Hausaufgabe perspektivische Projektion und Tests

.gitignore

@@ -0,0 +1,6 @@
+.venv/
+__pycache__/
+.pytest_cache/
+.ruff_cache/
+.idea/
+*.pyc

AGENTS.md

@@ -0,0 +1,4 @@
+# Regeln für dieses Projekt
+- Code nach PEP 8, Zeilenlänge maximal 88 Zeichen.
+- Jede Funktion und Methode hat einen Docstring und Type Hints.
+- Vor jedem Commit: `ruff check` und `ruff format`.

compute.py

@@ -1,143 +0,0 @@
-"""
-Matrix multiplication for nested list matrices.
-
-This module contains the :func:`matmul` function, which multiplies two
-matrices represented as nested Python lists.  The matrices are
-expected to be rectangular (each sub‑list has the same length).  A
-:class:`ValueError` is raised if the inner dimensions do not match.
-
-Example
--------
->>> a = [[1, 2], [3, 4]]
->>> b = [[5, 6], [7, 8]]
->>> matmul(a, b)
-[[19.0, 22.0], [43.0, 50.0]]
-
-The function is intentionally simple and performs no type checking
-of the inner elements; it simply forwards the arithmetic operations to
-Python's built‑in integer and float handling.
-"""
-
-import math
-
-
-def rot_2D(theta: float) -> list[list[float]]:
-    """Return the 2‑D rotation matrix for a given angle.
-
-    Parameters
-    ----------
-    theta : float
-        Angle in radians to rotate counter‑clockwise around the origin.
-
-    Returns
-    -------
-    list[list[float]]
-        2x2 rotation matrix
-
-    Examples
-    --------
-    >>> rot_2D(0)  # identity
-    [[1.0, -0.0], [0.0, 1.0]]
-    """
-    c = math.cos(theta)
-    s = math.sin(theta)
-    return [[c, -s], [s, c]]
-
-
-def matmul(a: list[list[float | int]], b: list[list[float | int]]) -> list[list[float]]:
-    """Return the matrix product of *a* and *b*.
-
-    Parameters
-    ----------
-    a : list[list[float | int]]
-        First matrix, shape ``(m, n)``.
-    b : list[list[float | int]]
-        Second matrix, shape ``(n, p)``.
-
-    Returns
-    -------
-    list[list[float]]
-        The result matrix of shape ``(m, p)``.
-
-    Raises
-    ------
-    ValueError
-        If the number of columns of ``a`` does not equal the number of
-        rows of ``b``.
-    """
-    n_cols_a = len(a[0]) if a else 0
-    n_rows_b = len(b)
-    if n_cols_a != n_rows_b:
-        raise ValueError(
-            f"inner dimensions must match: {n_cols_a} (a columns) != {n_rows_b} (b rows)"
-        )
-
-    m = len(a)
-    p = len(b[0]) if b else 0
-    # Pre‑allocate result matrix
-    result: list[list[float]] = [[0.0 for _ in range(p)] for _ in range(m)]
-
-    for i in range(m):
-        for k in range(n_cols_a):  # using k as column index of a, row of b
-            a_val = a[i][k]
-            for j in range(p):
-                result[i][j] += a_val * b[k][j]
-    return result
-
-
-
-def transpose(matrix: list[list[float | int]]) -> list[list[float | int]]:
-    """Return the transpose of the given matrix.
-
-    Parameters
-    ----------
-    matrix : list[list[float | int]]
-        Matrix to transpose.  All rows must have the same length.
-
-    Returns
-    -------
-    list[list[float | int]]
-        Transposed matrix.
-
-    Raises
-    ------
-    ValueError
-        If ``matrix`` is empty or rows have differing lengths.
-
-    Examples
-    --------
-    >>> mat = [[1, 2, 3], [4, 5, 6]]
-    >>> transpose(mat)
-    [[1, 4], [2, 5], [3, 6]]
-    """
-    if not matrix:
-        raise ValueError("Matrix must not be empty")
-    row_length = len(matrix[0])
-    if any(len(row) != row_length for row in matrix):
-        raise ValueError("All rows must have the same number of columns")
-    return [list(col) for col in zip(*matrix)]
-
-
-if __name__ == "__main__":
-    matrix_a = [
-        [3, 4, -1, 4],
-        [-2, 2, 5, 1],
-    ]
-    matrix_b = [
-        [1, 3, -2],
-        [2, 5, 1],
-        [-1, 4, -4],
-        [2, 3, 6],
-    ]
-    matrix = [
-        [1, 2, 3],
-        [4, 5, 6],
-    ]
-
-    print("Transposed Matrix:\n", transpose(matrix))
-    print("\nMatrix multiplication result:\n")
-    matrix_c = matmul(matrix_a, matrix_b)
-    for row in matrix_c:
-        print(row)
-    print("\nRotation matrix 90°:\n", rot_2D(math.pi/2))
-

