden - All Rights Reserved”.
|
||||
|
||||
The branch published only includes files under free software licences.
|
||||
Sadly, that makes them very incomplete,
|
||||
because most implementations done by me are in files from the template,
|
||||
which makes my additions a derivative work.
|
||||
All files not marked differently, are released under GPL-3.0-or-later.
|
||||
|
||||
See [gpl-3.0.txt](./gpl-3.0.txt) and [lgpl-3.0.txt](./lgpl-3.0.txt) for details.
|
9
filter.sh
Executable file
9
filter.sh
Executable file
|
@ -0,0 +1,9 @@
|
|||
#!/usr/bin/env bash
|
||||
# SPDX-License-Identifier: GPL-3.0-or-later
|
||||
set -euo pipefail
|
||||
export FILTER_BRANCH_SQUELCH_WARNING=1
|
||||
git branch -D filtered
|
||||
git switch -c filtered
|
||||
git filter-branch -f --tree-filter "rm -f $(rg --files-without-match 'SPDX-License-Identifier: (L)?GPL-3.0-or-later' -g '/u??/**/*' | tr '\n' ' ')" HEAD
|
||||
git push -f -u filtered filtered
|
||||
git switch -
|
|
@ -20,16 +20,16 @@
|
|||
},
|
||||
"nixpkgs": {
|
||||
"locked": {
|
||||
"lastModified": 1681759395,
|
||||
"narHash": "sha256-7aaRtLxLAy8qFVIA26ulB+Q5nDVzuQ71qi0s0wMjAws=",
|
||||
"lastModified": 1683408522,
|
||||
"narHash": "sha256-9kcPh6Uxo17a3kK3XCHhcWiV1Yu1kYj22RHiymUhMkU=",
|
||||
"owner": "nixos",
|
||||
"repo": "nixpkgs",
|
||||
"rev": "cd749f58ba83f7155b7062dd49d08e5e47e44d50",
|
||||
"rev": "897876e4c484f1e8f92009fd11b7d988a121a4e7",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "nixos",
|
||||
"ref": "nixos-22.11",
|
||||
"ref": "nixos-unstable",
|
||||
"repo": "nixpkgs",
|
||||
"type": "github"
|
||||
}
|
||||
|
|
16
flake.nix
16
flake.nix
|
@ -1,6 +1,6 @@
|
|||
{
|
||||
inputs = {
|
||||
nixpkgs.url = "github:nixos/nixpkgs/nixos-22.11";
|
||||
nixpkgs.url = "github:nixos/nixpkgs/nixos-unstable";
|
||||
flake-utils.url = "github:numtide/flake-utils";
|
||||
};
|
||||
|
||||
|
@ -21,10 +21,22 @@
|
|||
doCheck = true;
|
||||
})
|
||||
{ };
|
||||
|
||||
u02 = pkgs.callPackage
|
||||
({ stdenv, catch2_3, cmake, freeglut, libGL, libGLU }: stdenv.mkDerivation {
|
||||
name = "ecg-u02";
|
||||
|
||||
src = ./u02;
|
||||
|
||||
nativeBuildInputs = [ catch2_3 cmake freeglut libGL libGLU ];
|
||||
|
||||
doCheck = true;
|
||||
})
|
||||
{ };
|
||||
};
|
||||
|
||||
devShells.default = pkgs.mkShell {
|
||||
nativeBuildInputs = with pkgs; [ catch2_3 cmake ];
|
||||
nativeBuildInputs = with pkgs; [ catch2_3 cmake freeglut libGL libGLU ];
|
||||
};
|
||||
});
|
||||
}
|
||||
|
|
674
gpl-3.0.txt
Normal file
674
gpl-3.0.txt
Normal file
|
@ -0,0 +1,674 @@
|
|||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 3, 29 June 2007
|
||||
|
||||
Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The GNU General Public License is a free, copyleft license for
|
||||
software and other kinds of works.
|
||||
|
||||
The licenses for most software and other practical works are designed
|
||||
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
|
||||
share and change all versions of a program--to make sure it remains free
|
||||
software for all its users. We, the Free Software Foundation, use the
|
||||
GNU General Public License for most of our software; it applies also to
|
||||
any other work released this way by its authors. You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
them if you wish), that you receive source code or can get it if you
|
||||
want it, that you can change the software or use pieces of it in new
|
||||
free programs, and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to prevent others from denying you
|
||||
these rights or asking you to surrender the rights. Therefore, you have
|
||||
certain responsibilities if you distribute copies of the software, or if
|
||||
you modify it: responsibilities to respect the freedom of others.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must pass on to the recipients the same
|
||||
freedoms that you received. You must make sure that they, too, receive
|
||||
or can get the source code. And you must show them these terms so they
|
||||
know their rights.
|
||||
|
||||
Developers that use the GNU GPL protect your rights with two steps:
|
||||
(1) assert copyright on the software, and (2) offer you this License
|
||||
giving you legal permission to copy, distribute and/or modify it.
|
||||
|
||||
For the developers' and authors' protection, the GPL clearly explains
|
||||
that there is no warranty for this free software. For both users' and
|
||||
authors' sake, the GPL requires that modified versions be marked as
|
||||
changed, so that their problems will not be attributed erroneously to
|
||||
authors of previous versions.
|
||||
|
||||
Some devices are designed to deny users access to install or run
|
||||
modified versions of the software inside them, although the manufacturer
|
||||
can do so. This is fundamentally incompatible with the aim of
|
||||
protecting users' freedom to change the software. The systematic
|
||||
pattern of such abuse occurs in the area of products for individuals to
|
||||
use, which is precisely where it is most unacceptable. Therefore, we
|
||||
have designed this version of the GPL to prohibit the practice for those
|
||||
products. If such problems arise substantially in other domains, we
|
||||
stand ready to extend this provision to those domains in future versions
|
||||
of the GPL, as needed to protect the freedom of users.
|
||||
|
||||
Finally, every program is threatened constantly by software patents.
|
||||
States should not allow patents to restrict development and use of
|
||||
software on general-purpose computers, but in those that do, we wish to
|
||||
avoid the special danger that patents applied to a free program could
|
||||
make it effectively proprietary. To prevent this, the GPL assures that
|
||||
patents cannot be used to render the program non-free.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
TERMS AND CONDITIONS
|
||||
|
||||
0. Definitions.
|
||||
|
||||
"This License" refers to version 3 of the GNU General Public License.
|
||||
|
||||
"Copyright" also means copyright-like laws that apply to other kinds of
|
||||
works, such as semiconductor masks.
|
||||
|
||||
"The Program" refers to any copyrightable work licensed under this
|
||||
License. Each licensee is addressed as "you". "Licensees" and
|
||||
"recipients" may be individuals or organizations.
|
||||
|
||||
To "modify" a work means to copy from or adapt all or part of the work
|
||||
in a fashion requiring copyright permission, other than the making of an
|
||||
exact copy. The resulting work is called a "modified version" of the
|
||||
earlier work or a work "based on" the earlier work.
|
||||
|
||||
A "covered work" means either the unmodified Program or a work based
|
||||
on the Program.
|
||||
|
||||
To "propagate" a work means to do anything with it that, without
|
||||
permission, would make you directly or secondarily liable for
|
||||
infringement under applicable copyright law, except executing it on a
|
||||
computer or modifying a private copy. Propagation includes copying,
|
||||
distribution (with or without modification), making available to the
|
||||
public, and in some countries other activities as well.
|
||||
|
||||
To "convey" a work means any kind of propagation that enables other
|
||||
parties to make or receive copies. Mere interaction with a user through
|
||||
a computer network, with no transfer of a copy, is not conveying.
|
||||
|
||||
An interactive user interface displays "Appropriate Legal Notices"
|
||||
to the extent that it includes a convenient and prominently visible
|
||||
feature that (1) displays an appropriate copyright notice, and (2)
|
||||
tells the user that there is no warranty for the work (except to the
|
||||
extent that warranties are provided), that licensees may convey the
|
||||
work under this License, and how to view a copy of this License. If
|
||||
the interface presents a list of user commands or options, such as a
|
||||
menu, a prominent item in the list meets this criterion.
|
||||
|
||||
1. Source Code.
|
||||
|
||||
The "source code" for a work means the preferred form of the work
|
||||
for making modifications to it. "Object code" means any non-source
|
||||
form of a work.
|
||||
|
||||
A "Standard Interface" means an interface that either is an official
|
||||
standard defined by a recognized standards body, or, in the case of
|
||||
interfaces specified for a particular programming language, one that
|
||||
is widely used among developers working in that language.
|
||||
|
||||
The "System Libraries" of an executable work include anything, other
|
||||
than the work as a whole, that (a) is included in the normal form of
|
||||
packaging a Major Component, but which is not part of that Major
|
||||
Component, and (b) serves only to enable use of the work with that
|
||||
Major Component, or to implement a Standard Interface for which an
|
||||
implementation is available to the public in source code form. A
|
||||
"Major Component", in this context, means a major essential component
|
||||
(kernel, window system, and so on) of the specific operating system
|
||||
(if any) on which the executable work runs, or a compiler used to
|
||||
produce the work, or an object code interpreter used to run it.
|
||||
|
||||
The "Corresponding Source" for a work in object code form means all
|
||||
the source code needed to generate, install, and (for an executable
|
||||
work) run the object code and to modify the work, including scripts to
|
||||
control those activities. However, it does not include the work's
|
||||
System Libraries, or general-purpose tools or generally available free
|
||||
programs which are used unmodified in performing those activities but
|
||||
which are not part of the work. For example, Corresponding Source
|
||||
includes interface definition files associated with source files for
|
||||
the work, and the source code for shared libraries and dynamically
|
||||
linked subprograms that the work is specifically designed to require,
|
||||
such as by intimate data communication or control flow between those
|
||||
subprograms and other parts of the work.
