In the Beginning there was

the Cube

.gitignore

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+.venv/
+__pycache__/
+.env

.idea/.gitignore

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+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/Wuerfel.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$">
+      <excludeFolder url="file://$MODULE_DIR$/.venv" />
+    </content>
+    <orderEntry type="jdk" jdkName="Python 3.13 virtualenv at C:\Users\steph\Documents\Ohm\Media Engineering\Media Engineering SoSe26\Prog2A\.venv" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

.idea/inspectionProfiles/Project_Default.xml

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+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="PyPep8Inspection" enabled="true" level="INFORMATION" enabled_by_default="true">
+      <option name="ignoredErrors">
+        <list>
+          <option value="W292" />
+        </list>
+      </option>
+    </inspection_tool>
+  </profile>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.14 (Wuerfel)" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.13 virtualenv at C:\Users\steph\Documents\Ohm\Media Engineering\Media Engineering SoSe26\Prog2A\.venv" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/Wuerfel.iml" filepath="$PROJECT_DIR$/.idea/Wuerfel.iml" />
+    </modules>
+  </component>
+</project>

.idea/vcs.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>

Spiel/compute.py

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+import math
+
+from tabulate import tabulate
+
+
+def matmul(matrix_a:list[list[float]], matrix_b: list[list[float]]) -> list[list[float]]:
+    """
+    Add two numbers together.
+    :param matrix_a: The first Matrix
+    :type matrix_a: list[list[float]]
+    :param matrix_b: The second Matrix
+    :type matrix_b: list[list[float]]
+    :return: The Matrix Multiplication of matrix_a and matrix_b
+    :rtype: list[list[float]]
+    """
+    try:
+        if len(matrix_a[0]) != len(matrix_b):
+            raise ValueError("Differing Matrix Size")
+        target_height = len(matrix_a)
+        target_width = len(matrix_b[0])
+
+        end_matrix : list[list[float]]= []
+
+
+        for height in range(target_height):
+            end_matrix.append([])
+            for width in range(target_width):
+                row = matrix_a[height]
+                column_ = []
+                for b in matrix_b:
+                    column_.append(b[width])
+                result_quarter = 0
+                for i in range(len(row)):
+                    result_quarter += row[i] * column_[i]
+                end_matrix[height].append(float(result_quarter))
+
+        return end_matrix
+    except ValueError:
+        print("An Error has occurred")
+    except IndexError:
+        print("Tried to call non-existing Index")
+    except TypeError:
+        print("Tried to insert not a Number")
+
+
+
+def transpose(matrix:list[list[float]]) -> list[list[float]]:
+    """
+    Transposes a matrix.
+    :param matrix: The Matrix, that will be transposed
+    :type matrix: list[list[float]]
+    :return: The transposed matrix
+    :rtype: list[list[float]]
+    """
+
+    transposed_matrix = []
+    for x in range(len(matrix[0])):
+        column = []
+        for b in matrix:
+            column.append(b[x])
+        transposed_matrix.append(column)
+
+    return transposed_matrix
+
+def rot_2d(angle:float) -> list[list[float]]:
+    """
+    Creates a Rotation Matrix out of the given angle
+    :param angle: The rotation in radians
+    :type angle: float
+    :return: The Rotation Matrix
+    :rtype: list[list[float]]
+    """
+    sin = round(math.sin(angle), 4)
+    cos = round(math.cos(angle), 4)
+    return [[cos, -sin],
+            [sin, cos]]
+
+def rot_3d(angle: float, axis: str) -> list[list[float]]:
+    """
+    Creates a 3D Rotation Matrix out of the given angle and axis
+    :param angle: The rotation in radians
+    :type angle: float
+    :param axis: The Axis on which it rotates; only "x", "y" or "z"
+    :type axis: str
+    :return: The 3D Rotation Matrix
+    :rtype: list[list[float]]
+    """
+    axis = axis.lower()
+    sin = round(math.sin(angle), 4)
+    cos = round(math.cos(angle), 4)
+    if axis == "x":
+        return[[1, 0, 0],
+                [0, cos, -sin],
+                [0, sin, cos]]
+    if axis == "y":
+        return[[cos, 0, sin],
+                [0, 1, 0],
+                [-sin, 0, cos]]
+    if axis == "z":
+        return [[cos, -sin, 0],
+                [sin, cos, 0],
+                     [0, 0, 1]]
+
+    raise ValueError
+
+# For Both below add the Doc String!
+def project_ortho(point: tuple[float, float, float], scale: float = 1) -> tuple[float, float]:
+    """
+    Projects a 3D Position into an orthogonal 2D View
+    :param point: The 3D Point
+    :type point: tuple[float, float, float]
+    :param scale: The scale by which the point gets scaled; regular is 1.0
+    :type scale: float
+    :return: The 3D Point on a 2D plane
+    :rtype: tuple[float, float]
+    """
+    return (point[0] * scale,
+            point[1] * scale)
+
+def project_perspective(point: tuple[float, float, float], focal_length: float = 1.0,
+                        scale: float = 1.0, camera_distance: float = 4.0) -> tuple[float, float]:
+    """
+    Projects a 3D Position into a perspective 2D View
+    :param point: The 3D Point
+    :type point: tuple[float, float, float]
+    :param focal_length: strength of perspective; regular is 1.0
+    :type focal_length: float
+    :param scale: The scale by which the point gets scaled; regular is 1.0
+    :type scale: float
+    :param camera_distance: How far the Camera is away from the point; regular is 4.0
+    :return: The 3D Point on a 2D plane
+    :rtype: tuple[float, float]
+    """
+    return (point[0] * focal_length * scale / (point[2] + camera_distance),
+            point[1] * focal_length * scale / (point[2] + camera_distance), )
+
+
+def print_matrix(matrix:list[list[float]]) -> None:
+    for row in matrix:
+        print(row)
+
+if __name__ == "__main__":
+    matrix_bsp_a = [[1, 2, 3], [4, 5, 6]]
+    matrix_bsp_b = [[1, 2], [3, 4], [5, 6]]
+    matrix_bsp_c = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
+    matrix_bsp_d = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
+
+    if False:
+        matrix_bsp_result = matmul(matrix_bsp_c, matrix_bsp_d)
+        print_matrix(matrix_bsp_result)
+
+    if False:
+        matrix_bsp_result = transpose(matrix_bsp_d)
+        #print_matrix(matrix_bsp_c)
+        print_matrix(matrix_bsp_result)
+
+    if True:
+        #print_matrix(rot_2d(math.pi*.25))
+        print(tabulate(rot_2d(1.33)))
+
+
+    # Test Kommenter
+
+    print("Done")

