Compare commits
32 commits
da149b7dfc
...
dbf298940e
Author | SHA1 | Date | |
---|---|---|---|
Simon Bruder | dbf298940e | ||
Simon Bruder | 5296a3f361 | ||
Simon Bruder | 179a198e11 | ||
Simon Bruder | b0e754cddb | ||
Simon Bruder | 49cd0f201a | ||
Simon Bruder | 1f6f079edf | ||
Simon Bruder | 8822dbe7df | ||
Simon Bruder | 7de6c3cae3 | ||
Simon Bruder | 04527ef711 | ||
Simon Bruder | 2fd207f5f4 | ||
Simon Bruder | 0de522004b | ||
Simon Bruder | 11da9a4d79 | ||
Simon Bruder | e942c62ad6 | ||
Simon Bruder | 6b63595986 | ||
Simon Bruder | f81098f259 | ||
Simon Bruder | b780d4b8c4 | ||
Simon Bruder | 5a1ba0ca93 | ||
Simon Bruder | dfeb329a52 | ||
Simon Bruder | 625c257f3f | ||
Simon Bruder | c851767445 | ||
Simon Bruder | 649d5da18a | ||
Simon Bruder | 240d5435f2 | ||
Simon Bruder | 8b88c14b02 | ||
Simon Bruder | 708e501245 | ||
Simon Bruder | fab356c308 | ||
Simon Bruder | 18456541aa | ||
Simon Bruder | 837a1e5519 | ||
Simon Bruder | d5340b315b | ||
Simon Bruder | 60eb346e2c | ||
Simon Bruder | dfa6d381ca | ||
Simon Bruder | cc32e483e0 | ||
Simon Bruder | 2c741916bf |
14
COPYING
14
COPYING
|
@ -1,14 +0,0 @@
|
||||||
Copyright (C) 2023 Simon Bruder
|
|
||||||
|
|
||||||
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/>.
|
|
28
README.md
28
README.md
|
@ -8,6 +8,19 @@ Each exercise includes a separate `readme.txt`
|
||||||
that describes things specific to how I implemented the task.
|
that describes things specific to how I implemented the task.
|
||||||
However, those documents are in German, which is a requirement.
|
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
|
## Usage
|
||||||
|
|
||||||
### Build
|
### Build
|
||||||
|
@ -39,5 +52,16 @@ ln -sf build/compile_commands.json ..
|
||||||
|
|
||||||
## Licence
|
## Licence
|
||||||
|
|
||||||
[GPL-3.0-or-later](https://spdx.org/licenses/GPL-3.0-or-later.html).
|
Depending on the file,
|
||||||
See [COPYING](./COPYING) and [gpl-3.0.txt](./gpl-3.0.txt) for details.
|
[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 published version 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": {
|
"nixpkgs": {
|
||||||
"locked": {
|
"locked": {
|
||||||
"lastModified": 1681759395,
|
"lastModified": 1683408522,
|
||||||
"narHash": "sha256-7aaRtLxLAy8qFVIA26ulB+Q5nDVzuQ71qi0s0wMjAws=",
|
"narHash": "sha256-9kcPh6Uxo17a3kK3XCHhcWiV1Yu1kYj22RHiymUhMkU=",
|
||||||
"owner": "nixos",
|
"owner": "nixos",
|
||||||
"repo": "nixpkgs",
|
"repo": "nixpkgs",
|
||||||
"rev": "cd749f58ba83f7155b7062dd49d08e5e47e44d50",
|
"rev": "897876e4c484f1e8f92009fd11b7d988a121a4e7",
|
||||||
"type": "github"
|
"type": "github"
|
||||||
},
|
},
|
||||||
"original": {
|
"original": {
|
||||||
"owner": "nixos",
|
"owner": "nixos",
|
||||||
"ref": "nixos-22.11",
|
"ref": "nixos-unstable",
|
||||||
"repo": "nixpkgs",
|
"repo": "nixpkgs",
|
||||||
"type": "github"
|
"type": "github"
|
||||||
}
|
}
|
||||||
|
|
16
flake.nix
16
flake.nix
|
@ -1,6 +1,6 @@
|
||||||
{
|
{
|
||||||
inputs = {
|
inputs = {
|
||||||
nixpkgs.url = "github:nixos/nixpkgs/nixos-22.11";
|
nixpkgs.url = "github:nixos/nixpkgs/nixos-unstable";
|
||||||
flake-utils.url = "github:numtide/flake-utils";
|
flake-utils.url = "github:numtide/flake-utils";
|
||||||
};
|
};
|
||||||
|
|
||||||
|
@ -21,10 +21,22 @@
|
||||||
doCheck = true;
|
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 {
|
devShells.default = pkgs.mkShell {
|
||||||
nativeBuildInputs = with pkgs; [ catch2_3 cmake ];
|
nativeBuildInputs = with pkgs; [ catch2_3 cmake freeglut libGL libGLU ];
|
||||||
};
|
};
|
||||||
});
|
});
|
||||||
}
|
}
|
||||||
|
|
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.
|
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