|
||||
|
||||
The Corresponding Source need not include anything that users
|
||||
can regenerate automatically from other parts of the Corresponding
|
||||
Source.
|
||||
|
||||
The Corresponding Source for a work in source code form is that
|
||||
same work.
|
||||
|
||||
2. Basic Permissions.
|
||||
|
||||
All rights granted under this License are granted for the term of
|
||||
copyright on the Program, and are irrevocable provided the stated
|
||||
conditions are met. This License explicitly affirms your unlimited
|
||||
permission to run the unmodified Program. The output from running a
|
||||
covered work is covered by this License only if the output, given its
|
||||
content, constitutes a covered work. This License acknowledges your
|
||||
rights of fair use or other equivalent, as provided by copyright law.
|
||||
|
||||
You may make, run and propagate covered works that you do not
|
||||
convey, without conditions so long as your license otherwise remains
|
||||
in force. You may convey covered works to others for the sole purpose
|
||||
of having them make modifications exclusively for you, or provide you
|
||||
with facilities for running those works, provided that you comply with
|
||||
the terms of this License in conveying all material for which you do
|
||||
not control copyright. Those thus making or running the covered works
|
||||
for you must do so exclusively on your behalf, under your direction
|
||||
and control, on terms that prohibit them from making any copies of
|
||||
your copyrighted material outside their relationship with you.
|
||||
|
||||
Conveying under any other circumstances is permitted solely under
|
||||
the conditions stated below. Sublicensing is not allowed; section 10
|
||||
makes it unnecessary.
|
||||
|
||||
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
|
||||
|
||||
No covered work shall be deemed part of an effective technological
|
||||
measure under any applicable law fulfilling obligations under article
|
||||
11 of the WIPO copyright treaty adopted on 20 December 1996, or
|
||||
similar laws prohibiting or restricting circumvention of such
|
||||
measures.
|
||||
|
||||
When you convey a covered work, you waive any legal power to forbid
|
||||
circumvention of technological measures to the extent such circumvention
|
||||
is effected by exercising rights under this License with respect to
|
||||
the covered work, and you disclaim any intention to limit operation or
|
||||
modification of the work as a means of enforcing, against the work's
|
||||
users, your or third parties' legal rights to forbid circumvention of
|
||||
technological measures.
|
||||
|
||||
4. Conveying Verbatim Copies.
|
||||
|
||||
You may convey verbatim copies of the Program's source code as you
|
||||
receive it, in any medium, provided that you conspicuously and
|
||||
appropriately publish on each copy an appropriate copyright notice;
|
||||
keep intact all notices stating that this License and any
|
||||
non-permissive terms added in accord with section 7 apply to the code;
|
||||
keep intact all notices of the absence of any warranty; and give all
|
||||
recipients a copy of this License along with the Program.
|
||||
|
||||
You may charge any price or no price for each copy that you convey,
|
||||
and you may offer support or warranty protection for a fee.
|
||||
|
||||
5. Conveying Modified Source Versions.
|
||||
|
||||
You may convey a work based on the Program, or the modifications to
|
||||
produce it from the Program, in the form of source code under the
|
||||
terms of section 4, provided that you also meet all of these conditions:
|
||||
|
||||
a) The work must carry prominent notices stating that you modified
|
||||
it, and giving a relevant date.
|
||||
|
||||
b) The work must carry prominent notices stating that it is
|
||||
released under this License and any conditions added under section
|
||||
7. This requirement modifies the requirement in section 4 to
|
||||
"keep intact all notices".
|
||||
|
||||
c) You must license the entire work, as a whole, under this
|
||||
License to anyone who comes into possession of a copy. This
|
||||
License will therefore apply, along with any applicable section 7
|
||||
additional terms, to the whole of the work, and all its parts,
|
||||
regardless of how they are packaged. This License gives no
|
||||
permission to license the work in any other way, but it does not
|
||||
invalidate such permission if you have separately received it.
|
||||
|
||||
d) If the work has interactive user interfaces, each must display
|
||||
Appropriate Legal Notices; however, if the Program has interactive
|
||||
interfaces that do not display Appropriate Legal Notices, your
|
||||
work need not make them do so.
|
||||
|
||||
A compilation of a covered work with other separate and independent
|
||||
works, which are not by their nature extensions of the covered work,
|
||||
and which are not combined with it such as to form a larger program,
|
||||
in or on a volume of a storage or distribution medium, is called an
|
||||
"aggregate" if the compilation and its resulting copyright are not
|
||||
used to limit the access or legal rights of the compilation's users
|
||||
beyond what the individual works permit. Inclusion of a covered work
|
||||
in an aggregate does not cause this License to apply to the other
|
||||
parts of the aggregate.
|
||||
|
||||
6. Conveying Non-Source Forms.
|
||||
|
||||
You may convey a covered work in object code form under the terms
|
||||
of sections 4 and 5, provided that you also convey the
|
||||
machine-readable Corresponding Source under the terms of this License,
|
||||
in one of these ways:
|
||||
|
||||
a) Convey the object code in, or embodied in, a physical product
|
||||
(including a physical distribution medium), accompanied by the
|
||||
Corresponding Source fixed on a durable physical medium
|
||||
customarily used for software interchange.
|
||||
|
||||
b) Convey the object code in, or embodied in, a physical product
|
||||
(including a physical distribution medium), accompanied by a
|
||||
written offer, valid for at least three years and valid for as
|
||||
long as you offer spare parts or customer support for that product
|
||||
model, to give anyone who possesses the object code either (1) a
|
||||
copy of the Corresponding Source for all the software in the
|
||||
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>.
|
165
lgpl-3.0.txt
Normal file
165
lgpl-3.0.txt
Normal file
|
@ -0,0 +1,165 @@
|
|||
GNU LESSER GENERAL PUBLIC LICENSE
|
||||
Version 3, 29 June 2007
|
||||
|
||||
Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
|
||||
This version of the GNU Lesser General Public License incorporates
|
||||
the terms and conditions of version 3 of the GNU General Public
|
||||
License, supplemented by the additional permissions listed below.
|
||||
|
||||
0. Additional Definitions.
|
||||
|
||||
As used herein, "this License" refers to version 3 of the GNU Lesser
|
||||
General Public License, and the "GNU GPL" refers to version 3 of the GNU
|
||||
General Public License.
|
||||
|
||||
"The Library" refers to a covered work governed by this License,
|
||||
other than an Application or a Combined Work as defined below.
|
||||
|
||||
An "Application" is any work that makes use of an interface provided
|
||||
by the Library, but which is not otherwise based on the Library.
|
||||
Defining a subclass of a class defined by the Library is deemed a mode
|
||||
of using an interface provided by the Library.
|
||||
|
||||
A "Combined Work" is a work produced by combining or linking an
|
||||
Application with the Library. The particular version of the Library
|
||||
with which the Combined Work was made is also called the "Linked
|
||||
Version".
|
||||
|
||||
The "Minimal Corresponding Source" for a Combined Work means the
|
||||
Corresponding Source for the Combined Work, excluding any source code
|
||||
for portions of the Combined Work that, considered in isolation, are
|
||||
based on the Application, and not on the Linked Version.
|
||||
|
||||
The "Corresponding Application Code" for a Combined Work means the
|
||||
object code and/or source code for the Application, including any data
|
||||
and utility programs needed for reproducing the Combined Work from the
|
||||
Application, but excluding the System Libraries of the Combined Work.
|
||||
|
||||
1. Exception to Section 3 of the GNU GPL.
|
||||
|
||||
You may convey a covered work under sections 3 and 4 of this License
|
||||
without being bound by section 3 of the GNU GPL.
|
||||
|
||||
2. Conveying Modified Versions.
|
||||
|
||||
If you modify a copy of the Library, and, in your modifications, a
|
||||
facility refers to a function or data to be supplied by an Application
|
||||
that uses the facility (other than as an argument passed when the
|
||||
facility is invoked), then you may convey a copy of the modified
|
||||
version:
|
||||
|
||||
a) under this License, provided that you make a good faith effort to
|
||||
ensure that, in the event an Application does not supply the
|
||||
function or data, the facility still operates, and performs
|
||||
whatever part of its purpose remains meaningful, or
|
||||
|
||||
b) under the GNU GPL, with none of the additional permissions of
|
||||
this License applicable to that copy.
|
||||
|
||||
3. Object Code Incorporating Material from Library Header Files.
|
||||
|
||||
The object code form of an Application may incorporate material from
|
||||
a header file that is part of the Library. You may convey such object
|
||||
code under terms of your choice, provided that, if the incorporated
|
||||
material is not limited to numerical parameters, data structure
|
||||
layouts and accessors, or small macros, inline functions and templates
|
||||
(ten or fewer lines in length), you do both of the following:
|
||||
|
||||
a) Give prominent notice with each copy of the object code that the
|
||||
Library is used in it and that the Library and its use are
|
||||
covered by this License.
|
||||
|
||||
b) Accompany the object code with a copy of the GNU GPL and this license
|
||||
document.
|
||||
|
||||
4. Combined Works.
|
||||
|
||||
You may convey a Combined Work under terms of your choice that,
|
||||
taken together, effectively do not restrict modification of the
|
||||
portions of the Library contained in the Combined Work and reverse
|
||||
engineering for debugging such modifications, if you also do each of
|
||||
the following:
|
||||
|
||||
a) Give prominent notice with each copy of the Combined Work that
|
||||
the Library is used in it and that the Library and its use are
|
||||
covered by this License.