Spiel/cube_game.py

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+import pygame
+from game import Game
+import compute
+
+BLACK = (0, 0, 0)
+GREEN = (0, 255, 0)
+RED = (255, 0, 0)
+
+class CubeGame(Game):
+    """Der Mond kreist um die Erde."""
+    def __init__(self,title: str = "Cube: The Game", fps: int = 60, size: tuple[int, int] = (1280, 800),) -> None:
+        """Legt Startposition, Drehwinkel und Rotationsmatrix fest."""
+        super().__init__(title, fps, size)
+
+        self.cube_corner_points = [(-1, -1, -1), ( 1, -1, -1),
+                                    (1, 1, -1), (-1, 1, -1),
+                                    (-1, -1, 1), ( 1, -1, 1),
+                                    ( 1, 1, 1), (-1, 1, 1)]
+
+        self.cube_edges = [(0, 1), (0, 3), (0, 4),
+                           (6, 2), (6, 7), (6, 5),
+                           (1, 2), (1, 5),
+                           (3, 7), (3, 2),
+                           (4, 5), (4, 7)]
+
+        self.screen_middle = (self.size[0]// 2, self.size[1] // 2)
+
+        self.spin = .05
+        self.camera_scale_ortho = 150
+        self.camera_scale_project = 400
+        self.orthogonal = False
+        self.direction = (0, 0)
+
+
+    def handle_event(self, event):
+        if not super().handle_event(event):
+            return False
+        if event.type == pygame.KEYDOWN:
+            print(self.direction)
+            if event.key == pygame.K_UP:
+                self.direction = (max(-1, self.direction[0] - .1), self.direction[1])
+            if event.key == pygame.K_DOWN:
+                self.direction = (min(1, self.direction[0] + .1), self.direction[1])
+            if event.key == pygame.K_RIGHT:
+                self.direction = (self.direction[0], max(-1, self.direction[1] - .1))
+            if event.key == pygame.K_LEFT:
+                self.direction = ( self.direction[0], min(1, self.direction[1] + .1))
+            if event.key == pygame.K_SPACE:
+                self.orthogonal = not self.orthogonal
+        return True
+
+    def rotate(self, axis, dir=1):
+        for point in range(len(self.cube_corner_points)):
+            point_matrix = [[self.cube_corner_points[point][0]],
+                            [self.cube_corner_points[point][1]],
+                            [self.cube_corner_points[point][2]]]
+            point_temp = compute.matmul(compute.rot_3d(self.spin*dir, axis), point_matrix)
+            self.cube_corner_points[point] = (point_temp[0][0], point_temp[1][0], point_temp[2][0])
+
+    def update_game(self) -> bool:
+        """Dreht den Mond ein Stück weiter."""
+        if self.direction[0] != 0:
+            self.rotate("x", self.direction[0])
+        if self.direction[1] != 0:
+            self.rotate("y", self.direction[1])
+        self.direction = (round(self.direction[0], 4), round(self.direction[1], 4))
+
+        return True
+
+    def draw_game(self) -> None:
+        """Zeichnet Erde und Mond."""
+        self.screen.fill(BLACK)
+
+        for edge in self.cube_edges:
+            point2d_a = self.to_middle(self.perspective(self.cube_corner_points[edge[0]]))
+            point2d_b = self.to_middle(self.perspective(self.cube_corner_points[edge[1]]))
+            pygame.draw.line(self.screen, RED, point2d_a, point2d_b)
+
+        for point in self.cube_corner_points:
+            point2d = self.to_middle(self.perspective(point))
+            pygame.draw.circle(self.screen, GREEN, point2d, 5)
+
+
+        pygame.display.flip()
+
+    def perspective(self, point):
+        if self.orthogonal:
+            return self.orthogonal_perspective(point)