|
||||
|
||||
b) Accompany the Combined Work with a copy of the GNU GPL and this license
|
||||
document.
|
||||
|
||||
c) For a Combined Work that displays copyright notices during
|
||||
execution, include the copyright notice for the Library among
|
||||
these notices, as well as a reference directing the user to the
|
||||
copies of the GNU GPL and this license document.
|
||||
|
||||
d) Do one of the following:
|
||||
|
||||
0) Convey the Minimal Corresponding Source under the terms of this
|
||||
License, and the Corresponding Application Code in a form
|
||||
suitable for, and under terms that permit, the user to
|
||||
recombine or relink the Application with a modified version of
|
||||
the Linked Version to produce a modified Combined Work, in the
|
||||
manner specified by section 6 of the GNU GPL for conveying
|
||||
Corresponding Source.
|
||||
|
||||
1) Use a suitable shared library mechanism for linking with the
|
||||
Library. A suitable mechanism is one that (a) uses at run time
|
||||
a copy of the Library already present on the user's computer
|
||||
system, and (b) will operate properly with a modified version
|
||||
of the Library that is interface-compatible with the Linked
|
||||
Version.
|
||||
|
||||
e) Provide Installation Information, but only if you would otherwise
|
||||
be required to provide such information under section 6 of the
|
||||
GNU GPL, and only to the extent that such information is
|
||||
necessary to install and execute a modified version of the
|
||||
Combined Work produced by recombining or relinking the
|
||||
Application with a modified version of the Linked Version. (If
|
||||
you use option 4d0, the Installation Information must accompany
|
||||
the Minimal Corresponding Source and Corresponding Application
|
||||
Code. If you use option 4d1, you must provide the Installation
|
||||
Information in the manner specified by section 6 of the GNU GPL
|
||||
for conveying Corresponding Source.)
|
||||
|
||||
5. Combined Libraries.
|
||||
|
||||
You may place library facilities that are a work based on the
|
||||
Library side by side in a single library together with other library
|
||||
facilities that are not Applications and are not covered by this
|
||||
License, and convey such a combined library under terms of your
|
||||
choice, if you do both of the following:
|
||||
|
||||
a) Accompany the combined library with a copy of the same work based
|
||||
on the Library, uncombined with any other library facilities,
|
||||
conveyed under the terms of this License.
|
||||
|
||||
b) Give prominent notice with the combined library that part of it
|
||||
is a work based on the Library, and explaining where to find the
|
||||
accompanying uncombined form of the same work.
|
||||
|
||||
6. Revised Versions of the GNU Lesser General Public License.
|
||||
|
||||
The Free Software Foundation may publish revised and/or new versions
|
||||
of the GNU Lesser 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
|
||||
Library as you received it specifies that a certain numbered version
|
||||
of the GNU Lesser General Public License "or any later version"
|
||||
applies to it, you have the option of following the terms and
|
||||
conditions either of that published version or of any later version
|
||||
published by the Free Software Foundation. If the Library as you
|
||||
received it does not specify a version number of the GNU Lesser
|
||||
General Public License, you may choose any version of the GNU Lesser
|
||||
General Public License ever published by the Free Software Foundation.
|
||||
|
||||
If the Library as you received it specifies that a proxy can decide
|
||||
whether future versions of the GNU Lesser General Public License shall
|
||||
apply, that proxy's public statement of acceptance of any version is
|
||||
permanent authorization for you to choose that version for the
|
||||
Library.
|
|
@ -1,16 +1,15 @@
|
|||
# SPDX-License-Identifier: GPL-3.0-or-later
|
||||
cmake_minimum_required(VERSION 3.20)
|
||||
project(ecg-u01)
|
||||
project(ecg_tree)
|
||||
|
||||
add_library(tree SHARED node.cpp)
|
||||
# ~~~~~~
|
||||
# This can be changed to STATIC to build and link a static library.
|
||||
add_library(tree node.cpp)
|
||||
add_executable(main main.cpp)
|
||||
target_link_libraries(main ecg_tree)
|
||||
target_link_libraries(main tree)
|
||||
|
||||
find_package(Catch2 3)
|
||||
if(Catch2_FOUND)
|
||||
add_executable(tests tests.cpp)
|
||||
target_link_libraries(tests PRIVATE Catch2::Catch2WithMain ecg_tree)
|
||||
target_link_libraries(tests PRIVATE Catch2::Catch2WithMain tree)
|
||||
|
||||
include(CTest)
|
||||
include(Catch)
|
||||
|
@ -18,4 +17,4 @@ if(Catch2_FOUND)
|
|||
endif()
|
||||
|
||||
install(TARGETS main)
|
||||
install(TARGETS ecg_tree DESTINATION lib)
|
||||
install(TARGETS tree DESTINATION lib)
|
||||
|
|
|
@ -1,3 +1,4 @@
|
|||
// SPDX-License-Identifier: GPL-3.0-or-later
|
||||
#include <iostream>
|
||||
|
||||
#include "node.h"
|
||||
|
|
21
u01/node.cpp
21
u01/node.cpp
|
@ -1,3 +1,4 @@
|
|||
// SPDX-License-Identifier: GPL-3.0-or-later
|
||||
#include <iostream>
|
||||
#include <sstream>
|
||||
#include <stack>
|
||||
|
@ -28,22 +29,22 @@ node::~node() {
|
|||
|
||||
std::string node::get_name() const { return name; }
|
||||
|
||||
void node::set_name(const std::string new_name) { this->name = new_name; }
|
||||
void node::set_name(const std::string& new_name) { this->name = new_name; }
|
||||
|
||||
unsigned int node::get_nr_children() const { return children.size(); }
|
||||
std::size_t node::get_nr_children() const { return children.size(); }
|
||||
|
||||
node *node::get_child(std::size_t i) const { return children[i]; }
|
||||
|
||||
void node::add_child(node *child) { children.push_back(child); }
|
||||
|
||||
void node::print(std::ostream &str, std::size_t depth) const {
|
||||
void node::print(std::ostream &str, unsigned int depth) const {
|
||||
str << std::string(depth, '\t') << get_name() << std::endl;
|
||||
for (node *child : children) {
|
||||
child->print(str, depth + 1);
|
||||
}
|
||||
}
|
||||
|
||||
std::string node::print_recursive(std::size_t depth,
|
||||
std::string node::print_recursive(unsigned int depth,
|
||||
std::set<const node *> visited) const {
|
||||
std::stringstream output;
|
||||
output << std::string(depth, '\t') << get_name();
|
||||
|
@ -63,24 +64,24 @@ std::string node::print_recursive(std::size_t depth,
|
|||
|
||||
std::string node::print_iterative() const {
|
||||
std::stringstream output;
|
||||
std::stack<std::pair<const node *, size_t>> stack;
|
||||
stack.push(std::make_pair(this, 0));
|
||||
std::stack<std::pair<const node *, unsigned int>> stack;
|
||||
stack.push({this, 0});
|
||||
std::set<const node *> visited = {};
|
||||
|
||||
while (!stack.empty()) {
|
||||
const node *n = nullptr;
|
||||
size_t depth;
|
||||
unsigned int depth;
|
||||
std::tie(n, depth) = stack.top();
|
||||
stack.pop();
|
||||
if (visited.find(n) == visited.end()) {
|
||||
if (n != this)
|
||||
output << std::endl;
|
||||
output << std::string(depth, '\t') << n->get_name();
|
||||
// Complex iteration (not default vector iteration is necessary,
|
||||
// Complex iteration (not default vector iteration) is necessary,
|
||||
// to achieve the same output as the recursive approach.
|
||||
// Otherwise, the order of the children is reversed (due to LIFO).
|
||||
for (size_t i = n->get_nr_children(); i > 0; i--) {
|
||||
stack.push(std::make_pair(n->get_child(i - 1), depth + 1));
|
||||
for (std::size_t i = n->get_nr_children(); i > 0; i--) {
|
||||
stack.push({n->get_child(i - 1), depth + 1});
|
||||
}
|
||||
} else {
|
||||
output << " [↝ " << n->get_name() << "]";
|
||||
|
|
|
@ -1,3 +1,4 @@
|
|||
// SPDX-License-Identifier: GPL-3.0-or-later
|
||||
#pragma once
|
||||
|
||||
#include <memory>
|
||||
|
@ -10,12 +11,12 @@ public:
|
|||
node(const std::string &name = "");
|
||||
virtual ~node();
|
||||
std::string get_name() const;
|
||||
void set_name(const std::string new_name);
|
||||
unsigned int get_nr_children() const;
|
||||
void set_name(const std::string &new_name);
|
||||
std::size_t get_nr_children() const;
|
||||
node *get_child(std::size_t i) const;
|
||||
void add_child(node *child);
|
||||
void print(std::ostream &str, std::size_t depth = 0) const;
|
||||
std::string print_recursive(std::size_t depth = 0,
|
||||
void print(std::ostream &str, unsigned int depth = 0) const;
|
||||
std::string print_recursive(unsigned int depth = 0,
|
||||
std::set<const node *> visited = {}) const;
|
||||
std::string print_iterative() const;
|
||||
|
||||
|
|
43
u01/readme.txt
Normal file
43
u01/readme.txt
Normal file
|
@ -0,0 +1,43 @@
|
|||
<!-- vim: set ft=markdown: -->
|
||||
<!-- LTeX: language=de-DE -->
|
||||
<!-- SPDX-License-Identifier: GPL-3.0-or-later -->
|
||||
# Praxisaufgabe 1 Einführung in die Computergrafik
|
||||
|
||||
## Team
|
||||
|
||||
* Simon Bruder, Matrikelnummer: 5075324
|
||||
|
||||
## Bearbeitete Zusatzaufgaben
|
||||
|
||||
* Rekursive Traversierung: `node::print_recursive()`
|
||||
* Iterative Traversierung: `node::print_iterative()`
|
||||
* Bauen einer dynamischen Bibliothek `libtree.so` (siehe unten für Hinweise)
|
||||
* Bauen einer statischen Bibliothek `libtree.a`
|
||||
|
||||
## Hinweise
|
||||
|
||||
### Signatur der Traversierungsmethoden
|
||||
|
||||
Die rekursive und iterative Traversierung sollen laut Aufgabenstellung
|
||||
„ähnlich zum `<<`-Operator“ implementiert werden.
|
||||
Da es aber pro Klasse nur eine Implementation des `<<`-Operators geben kann,
|
||||
habe ich die Funktionen so implementiert, dass sie `std::string` zurückgeben
|
||||
und damit die Anwendung ähnlich ist wie bei Verwendung von `print` (aus 1.2.3):
|
||||
|
||||
```cpp
|
||||
// statt
|
||||
std::cout << n;
|
||||
// ist es für die anderen Traversierungsmethoden
|
||||
std::cout << n.print_recursive();
|
||||
// bzw.
|
||||
std::cout << n.print_iterative();
|
||||
```
|
||||
|
||||
### Statische und dynamische Bibliothek
|
||||
|
||||
Im Normalfall baut das CMake-Projekt eine statische Bibliothek und linkt `main` dagegen.
|
||||
Damit ist Zusatzaufgabe 3 erfüllt.
|
||||
|
||||
Um eine dynamische Bibliothek zu bauen und `main` dagegen zu linken,
|
||||
kann CMake mit `-DBUILD_SHARED_LIBS=ON` aufgerufen werden.
|
||||
Da unter GNU keine spezifischen Annotationen dafür nötig sind, ist Zusatzaufgabe 4 erfüllt.
|
|
@ -1,3 +1,4 @@
|
|||
// SPDX-License-Identifier: GPL-3.0-or-later
|
||||
#include <catch2/catch_test_macros.hpp>
|
||||
#include <iostream>
|
||||
#include <sstream>
|
||||
|
@ -177,7 +178,31 @@ TEST_CASE("Cycle detection (iterative)") {
|
|||
delete n;
|
||||
}
|
||||
|
||||
TEST_CASE("Equivalence of interative and recursive print") {
|
||||
TEST_CASE("Very short cycle detection") {
|
||||
node *n = new node("foo");
|
||||
n->add_child(n);
|
||||
|
||||
std::stringstream output;
|
||||
output << n->print_recursive();
|
||||
|
||||
REQUIRE(output.str() == "foo [↝ foo]\n");
|
||||
|
||||
delete n;
|
||||
}
|
||||
|
||||
TEST_CASE("Very short cycle detection (iterative)") {
|
||||
node *n = new node("foo");
|
||||
n->add_child(n);
|
||||
|
||||
std::stringstream output;
|
||||
output << n->print_iterative();
|
||||
|
||||
REQUIRE(output.str() == "foo [↝ foo]\n");
|
||||
|
||||
delete n;
|
||||
}
|
||||
|
||||
TEST_CASE("Equivalence of iterative and recursive print") {
|
||||
node *n = new node();
|
||||
REQUIRE(n->print_recursive() == n->print_iterative());
|
||||
delete n;
|
||||
|
|
24
u02/include/sweep_line_tool.h
Normal file
24
u02/include/sweep_line_tool.h
Normal file
|
@ -0,0 +1,24 @@
|
|||
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||||
#pragma once
|
||||
|
||||
#include "tool_base.h"
|
||||
|
||||
class sweep_line_tool : public tool_base {
|
||||
public:
|
||||
sweep_line_tool(canvas_buffer &canvas);
|
||||
|
||||
// Draw example triangle
|
||||
void draw();
|
||||
// Compatibility for main application (only handles draw methods with one or two points)
|
||||
void draw(int _x, int _y);
|
||||
// Draw triangle provided by three given points
|
||||
void draw(int x0, int y0, int x1, int y1, int x2, int y2);
|
||||
|
||||
void set_text(std::stringstream &stream);
|
||||
|
||||
private:
|
||||
// Draw every pixel on the specified y coordinate,
|
||||
// in the interval given by the boundaries b1 and b2.
|
||||
// The boundaries do not need to be sorted.
|
||||
void draw_interval(int b1, int b2, int y);
|
||||
};
|
51
u02/include/util.h
Normal file
51
u02/include/util.h
Normal file
|
@ -0,0 +1,51 @@
|
|||
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||||
#pragma once
|
||||
#include <cstdint>
|
||||
#include <tuple>
|
||||
|
||||
typedef uint8_t Transformation;
|
||||
|
||||
const Transformation TRANSFORM_MIRROR_X = 1 << 0;
|
||||
const Transformation TRANSFORM_MIRROR_Y = 1 << 1;
|
||||
const Transformation TRANSFORM_ROTATE_CW = 1 << 2;
|
||||
const Transformation TRANSFORM_ROTATE_CCW = 1 << 3;
|
||||
|
||||
// Applies the provided transformation to the point, mutating it in place.
|
||||
// Rotation is done before mirroring.
|
||||
void transform_mut(Transformation transformation, int &x, int &y);
|
||||
// Applies the provided transformation to the point,
|
||||
// returning the transformed point.
|
||||
// Rotation is done before mirroring.
|
||||
std::pair<int, int> transform(Transformation transformation, int x, int y);
|
||||
|
||||
// Applies the inverse transformation to the point, mutating it in place.
|
||||
// Composition of this with the transformation is the identity function.
|
||||
void transform_inv_mut(Transformation transformation, int &x, int &y);
|
||||
// Applies the inverse transformation to the point,
|
||||
// returning the transformed point.
|
||||
// Composition of this with the transformation is the identity function.
|
||||
std::pair<int, int> transform_inv(Transformation transformation, int x, int y);
|
||||
|
||||
// Returns the transformation required
|
||||
// to make the given endpoints of a line conform
|
||||
// to the standard case for rasterization.
|
||||
Transformation transformation_to_standard_case(int x0, int y0, int x1, int y1);
|
||||
|
||||
// Returns the barycentric coordinates of the point given by (xp, yp)
|
||||
// in the triangle given by the three points (x0, y0), (x1, y1), (x2, y2).
|
||||
// May return non-real values when the points are on a straight line.
|
||||
std::tuple<float, float, float> barycentric_coordinates(int x0, int y0, int x1,
|
||||
int y1, int x2, int y2,
|
||||
int xp, int yp);
|
||||
|
||||
// Checks if the point given by (xp, yp) is inside the triangle
|
||||
// given by the three points (x0, y0), (x1, y1), (x2, y2).
|
||||
bool point_in_triangle(int x0, int y0, int x1, int y1, int x2, int y2, int xp,
|
||||
int yp);
|
||||
|
||||
// Sorts the points of a triangle to be in ascending order (y0 < y1 < y2).
|
||||
void sort_triangle_points(int &x0, int &y0, int &x1, int &y1, int &x2, int &y2);
|
||||
|
||||
// This calculates the slope of a line from (x0, y0) to (x1, y1).
|
||||
// It handles special cases to ensure the return value will be real.
|
||||
float slope(int x0, int y0, int x1, int y1);
|
100
u02/src/sweep_line_tool.cpp
Normal file
100
u02/src/sweep_line_tool.cpp
Normal file
|
@ -0,0 +1,100 @@
|
|||
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||||
#include "sweep_line_tool.h"
|
||||
#include "dda_line_tool.h"
|
||||
#include "util.h"
|
||||
#include <cmath>
|
||||
#include <iostream>
|
||||
#include <vector>
|
||||
|
||||
// Calculate the inverse of the DDA function.
|
||||
int dda_inv(int x0, int y0, float m, int y) {
|
||||
// This uses the regular function that is the basis of DDA
|
||||
//
|
||||
// y_i = y_0 + m·(x_i - x_0)
|
||||
//
|
||||
// but rearranges it to be the inverse function:
|
||||
//
|
||||
// y_i = y_0 + m·(x_i - x_0)
|
||||
// ⇔ y_i - y_0 + x_0·m = x_i·m
|
||||
// ⇔ x_i = (y_i - y_0)/m + x_0
|
||||
//
|
||||
// This returns a valid x coordinate on the line
|
||||
// starting from (x0, y0) with the slope m.