+        return self.project_perspective(point)
+
+    def orthogonal_perspective(self, point):
+        return compute.project_ortho(point, scale=self.camera_scale_ortho)
+
+    def project_perspective(self, point):
+        return compute.project_perspective(point, scale=self.camera_scale_project)
+
+    def to_middle(self, point):
+        return point[0] + self.screen_middle[0], point[1] + self.screen_middle[1]
+
+
+if __name__ == "__main__":
+    cube = CubeGame()
+    cube.run()

Spiel/game.py

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+"""Basisklasse ``Game`` für einfache pygame-Anwendungen."""
+
+import pygame
+
+
+class Game:
+    """Basisklasse für pygame-Spiele.
+
+    Unterklassen passen das Verhalten durch Überschreiben von
+    :meth:`handle_event`, :meth:`update_game` und :meth:`draw_game` an.
+    """
+
+    def __init__(
+        self,
+        title: str,
+        fps: int = 60,
+        size: tuple[int, int] = (640, 400),
+    ) -> None:
+        """Legt Fenstertitel, Bildrate und Fenstergröße fest.
+
+        Args:
+            title: Titel des Fensters.
+            fps: Maximale Bilder pro Sekunde.
+            size: Fenstergröße als (Breite, Höhe) in Pixeln.
+        """
+        self.title: str = title
+        self.fps: int = fps
+        self.size: tuple[int, int] = size
+        self.clock: pygame.time.Clock = pygame.time.Clock()
+        self.dt: float = 0
+        self.screen: pygame.Surface | None = None
+
+    def init_game(self) -> None:
+        """Initialisiert pygame und erzeugt das Fenster."""
+        pygame.init()
+        pygame.display.set_caption(self.title)
+        self.screen = pygame.display.set_mode(self.size)
+
+    def game_loop(self) -> None:
+        """Führt die Hauptschleife aus, bis Events oder Update ``False`` liefern."""
+        while True:
+            # Berechnung der Zeitdifferenz seit dem letzten Frame
+            self.dt = self.clock.tick(self.fps) / 1000
+            if self.event_handling() == False:
+                break
+            if self.update_game() == False:
+                break
+            self.draw_game()
+
+    def exit_game(self) -> None:
+        """Beendet pygame."""
+        pygame.quit()
+
+    def event_handling(self) -> bool:
+        """Verteilt alle anstehenden Events an :meth:`handle_event`.
+
+        Bleibt in der Unterklasse unverändert.
+
+        Returns:
+            ``False``, sobald ein Event das Spiel beenden soll, sonst ``True``.
+        """
+        for event in pygame.event.get():
+            if not self.handle_event(event):
+                return False
+        return True
+
+    def handle_event(self, event: pygame.event.Event) -> bool:
+        """Verarbeitet ein einzelnes Event.
+
+        Wird in der Unterklasse überschrieben.
+
+        Args:
+            event: Das zu verarbeitende pygame-Event.
+
+        Returns:
+            ``False`` bei ``pygame.QUIT``, sonst ``True``.
+        """
+        if event.type == pygame.QUIT:
+            return False
+        return True
+
+    def update_game(self) -> bool:
+        """Aktualisiert den Spielzustand um einen Frame.
+
+        Returns:
+            ``False``, wenn das Spiel beendet werden soll, sonst ``True``.
+        """
+        return True
+
+    def draw_game(self) -> None:
+        """Zeichnet den aktuellen Frame und bringt ihn zur Anzeige."""
+        pygame.display.flip()
+
+    def run(self) -> None:
+        """Startet das Spiel: Initialisierung, Hauptschleife, Beenden."""
+        self.init_game()
+        self.game_loop()
+        self.exit_game()