|
||||
|
||||
// Handle special case of flat line
|
||||
if (m == 0)
|
||||
return x0;
|
||||
else
|
||||
return round((y - y0) / m + x0);
|
||||
}
|
||||
|
||||
sweep_line_tool::sweep_line_tool(canvas_buffer &canvas) : tool_base(canvas) {
|
||||
shape = TS_NONE;
|
||||
is_draggable = false;
|
||||
}
|
||||
|
||||
void sweep_line_tool::draw_interval(int b1, int b2, int y) {
|
||||
for (int x = std::min(b1, b2); x <= std::max(b1, b2); x++) {
|
||||
canvas.set_pixel(x, y);
|
||||
}
|
||||
}
|
||||
|
||||
void sweep_line_tool::draw() { draw(10, 10, 90, 30, 30, 90); }
|
||||
|
||||
void sweep_line_tool::draw(int _x, int _y) { draw(); }
|
||||
|
||||
void sweep_line_tool::draw(int x0, int y0, int x1, int y1, int x2, int y2) {
|
||||
// Terminology:
|
||||
//
|
||||
// (x0, y0)
|
||||
// +
|
||||
// | \
|
||||
// | \ m_1
|
||||
// |first\
|
||||
// | pass \
|
||||
// m_shared |---------+ (x1, y1)
|
||||
// |second /
|
||||
// |pass /
|
||||
// | / m_2
|
||||
// | /
|
||||
// +
|
||||
// (x2, y2)
|
||||
|
||||
// Sort triangle points (in place) so that y0 < y1 < y2
|
||||
sort_triangle_points(x0, y0, x1, y1, x2, y2);
|
||||
|
||||
// Slope of the side limiting the first pass (only)
|
||||
float m_1 = slope(x0, y0, x1, y1);
|
||||
// Slope of the side limiting the second pass (only)
|
||||
float m_2 = slope(x1, y1, x2, y2);
|
||||
// Slope of the side limiting both passes
|
||||
float m_shared = slope(x0, y0, x2, y2);
|
||||
|
||||
// First pass
|
||||
if (y0 == y1) {
|
||||
// If the first two points are on the same height, only draw one line.
|
||||
// This is only needed for the first interval,
|
||||
// because in the case that y1 == y2,
|
||||
// the problematic line would have already been handled in the first pass.
|
||||
draw_interval(x0, x1, y0);
|
||||
} else {
|
||||
for (int y = y0; y <= y1; y++) {
|
||||
int b1 = dda_inv(x0, y0, m_1, y);
|
||||
int b2 = dda_inv(x0, y0, m_shared, y);
|
||||
draw_interval(b1, b2, y);
|
||||
}
|
||||
}
|
||||
|
||||
// Second pass
|
||||
// it can start iterating at y1 + 1,
|
||||
// because y1 is already included in the first pass.
|
||||
for (int y = y1 + 1; y <= y2; y++) {
|
||||
int b1 = dda_inv(x1, y1, m_2, y);
|
||||
int b2 = dda_inv(x0, y0, m_shared, y);
|
||||
draw_interval(b1, b2, y);
|
||||
}
|
||||
}
|
||||
|
||||
void sweep_line_tool::set_text(std::stringstream &stream) {
|
||||
stream << "Tool: Sweep-Line";
|
||||
}
|
524
u02/src/tests.cpp
Normal file
524
u02/src/tests.cpp
Normal file
|
@ -0,0 +1,524 @@
|
|||
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||||
#include <algorithm>
|
||||
#include <catch2/catch_test_macros.hpp>
|
||||
#include <catch2/generators/catch_generators.hpp>
|
||||
#include <catch2/generators/catch_generators_adapters.hpp>
|
||||
#include <catch2/generators/catch_generators_random.hpp>
|
||||
#include <catch2/matchers/catch_matchers_floating_point.hpp>
|
||||
|
||||
#include "bresenham_circle_tool.h"
|
||||
#include "bresenham_line_tool.h"
|
||||
#include "canvas_buffer.h"
|
||||
#include "dda_line_tool.h"
|
||||
#include "non_recursive_fill_tool.h"
|
||||
#include "rectangle_tool.h"
|
||||
#include "recursive_fill_tool.h"
|
||||
#include "sweep_line_tool.h"
|
||||
#include "util.h"
|
||||
|
||||
using Catch::Matchers::WithinRel;
|
||||
|
||||
TEST_CASE("Transform Mirror") {
|
||||
// elementary operations
|
||||
REQUIRE(transform(TRANSFORM_MIRROR_X, 10, 20) == std::make_pair(10, -20));
|
||||
REQUIRE(transform(TRANSFORM_MIRROR_Y, 10, 20) == std::make_pair(-10, 20));
|
||||
|
||||
// composite operations
|
||||
REQUIRE(transform(TRANSFORM_MIRROR_X | TRANSFORM_MIRROR_Y, 10, 20) ==
|
||||
std::make_pair(-10, -20));
|
||||
}
|
||||
|
||||
TEST_CASE("Transform Rotate") {
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW, 10, 20) ==
|
||||
std::make_pair(-20, 10)); // 4th quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW, -20, 10) ==
|
||||
std::make_pair(-10, -20)); // 3rd quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW, -10, -20) ==
|
||||
std::make_pair(20, -10)); // 2nd quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW, 20, -10) ==
|
||||
std::make_pair(10, 20)); // 1st quadrant
|
||||
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW, 20, -10) ==
|
||||
std::make_pair(-10, -20)); // 1nd quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW, -10, -20) ==
|
||||
std::make_pair(-20, 10)); // 2rd quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW, -20, 10) ==
|
||||
std::make_pair(10, 20)); // 3th quadrant
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW, 10, 20) ==
|
||||
std::make_pair(20, -10)); // 4st quadrant
|
||||
}
|
||||
|
||||
TEST_CASE("Transform Rotate + Mirror") {
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW | TRANSFORM_MIRROR_X, 10, 20) ==
|
||||
std::make_pair(-20, -10));
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CW | TRANSFORM_MIRROR_Y, 10, 20) ==
|
||||
std::make_pair(20, 10));
|
||||
REQUIRE(
|
||||
transform(TRANSFORM_ROTATE_CW | TRANSFORM_MIRROR_X | TRANSFORM_MIRROR_Y,
|
||||
10, 20) == std::make_pair(20, -10));
|
||||
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW | TRANSFORM_MIRROR_X, 10, 20) ==
|
||||
std::make_pair(20, 10));
|
||||
REQUIRE(transform(TRANSFORM_ROTATE_CCW | TRANSFORM_MIRROR_Y, 10, 20) ==
|
||||
std::make_pair(-20, -10));
|
||||
REQUIRE(
|
||||
transform(TRANSFORM_ROTATE_CCW | TRANSFORM_MIRROR_X | TRANSFORM_MIRROR_Y,
|
||||
10, 20) == std::make_pair(-20, 10));
|
||||
}
|
||||
|
||||
TEST_CASE("Transform = Inverse Transform ○ Transform") {
|
||||
const int x = GENERATE(take(10, random(-100, 100)));
|
||||
const int y = GENERATE(take(10, random(-100, 100)));
|
||||
// this iterates over all possible transformations,
|
||||
// even bogus ones (like rotating cw and ccw)
|
||||
for (Transformation transformation = 0; transformation < 0b10000;
|
||||
transformation++) {
|
||||
int xt, yt;
|
||||
std::tie(xt, yt) = transform(transformation, x, y);
|
||||
int xti, yti;
|
||||
std::tie(xti, yti) = transform_inv(transformation, xt, yt);
|
||||
REQUIRE(x == xti);
|
||||
REQUIRE(y == yti);
|
||||
}
|
||||
}
|
||||
|
||||
TEST_CASE("Transformation to standard case") {
|
||||
REQUIRE(transformation_to_standard_case(5, 20, 20, 10) == 0);
|
||||
REQUIRE(transformation_to_standard_case(5, 5, 20, 15) == TRANSFORM_MIRROR_X);
|
||||
REQUIRE(transformation_to_standard_case(20, 15, 5, 5) == TRANSFORM_MIRROR_Y);
|
||||
REQUIRE(transformation_to_standard_case(20, 10, 5, 20) ==
|
||||
(TRANSFORM_MIRROR_X | TRANSFORM_MIRROR_Y));
|
||||
|
||||
REQUIRE(transformation_to_standard_case(5, 20, 15, 5) ==
|
||||
(TRANSFORM_ROTATE_CW | TRANSFORM_MIRROR_X));
|
||||
REQUIRE(transformation_to_standard_case(5, 5, 15, 20) ==
|
||||
TRANSFORM_ROTATE_CCW);
|
||||
REQUIRE(transformation_to_standard_case(15, 5, 5, 20) ==
|
||||
(TRANSFORM_ROTATE_CCW | TRANSFORM_MIRROR_X));
|
||||
REQUIRE(transformation_to_standard_case(15, 20, 5, 5) == TRANSFORM_ROTATE_CW);
|
||||
}
|
||||
|
||||
TEST_CASE("Transformation to standard case (prop)") {
|
||||
int x0 = GENERATE(take(10, random(-100, 100)));
|
||||
int y0 = GENERATE(take(10, random(-100, 100)));
|
||||
int x1 = GENERATE(take(10, random(-100, 100)));
|
||||
int y1 = GENERATE(take(10, random(-100, 100)));
|
||||
|
||||
const Transformation transformation =
|
||||
transformation_to_standard_case(x0, y0, x1, y1);
|
||||
|
||||
transform_mut(transformation, x0, y0);
|
||||
transform_mut(transformation, x1, y1);
|
||||
|
||||
REQUIRE(x0 <= x1);
|
||||
REQUIRE(y0 >= y1);
|
||||
}
|
||||
|
||||
TEST_CASE("Bresenham/DDA line tool (prop: for every row/column, only one pixel "
|
||||
"is set)") {
|
||||
const int size = 100;
|
||||
canvas_buffer *canvas = new canvas_buffer(size, size);
|
||||
|
||||
bresenham_line_tool *tool_bresenham = new bresenham_line_tool(*canvas);
|
||||
dda_line_tool *tool_dda = new dda_line_tool(*canvas);
|
||||
|
||||
tool_base *tool;
|
||||
const int tool_idx = GENERATE(0, 1);
|
||||
switch (tool_idx) {
|
||||
case 0:
|
||||
tool = tool_bresenham;
|
||||
break;
|
||||
case 1:
|
||||
tool = tool_dda;
|
||||
break;
|
||||
}
|
||||
|
||||
const int x0 = GENERATE(take(10, random(0, size - 1)));
|
||||
const int y0 = GENERATE(take(10, random(0, size - 1)));
|
||||
const int x1 = GENERATE(take(10, random(0, size - 1)));
|
||||
const int y1 = GENERATE(take(10, random(0, size - 1)));
|
||||
|
||||
tool->draw(x0, y0, x1, y1);
|
||||
|
||||
const int x_min = std::min(x0, x1);
|
||||
const int x_max = std::max(x0, x1);
|
||||
const int y_min = std::min(y0, y1);
|
||||
const int y_max = std::max(y0, y1);
|
||||
|
||||
// Depending on what the direction of the line (rounded to the next 90°) is,
|
||||
// either every row or column has only one pixel set.
|
||||
bool vertical = false;
|
||||
int draw_direction_min;
|
||||
int draw_direction_max;
|
||||
int unique_direction_min;
|
||||
int unique_direction_max;
|
||||
if (abs(y1 - y0) > abs(x1 - x0)) {
|
||||
vertical = true;
|
||||
draw_direction_min = y_min;
|
||||
draw_direction_max = y_max;
|
||||
unique_direction_min = x_min;
|
||||
unique_direction_max = x_max;
|
||||
} else {
|
||||
draw_direction_min = x_min;
|
||||
draw_direction_max = x_max;
|
||||
unique_direction_min = y_min;
|
||||
unique_direction_max = y_max;
|
||||
}
|
||||
|
||||
bool all_sums_are_one = true;
|
||||
int sum;
|
||||
for (int dd = draw_direction_min; dd <= draw_direction_max; dd++) {
|
||||
sum = 0;
|
||||
for (int ud = unique_direction_min; ud <= unique_direction_max; ud++) {
|
||||
int x, y;
|
||||
if (vertical) {
|
||||
x = ud;
|
||||
y = dd;
|
||||
} else {
|
||||
x = dd;
|
||||
y = ud;
|
||||
}
|
||||
if (canvas->get_pixel(x, y))
|
||||
sum++;
|
||||
}
|
||||
if (sum != 1)
|
||||
all_sums_are_one = false;
|
||||
}
|
||||
|
||||
REQUIRE(all_sums_are_one);
|
||||
}
|
||||
|
||||
TEST_CASE("Fill (recursive and non recursive) test shape") {
|
||||
canvas_buffer *canvas = new canvas_buffer(100, 100);
|
||||
bresenham_line_tool *tool_line = new bresenham_line_tool(*canvas);
|
||||
recursive_fill_tool *tool_fill_recursive = new recursive_fill_tool(*canvas);
|
||||
non_recursive_fill_tool *tool_fill_non_recursive =
|
||||
new non_recursive_fill_tool(*canvas);
|
||||
|
||||
tool_base *tool_fill;
|
||||
const int tool_fill_idx = GENERATE(0, 1);
|
||||
switch (tool_fill_idx) {
|
||||
case 0:
|
||||
tool_fill = tool_fill_recursive;
|
||||
break;
|
||||
case 1:
|
||||
tool_fill = tool_fill_non_recursive;
|
||||
break;
|
||||
}
|
||||
|
||||
canvas->draw_test_shape();
|
||||
|
||||
REQUIRE_FALSE(canvas->get_pixel(50, 49));
|
||||
REQUIRE_FALSE(canvas->get_pixel(50, 25));
|
||||
REQUIRE_FALSE(canvas->get_pixel(50, 75));
|
||||
tool_fill->draw(50, 25);
|
||||
REQUIRE(canvas->get_pixel(50, 49));
|
||||
REQUIRE(canvas->get_pixel(50, 25));
|
||||
REQUIRE(canvas->get_pixel(50, 75));
|
||||
|
||||
REQUIRE_FALSE(canvas->get_pixel(75, 40));
|
||||
REQUIRE_FALSE(canvas->get_pixel(75, 60));
|
||||
tool_fill->draw(75, 50);
|
||||
REQUIRE(canvas->get_pixel(75, 40));
|
||||
REQUIRE(canvas->get_pixel(75, 60));
|
||||
|
||||
REQUIRE_FALSE(canvas->get_pixel(0, 0));
|
||||
REQUIRE_FALSE(canvas->get_pixel(99, 99));
|
||||
tool_fill->draw(25, 50);
|
||||
REQUIRE(canvas->get_pixel(0, 0));
|
||||
REQUIRE(canvas->get_pixel(99, 99));
|
||||
}
|
||||
|
||||
TEST_CASE("Fill recursive == Fill non recursive (prop, 5 random lines)") {
|
||||
const int size = 100;
|
||||
|
||||
canvas_buffer *canvas_recursive = new canvas_buffer(size, size);
|
||||
canvas_buffer *canvas_non_recursive = new canvas_buffer(size, size);
|
||||
|
||||
bresenham_line_tool *tool_line_recursive =
|
||||
new bresenham_line_tool(*canvas_recursive);
|
||||
bresenham_line_tool *tool_line_non_recursive =
|
||||
new bresenham_line_tool(*canvas_non_recursive);
|
||||
|
||||
recursive_fill_tool *tool_fill_recursive =
|
||||
new recursive_fill_tool(*canvas_recursive);
|
||||
non_recursive_fill_tool *tool_fill_non_recursive =
|
||||
new non_recursive_fill_tool(*canvas_non_recursive);
|
||||
|
||||
for (int i = 0; i < 5; i++) {
|
||||
const int x0 = GENERATE(take(1, random(0, size - 1)));
|
||||
const int y0 = GENERATE(take(1, random(0, size - 1)));
|
||||
const int x1 = GENERATE(take(1, random(0, size - 1)));
|
||||
const int y1 = GENERATE(take(1, random(0, size - 1)));
|
||||
tool_line_recursive->draw(x0, y0, x1, y1);
|
||||
tool_line_non_recursive->draw(x0, y0, x1, y1);
|
||||
}
|
||||
|
||||
const int x = GENERATE(take(3, random(0, size - 1)));
|
||||
const int y = GENERATE(take(3, random(0, size - 1)));
|
||||
tool_fill_recursive->draw(x, y);
|
||||
tool_fill_non_recursive->draw(x, y);
|
||||
|
||||
bool equal = true;
|
||||
for (int x = 0; x < size; x++) {
|
||||
for (int y = 0; y < size; y++) {
|
||||
if (canvas_recursive->get_pixel(x, y) !=
|
||||
canvas_non_recursive->get_pixel(x, y))
|
||||
equal = false;
|
||||
}
|
||||
}
|
||||
REQUIRE(equal);
|
||||
}
|
||||
|
||||
TEST_CASE("Rectangle (prop)") {
|
||||
const int size = 100;
|
||||
|
||||
const int x0 = GENERATE(take(5, random(0, size - 1)));
|
||||
const int y0 = GENERATE(take(5, random(0, size - 1)));
|
||||
const int x1 = GENERATE(take(5, random(0, size - 1)));
|
||||
const int y1 = GENERATE(take(5, random(0, size - 1)));
|
||||
|
||||
const int x_min = std::min(x0, x1);
|
||||
const int x_max = std::max(x0, x1);
|
||||
const int y_min = std::min(y0, y1);
|
||||
const int y_max = std::max(y0, y1);
|
||||
|
||||
canvas_buffer *canvas = new canvas_buffer(size, size);
|
||||
rectangle_tool *tool = new rectangle_tool(*canvas);
|
||||
|
||||
tool->draw(x0, y0, x1, y1);
|
||||
|
||||
bool pass = true;
|
||||
for (int x = 0; x < size; x++) {
|
||||
for (int y = 0; y < size; y++) {
|
||||
if (((x == x0 || x == x1) && (y >= y_min && y <= y_max)) ||
|
||||
((y == y0 || y == y1) && (x >= x_min && x <= x_max))) {
|
||||
if (!canvas->get_pixel(x, y))
|
||||
pass = false;
|
||||
} else {
|
||||
if (canvas->get_pixel(x, y))
|
||||
pass = false;
|
||||
}
|
||||
}
|
||||
}
|
||||
REQUIRE(pass);
|
||||
}
|
||||
|
||||
TEST_CASE("Bresenham circle (prop: √(x²+y²)-r<ε)") {
|
||||
// Let s be the size of the canvas (s,s).
|
||||
// Let m be the smallest coordinate (x and y) for random points
|
||||
// and M be the largest coordinate (x and y) for random points.
|
||||
//
|
||||
// The largest radius that can fit on canvas (for arbitrary centres) is m.
|
||||
// The largest radius that is possible to create is √(2)(M-m).
|
||||
//
|
||||
// ⇒ √(2)(M-m) ≥ m
|
||||
// ⇔ √(2)M-√(2)m ≥ m
|
||||
// ⇔ √(2)M ≥ (1+√(2))m
|
||||
// ⇔ m ≤ (√(2)/(1+√(2)))m
|
||||
// ⇔ m ≤ (2-√(2))M (1)
|
||||
//
|
||||
// Additionally, to have a centered point field,
|
||||
// s-M=m must hold
|
||||
//
|
||||
// s-M = m
|
||||
// ⇒ s-M ≤ (2-√(2))M
|
||||
// ⇔ s ≤ (3-√(2))M
|
||||
// ⇔ M ≥ s/(3-√(2)) (2)
|
||||
//
|
||||
// With this, it now is possible to express M and m in terms of s:
|
||||
//
|
||||
// m ≤ (2-√(2))M (1)
|
||||
// ⇔ m ≤ ((2-√(2))/(3-√(2)))s
|
||||
// ⇔ m ≤ ((4-√(2))/7)s (3)
|
||||
//
|
||||
// When the points are rounded to the nearest integer,
|
||||
// M must be rounded down and m rounded down.