install_dependencies.py

@@ -0,0 +1,146 @@
+#!/usr/bin/env python3
+"""Installiert die Abhängigkeiten aus pyproject.toml in die aktuelle Python-Umgebung.
+
+Ersatz für "Install requirements" aus PyCharm, wenn das Projekt eine pyproject.toml
+statt einer requirements.txt hat. Kein Build, keine besondere Projektstruktur nötig,
+nur Standardbibliothek (Python >= 3.11).
+
+Benutzung:
+  In PyCharm: Rechtsklick auf diese Datei -> Run 'install_dependencies'
+  Im Terminal (venv aktiv): python install_dependencies.py
+
+Ohne Parameter wird ALLES installiert:
+  [project].dependencies + alle [project.optional-dependencies] + alle [dependency-groups]
+
+Abweichendes Verhalten:
+  python install_dependencies.py --extra dev        nur Basis + Extra "dev"
+  python install_dependencies.py --group test       nur Basis + Gruppe "test"
+  python install_dependencies.py --no-main --group dev
+  python install_dependencies.py --list             nur anzeigen, nichts installieren
+  python install_dependencies.py --write            requirements.txt schreiben statt installieren
+  python install_dependencies.py --write -o reqs.txt
+"""
+from __future__ import annotations
+
+import sys
+
+if sys.version_info < (3, 11):
+    sys.exit("Dieses Skript braucht Python 3.11 oder neuer (tomllib). "
+             f"Aktuell: {sys.version.split()[0]}")
+
+import argparse
+import subprocess
+import tempfile
+import tomllib
+from pathlib import Path
+
+PROJECT_DIR = Path(__file__).resolve().parent
+
+
+def resolve_group(groups: dict, name: str, seen: set[str] | None = None) -> list[str]:
+    """Löst eine Dependency-Group inkl. {include-group = "..."} rekursiv auf."""
+    seen = set() if seen is None else seen
+    if name in seen:
+        raise ValueError(f"Zyklische include-group: {name}")
+    if name not in groups:
+        raise KeyError(f"Dependency-Group '{name}' nicht gefunden")
+    seen.add(name)
+    result: list[str] = []
+    for entry in groups[name]:
+        if isinstance(entry, str):
+            result.append(entry)
+        elif isinstance(entry, dict) and "include-group" in entry:
+            result.extend(resolve_group(groups, entry["include-group"], seen))
+    return result
+
+
+def collect(data: dict, extras: list[str], groups: list[str], no_main: bool) -> list[str]:
+    project = data.get("project", {})
+    optional = project.get("optional-dependencies", {})
+    dep_groups = data.get("dependency-groups", {})
+    deps: list[str] = []
+
+    if not no_main:
+        deps.extend(project.get("dependencies", []))
+    for extra in extras:
+        if extra not in optional:
+            raise KeyError(f"Optional-Dependency '{extra}' nicht gefunden")
+        deps.extend(optional[extra])
+    for group in groups:
+        deps.extend(resolve_group(dep_groups, group))
+
+    # Duplikate entfernen, Reihenfolge behalten
+    return list(dict.fromkeys(d.strip() for d in deps if d.strip()))
+
+
+def main() -> int:
+    p = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    p.add_argument("-p", "--pyproject", type=Path, default=PROJECT_DIR / "pyproject.toml",
+                   help="Pfad zur pyproject.toml (Standard: neben diesem Skript)")
+    p.add_argument("--extra", action="append", default=None,