|
||||
//
|
||||
// An interactive version of this can be found here:
|
||||
// https://www.desmos.com/calculator/kn19qhue20
|
||||
const int size = 100; // s
|
||||
const int max_c = std::floor(size / (3 - std::sqrt(2))); // M (2)
|
||||
const int min_c = std::ceil(((4 - std::sqrt(2)) / 7) * size); // m (3)
|
||||
|
||||
const int x0 = GENERATE_COPY(take(10, random(min_c, max_c)));
|
||||
const int y0 = GENERATE_COPY(take(10, random(min_c, max_c)));
|
||||
const int x1 = GENERATE_COPY(take(10, random(min_c, max_c)));
|
||||
const int y1 = GENERATE_COPY(take(10, random(min_c, max_c)));
|
||||
|
||||
if ((x0 == min_c || x0 == max_c) && (x1 == min_c || x1 == max_c) &&
|
||||
(y0 == min_c || y0 == max_c) && (y1 == min_c || y1 == max_c)) {
|
||||
SKIP("All coordinates have extreme value, skipping (avoid rounding error)");
|
||||
}
|
||||
|
||||
const int r =
|
||||
round(std::sqrt(std::pow((x1 - x0), 2) + std::pow((y1 - y0), 2)));
|
||||
|
||||
canvas_buffer *canvas = new canvas_buffer(size, size);
|
||||
bresenham_circle_tool *tool = new bresenham_circle_tool(*canvas);
|
||||
|
||||
tool->draw(x0, y0, x1, y1);
|
||||
|
||||
bool pass = true;
|
||||
for (int x = 0; x < size; x++) {
|
||||
for (int y = 0; y < size; y++) {
|
||||
double distance =
|
||||
std::abs(std::sqrt(std::pow(x0 - x, 2) + std::pow(y0 - y, 2)) - r);
|
||||
// Because of rounding errors, an exact test (for all pixels) is not
|
||||
// feasible.
|
||||
// Therefore, it is only tested if set pixels have a distance <= 1.
|
||||
if (canvas->get_pixel(x, y) && distance > 1) {
|
||||
pass = false;
|
||||
}
|
||||
}
|
||||
}
|
||||
REQUIRE(pass);
|
||||
}
|
||||
|
||||
TEST_CASE("Barycentric coordinates: Edge cases") {
|
||||
int x0 = 0, y0 = 0, x1 = 0, y1 = 10, x2 = 10, y2 = 0;
|
||||
float b1, b2, b3;
|
||||
|
||||
// point on vertex
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 0);
|
||||
REQUIRE(b1 == 1);
|
||||
REQUIRE(b2 == 0);
|
||||
REQUIRE(b3 == 0);
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 10);
|
||||
REQUIRE(b1 == 0);
|
||||
REQUIRE(b2 == 1);
|
||||
REQUIRE(b3 == 0);
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 10, 0);
|
||||
REQUIRE(b1 == 0);
|
||||
REQUIRE(b2 == 0);
|
||||
REQUIRE(b3 == 1);
|
||||
|
||||
// point on edge
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 5);
|
||||
REQUIRE(b1 == 0.5);
|
||||
REQUIRE(b2 == 0.5);
|
||||
REQUIRE(b3 == 0);
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 5, 0);
|
||||
REQUIRE(b1 == 0.5);
|
||||
REQUIRE(b2 == 0);
|
||||
REQUIRE(b3 == 0.5);
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 5, 5);
|
||||
REQUIRE(b1 == 0);
|
||||
REQUIRE(b2 == 0.5);
|
||||
REQUIRE(b3 == 0.5);
|
||||
|
||||
// All points on straight line
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(0, y0, 0, y1, 0, y2, 0, 0);
|
||||
REQUIRE(std::isnan(b1));
|
||||
REQUIRE(std::isnan(b2));
|
||||
REQUIRE(std::isnan(b3));
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, 0, x1, 0, x2, 0, 0, 0);
|
||||
REQUIRE(std::isnan(b1));
|
||||
REQUIRE(std::isnan(b2));
|
||||
REQUIRE(std::isnan(b3));
|
||||
}
|
||||
|
||||
TEST_CASE("Barycentric coordinates (prop: Σ = 1)") {
|
||||
int x0 = GENERATE(take(2, random(-100, 100)));
|
||||
int y0 = GENERATE(take(2, random(-100, 100)));
|
||||
int x1 = GENERATE(take(2, random(-100, 100)));
|
||||
int y1 = GENERATE(take(2, random(-100, 100)));
|
||||
int x2 = GENERATE(take(2, random(-100, 100)));
|
||||
int y2 = GENERATE(take(2, random(-100, 100)));
|
||||
|
||||
int x = GENERATE(take(5, random(-100, 100)));
|
||||
int y = GENERATE(take(5, random(-100, 100)));
|
||||
float b1, b2, b3;
|
||||
|
||||
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, x, y);
|
||||
|
||||
// If all points are on a straight line, the property does not hold
|
||||
if (!(x0 == x1 && x1 == x2) && !(y0 == y1 && y1 == y2)) {
|
||||
REQUIRE_THAT(b1 + b2 + b3, WithinRel(1.0, 0.01));
|
||||
}
|
||||
}
|
||||
|
||||
TEST_CASE("Sort triangle points") {
|
||||
int x0 = 10, y0 = 60, x1 = 50, y1 = 90, x2 = 40, y2 = 30;
|
||||
sort_triangle_points(x0, y0, x1, y1, x2, y2);
|
||||
REQUIRE(x0 == 40);
|
||||
REQUIRE(y0 == 30);
|
||||
REQUIRE(x1 == 10);
|
||||
REQUIRE(y1 == 60);
|
||||
REQUIRE(x2 == 50);
|
||||
REQUIRE(y2 == 90);
|
||||
}
|
||||
|
||||
TEST_CASE("Sort triangle points (prop: y0 < y1 < y2)") {
|
||||
int x0 = GENERATE(take(3, random(-100, 100)));
|
||||
int y0 = GENERATE(take(3, random(-100, 100)));
|
||||
int x1 = GENERATE(take(3, random(-100, 100)));
|
||||
int y1 = GENERATE(take(3, random(-100, 100)));
|
||||
int x2 = GENERATE(take(3, random(-100, 100)));
|
||||
int y2 = GENERATE(take(3, random(-100, 100)));
|
||||
|
||||
sort_triangle_points(x0, y0, x1, y1, x2, y2);
|
||||
|
||||
REQUIRE(y0 <= y1);
|
||||
REQUIRE(y1 <= y2);
|
||||
}
|
||||
|
||||
TEST_CASE("Slope") {
|
||||
REQUIRE(slope(5, 10, 20, 10) == 0.0);
|
||||
REQUIRE(slope(0, 0, 10, 10) == 1.0);
|
||||
REQUIRE(slope(0, 0, 10, -10) == -1.0);
|
||||
REQUIRE(slope(0, 0, 10, 5) == 0.5);
|
||||
REQUIRE(slope(0, 0, 10, -5) == -0.5);
|
||||
REQUIRE(slope(0, 10, 10, 40) == 3.0);
|
||||
REQUIRE(slope(0, 10, 10, -40) == -5.0);
|
||||
|
||||
// Special case: Infinite slope, must be normalized
|
||||
REQUIRE(slope(10, 10, 10, 40) == 0.0);
|
||||
}
|
||||
|
||||
TEST_CASE("Sweep line (prop: Barycentric coordinates)") {
|
||||
const int size = 100;
|
||||
int x0 = GENERATE(take(3, random(0, size - 1)));
|
||||
int y0 = GENERATE(take(3, random(0, size - 1)));
|
||||
int x1 = GENERATE(take(3, random(0, size - 1)));
|
||||
int y1 = GENERATE(take(3, random(0, size - 1)));
|
||||
int x2 = GENERATE(take(3, random(0, size - 1)));
|
||||
int y2 = GENERATE(take(3, random(0, size - 1)));
|
||||
|
||||
canvas_buffer *canvas = new canvas_buffer(size, size);
|
||||
sweep_line_tool *tool = new sweep_line_tool(*canvas);
|
||||
|
||||
tool->draw(x0, y0, x1, y1, x2, y2);
|
||||
|
||||
int deviating = 0;
|
||||
bool pass = true;
|
||||
for (int x = 0; x < size; x++) {
|
||||
for (int y = 0; y < size; y++) {
|
||||
if (point_in_triangle(x0, y0, x1, y1, x2, y2, x, y)) {
|
||||
if (!canvas->get_pixel(x, y)) {
|
||||
// Barycentric coordinates say, point is not in triangle,
|
||||
// but point is not set.
|
||||
// This must not happen → fail test.
|
||||
pass = false;
|
||||
}
|
||||
} else if (canvas->get_pixel(x, y)) {
|
||||
// Barycentric coordinates say, point is not in triangle,
|
||||
// but point is set.
|
||||
// The point is most likely on edge → mark it as deviating.
|
||||
deviating++;
|
||||
}
|
||||
}
|
||||
}
|
||||
REQUIRE(pass);
|
||||
// Crude heuristic:
|
||||
// No more than differences of all edge point coordinates can fail.
|
||||
// This ist not accurate (false positives possible) on small/spiky triangles,
|
||||
// but overall it gives an okayish result.
|
||||
REQUIRE(deviating < abs(y1 - y0) + abs(y2 - y1) + abs(y0 - y2) +
|
||||
abs(x1 - x0) + abs(x2 - x1) + abs(x0 - x2));
|
||||
}
|
207
u02/src/util.cpp
Normal file
207
u02/src/util.cpp
Normal file
|
@ -0,0 +1,207 @@
|
|||
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||||
#include "util.h"
|
||||
#include <cmath>
|
||||
|
||||
void transform_mut(Transformation transformation, int &x, int &y) {
|
||||
if (transformation & TRANSFORM_ROTATE_CW) {
|
||||
std::swap(x, y);
|
||||
x = -x;
|
||||
}
|
||||
if (transformation & TRANSFORM_ROTATE_CCW) {
|
||||
std::swap(x, y);
|
||||
y = -y;
|
||||
}
|
||||
if (transformation & TRANSFORM_MIRROR_X) {
|
||||
y = -y;
|
||||
}
|
||||
if (transformation & TRANSFORM_MIRROR_Y) {
|
||||
x = -x;
|
||||
}
|
||||
}
|
||||
|
||||
std::pair<int, int> transform(Transformation transformation, int x, int y) {
|
||||
transform_mut(transformation, x, y);
|
||||
return std::make_pair(x, y);
|
||||
}
|
||||
|
||||
void transform_inv_mut(Transformation transformation, int &x, int &y) {
|
||||
if (transformation & TRANSFORM_MIRROR_Y) {
|
||||
x = -x;
|
||||
}
|
||||
if (transformation & TRANSFORM_MIRROR_X) {
|
||||
y = -y;
|
||||
}
|
||||
if (transformation & TRANSFORM_ROTATE_CCW) {
|
||||
// does clockwise rotation
|
||||
std::swap(x, y);
|
||||
x = -x;
|
||||
}
|
||||
if (transformation & TRANSFORM_ROTATE_CW) {
|
||||
// does counterclockwise rotation
|
||||
std::swap(x, y);
|
||||
y = -y;
|
||||
}
|
||||
}
|
||||
|
||||
std::pair<int, int> transform_inv(Transformation transformation, int x, int y) {
|
||||
transform_inv_mut(transformation, x, y);
|
||||
return std::make_pair(x, y);
|
||||
}
|
||||
|
||||
/*
|
||||
* After it took me many hours to get this right,
|
||||
* I at least want to document how I got to it:
|
||||
*
|
||||
* N.B. In the following,
|
||||
* Modulo is *not* the remainder of the euclidean division,
|
||||
* but instead the remainder of truncated division
|
||||
* (i.e., negative quotients produce negative results).
|
||||
*
|
||||
* There are two main cases:
|
||||
* The simple one is where angle % 90° ≤ 45°.
|
||||
* To transform this into the standard case,
|
||||
* only mirrors are needed.
|
||||
* The more complicated is when angle % 90° ≥ 45°.
|
||||
* To transform this into the standard case,
|
||||
* a rotation has to be done, followed by a mirror in some cases.
|
||||
*
|
||||
* The following matrices show what must be done when.
|
||||
* The ASCII art arrows show the line as it should be drawn,
|
||||
* the the column/row headings show how they can be identified in code,
|
||||
* the capital letters in the field show what needs to be done
|
||||
* to reach the standard case
|
||||
* (X/Y: mirror X/Y; CW/CCW: rotate CW/CCW).
|
||||
* Because there is no nice way to draw arrows with an angle < 45°,
|
||||
* they are just differentiated by the heading.
|
||||
*
|
||||
* Let (x_0, y_0) be the starting point and (x_1, y_1) the end point.
|
||||
* Let Δx = x_1 - x_0, Δy = y_1 - y_0.
|
||||
* Let m = Δy/Δx, α = atan(m).
|
||||
*
|
||||
* α ≤ 45°:
|
||||
*
|
||||
* Δx>0 Δx<0
|
||||
*
|
||||
* A | A
|
||||
* Δy<0 / | \
|
||||
* / | \
|
||||
* / - | Y \
|
||||
* ------+------
|
||||
* \ X | XY /
|
||||
* \ | /
|
||||
* Δy>0 \ | /
|
||||
* V | V
|
||||
*
|
||||
* α ≥ 45°:
|
||||
*
|
||||
* Δx>0 Δx<0 Δx>0 Δx<0
|
||||
*
|
||||
* A | A \ | A
|
||||
* Δy<0 / | \ Δy<0 \ | /
|
||||
* / | \ \ | /
|
||||
* / CW | CW \ X V | /
|
||||
* -------+------- → after rotation → ------+-----
|
||||
* \ CCW | CCW / A | \
|
||||
* \ | / / | \
|
||||
* Δy>0 \ | / Δy>0 / | \
|
||||
* V | V / | X V
|
||||
*/
|
||||
Transformation transformation_to_standard_case(int x0, int y0, int x1, int y1) {
|
||||
Transformation transformation = 0;
|
||||
|
||||
int delta_y = y1 - y0;
|
||||
int delta_x = x1 - x0;
|
||||
// checks if angle ∈ (-90°, 90°) is ≥ 45°
|
||||
// this is a simplified version of atan(Δy/Δx) > π/4:
|
||||
// atan(Δy/Δx) > π/4 | tan(…)
|
||||
// ⇔ Δx/Δy > 1 | Δy
|
||||
// ⇔ Δx > Δy
|
||||
if (abs(delta_y) > abs(delta_x)) {
|
||||
// if-else is needed, because of special case Δy = 0
|
||||
if (delta_y < 0) {
|
||||
transformation |= TRANSFORM_ROTATE_CW;
|
||||
} else if (delta_y > 0) {
|
||||
transformation |= TRANSFORM_ROTATE_CCW;
|
||||
}
|
||||
// the sign of Δx and Δy (pre-rotation!) differ,
|
||||
// an additional mirror is needed
|
||||
if (delta_x * delta_y < 0) {
|
||||
transformation |= TRANSFORM_MIRROR_X;
|
||||
}
|
||||
} else {
|
||||
if (delta_x < 0) {
|
||||
transformation |= TRANSFORM_MIRROR_Y;
|
||||
}
|
||||
if (delta_y > 0) {
|
||||
transformation |= TRANSFORM_MIRROR_X;
|
||||
}
|
||||
}
|
||||
|
||||
return transformation;
|
||||
}
|
||||
|
||||
std::tuple<float, float, float> barycentric_coordinates(int x0, int y0, int x1,
|
||||
int y1, int x2, int y2,
|
||||
int xp, int yp) {
|
||||
// Source:
|
||||
// https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Vertex_approach
|
||||
float b1 = x1 * y2 - x2 * y1 + xp * (y1 - y2) + yp * (x2 - x1);
|
||||
float b2 = x2 * y0 - x0 * y2 + xp * (y2 - y0) + yp * (x0 - x2);
|
||||
float b3 = x0 * y1 - x1 * y0 + xp * (y0 - y1) + yp * (x1 - x0);
|
||||
|
||||
// reciprocal computed directly for performance
|
||||
float area_factor =
|
||||
1 / static_cast<float>(x0 * (y1 - y2) + x1 * (y2 - y0) + x2 * (y0 - y1));
|
||||
|
||||
b1 *= area_factor;
|
||||
b2 *= area_factor;
|
||||
b3 *= area_factor;
|
||||
|
||||
return {b1, b2, b3};
|
||||
}
|
||||
|
||||
bool point_in_triangle(int x0, int y0, int x1, int y1, int x2, int y2, int xp,
|
||||
int yp) {
|
||||
float b1, b2, b3;
|
||||
std::tie(b1, b2, b3) =
|
||||
barycentric_coordinates(x0, y0, x1, y1, x2, y2, xp, yp);
|
||||
return b1 >= 0.0 && b1 <= 1.0 && b2 >= 0.0 && b2 <= 1.0 && b3 >= 0.0 &&
|
||||
b3 <= 1.0;
|
||||
}
|
||||
|
||||
void sort_triangle_points(int &x0, int &y0, int &x1, int &y1, int &x2,
|
||||
int &y2) {
|
||||
// Bubble sort is not really ideal in general.
|
||||
// It could be changed to use a more efficient algorithm,
|
||||
// but for only 3 values, it should suffice.
|
||||
// Moreover, implementing sorting on an array/vector of tuples
|
||||
// is probably more overhead.
|
||||
if (y0 > y1) {
|
||||
std::swap(x0, x1);
|
||||
std::swap(y0, y1);
|
||||
}
|
||||
if (y0 > y2) {
|
||||
std::swap(x0, x2);
|
||||
std::swap(y0, y2);
|
||||
}
|
||||
if (y1 > y2) {
|
||||
std::swap(x1, x2);
|
||||
std::swap(y1, y2);
|
||||
}
|
||||
}
|
||||
|
||||
float slope(int x0, int y0, int x1, int y1) {
|
||||
float m = ((float)(y1 - y0)) / ((float)(x1 - x0));
|
||||
if (std::isinf(m) || std::isnan(m)) {
|
||||
// This is a special case for two things:
|
||||
//
|
||||
// IEEE 754 specifies ∞ × 0 / 0 × ∞ to be an invalid operation,
|
||||
// and therefore return NaN.
|
||||
// That makes the computation of Δy fail when x0 == x1.
|
||||
//
|
||||
// In the case that additionally y0 == y1,
|
||||
// the expression is 0/0, also defined in IEEE 754 as invalid.
|
||||
m = 0;
|
||||
}
|
||||
return m;
|
||||
}
|
Reference in a new issue