+                   help="nur diese optional-dependencies (mehrfach möglich)")
+    p.add_argument("--group", action="append", default=None,
+                   help="nur diese dependency-groups (mehrfach möglich)")
+    p.add_argument("--no-main", action="store_true", help="[project].dependencies weglassen")
+    p.add_argument("--list", action="store_true", help="Abhängigkeiten nur anzeigen")
+    p.add_argument("--write", action="store_true", help="requirements-Datei schreiben statt installieren")
+    p.add_argument("-o", "--output", type=Path, default=PROJECT_DIR / "requirements.txt",
+                   help="Zieldatei für --write")
+    args = p.parse_args()
+
+    if not args.pyproject.exists():
+        print(f"{args.pyproject} nicht gefunden", file=sys.stderr)
+        return 1
+    data = tomllib.loads(args.pyproject.read_text(encoding="utf-8"))
+    all_extras = list(data.get("project", {}).get("optional-dependencies", {}))
+    all_groups = list(data.get("dependency-groups", {}))
+
+    # Ohne --extra/--group: alles. Mit einem davon: nur das Gewählte.
+    selective = args.extra is not None or args.group is not None
+    extras = (args.extra or []) if selective else all_extras
+    groups = (args.group or []) if selective else all_groups
+
+    try:
+        deps = collect(data, extras, groups, args.no_main)
+    except (KeyError, ValueError) as e:
+        print(f"Fehler: {e.args[0]}", file=sys.stderr)
+        print(f"  Vorhandene --extra: {', '.join(all_extras) or '(keine)'}", file=sys.stderr)
+        print(f"  Vorhandene --group: {', '.join(all_groups) or '(keine)'}", file=sys.stderr)
+        return 1
+
+    parts = ([] if args.no_main else ["Basis"]) + [f"extra:{e}" for e in extras] + [f"group:{g}" for g in groups]
+    print(f"Auswahl: {', '.join(parts) or '(nichts)'}")
+
+    if args.list:
+        print("\n".join(deps) or "(keine Abhängigkeiten)")
+        return 0
+
+    content = f"# Automatisch erzeugt aus {args.pyproject.name} – nicht von Hand bearbeiten\n" + "\n".join(deps) + "\n"
+
+    if args.write:
+        args.output.write_text(content, encoding="utf-8")
+        print(f"{len(deps)} Abhängigkeiten -> {args.output}")
+        return 0
+
+    if not deps:
+        print("Keine Abhängigkeiten gefunden – nichts zu tun.")
+        return 0
+
+    if sys.prefix == sys.base_prefix:
+        print("WARNUNG: Es ist kein virtuelles Environment aktiv – es wird in die globale "
+              f"Python-Installation installiert:\n  {sys.prefix}", file=sys.stderr)
+        if sys.stdin.isatty() and input("Trotzdem fortfahren? [j/N] ").strip().lower() not in ("j", "ja", "y", "yes"):
+            return 1
+
+    with tempfile.NamedTemporaryFile("w", suffix=".txt", delete=False, encoding="utf-8") as tmp:
+        tmp.write(content)
+        tmp_path = Path(tmp.name)
+    try:
+        print(f"Installiere {len(deps)} Abhängigkeiten in {sys.prefix}\n")
+        return subprocess.call([sys.executable, "-m", "pip", "install", "-r", str(tmp_path)])
+    finally:
+        tmp_path.unlink(missing_ok=True)
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())

pyproject.toml

@@ -0,0 +1,7 @@
+[project]
+name = "Wuerfel"
+version = "0.1.0"
+dependencies = ["tabulate", "ruff"]
+
+[project.optional-dependencies]
+dev = ["pytest", "ruff", "pytest-cov", "pygame"]