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())

matrixmania/compute.py

@@ -0,0 +1,176 @@
+
+"""Matrixfunktionen für MatrixMania."""
+
+import math
+
+from tabulate import tabulate
+
+
+def rot_2D(theta: float) -> list[list[float]]:
+    """Berechnet eine 2D-Rotationsmatrix."""
+    c = math.cos(theta)
+    s = math.sin(theta)
+
+    return [[c, -s], [s, c]]
+
+
+def rot_3D(angle: float, axis: str) -> list[list[float]]:
+    """Berechnet eine 3D-Rotationsmatrix um die x-, y- oder z-Achse."""
+    c = math.cos(angle)
+    s = math.sin(angle)
+
+    if axis == "x":
+        return [
+            [1.0, 0.0, 0.0],
+            [0.0, c, -s],
+            [0.0, s, c],
+        ]
+
+    if axis == "y":
+        return [
+            [c, 0.0, s],
+            [0.0, 1.0, 0.0],
+            [-s, 0.0, c],
+        ]
+
+    if axis == "z":
+        return [
+            [c, -s, 0.0],
+            [s, c, 0.0],
+            [0.0, 0.0, 1.0],
+        ]
+
+    raise ValueError("axis muss 'x', 'y' oder 'z' sein")
+
+
+def project_ortho(
+    point: tuple[float, float, float],
+    scale: float = 1,
+) -> tuple[float, float]:
+    """Projiziert einen 3D-Punkt auf die x-y-Ebene."""
+    x, y, z = point
+
+    return (x * scale, y * scale)
+
+
+# ============================================================
+# NEU: HAUSAUFGABE – PERSPEKTIVISCHE PROJEKTION
+# ============================================================
+
+def project_perspective(
+    point: tuple[float, float, float],
+    focal_length: float = 1,
+    camera_distance: float = 4.0 ,
+    scale: float = 1,
+) -> tuple[float, float]:
+    """Projiziert einen 3D-Punkt perspektivisch auf die 2D-Ebene."""
+
+    x, y, z = point  # NEU: 3D-Koordinaten auslesen
+
+    distance = z + camera_distance  # NEU: Entfernung berechnen
+
+    if distance == 0:  # NEU: Division durch null verhindern
+        raise ValueError("Der Punkt liegt auf der Kameraebene.")
+
+    x_new = (x * focal_length / distance) * scale  # NEU: x projizieren
+    y_new = (y * focal_length / distance) * scale  # NEU: y projizieren
+
+    return (x_new, y_new)  # NEU: 2D-Koordinaten zurückgeben
+
+# ============================================================
+# ENDE DER NEUEN HAUSAUFGABE
+# ============================================================
+
+
+def matmul(
+    a: list[list[float | int]],
+    b: list[list[float | int]],
+) -> list[list[float]]:
+    """Multipliziert zwei Matrizen."""
+    n_cols_a = len(a[0]) if a else 0
+    n_rows_b = len(b)
+
+    if n_cols_a != n_rows_b:
+        raise ValueError(
+            f"inner dimensions must match: "
+            f"{n_cols_a} (a columns) != {n_rows_b} (b rows)"
+        )
+
+    m = len(a)
+    p = len(b[0]) if b else 0
+
+    result: list[list[float]] = [
+        [0.0 for _ in range(p)] for _ in range(m)
+    ]
+
+    for i in range(m):
+        for k in range(n_cols_a):
+            a_val = a[i][k]
+            for j in range(p):
+                result[i][j] += a_val * b[k][j]
+
+    return result
+
+
+def transpose(
+    matrix: list[list[float | int]],
+) -> list[list[float | int]]:
+    """Transponiert eine Matrix."""
+    if not matrix:
+        raise ValueError("Matrix must not be empty")
+
+    row_length = len(matrix[0])
+
+    if any(len(row) != row_length for row in matrix):
+        raise ValueError(
+            "All rows must have the same number of columns"
+        )
+
+    return [list(col) for col in zip(*matrix)]
+
+
+if __name__ == "__main__":
+    matrix_a = [
+        [3, 4, -1, 4],
+        [-2, 2, 5, 1],
+    ]
+
+    matrix_b = [
+        [1, 3, -2],
+        [2, 5, 1],
+        [-1, 4, -4],
+        [2, 3, 6],
+    ]
+
+    matrix = [
+        [1, 2, 3],
+        [4, 5, 6],
+    ]
+
+    print("Transposed Matrix:\n", transpose(matrix))
+
+    print("\nMatrix multiplication result:\n")
+    matrix_c = matmul(matrix_a, matrix_b)
+
+    for row in matrix_c:
+        print(row)
+
+    print("\nRotation matrix 90°:\n", rot_2D(math.pi / 2))
+    print(tabulate(rot_2D(1.0)))
+
+    print("\n3D-Rotation um die X-Achse:")
+    print(tabulate(rot_3D(math.pi / 2, "x")))
+
+    print("\n3D-Rotation um die Y-Achse:")
+    print(tabulate(rot_3D(math.pi / 2, "y")))
+
+    print("\n3D-Rotation um die Z-Achse:")
+    print(tabulate(rot_3D(math.pi / 2, "z")))
+
+    # NEU: HAUSAUFGABE – Perspektivische Projektion testen
+    print("\nPerspektivische Projektion:")
+    print(project_perspective((1.0, 2.0, 3.0)))
+
+    # NEU: HAUSAUFGABE – Perspektivische Projektion mit Skalierung testen
+    print("\nPerspektivische Projektion mit Skalierung 100:")
+    print(project_perspective((1.0, 2.0, 3.0), scale=100))

pyproject.toml

@@ -0,0 +1,6 @@
+[project]
+name = "matrixmania"
+version = "0.1.0"
+dependencies = ["tabulate", "ruff"]
+[project.optional-dependencies]
+dev = ["pytest", "ruff", "pytest-cov"]

test/test_matrixmania/test_projection.py

@@ -0,0 +1,52 @@
+
+import pytest
+
+from matrixmania.compute import project_ortho, project_perspective
+
+
+def test_project_ortho_default():
+    # Arrange
+    point = (1.0, 2.0, 3.0)
+    expected = (1.0, 2.0)
+
+    # Act
+    result = project_ortho(point)
+
+    # Assert
+    assert result == expected
+
+
+def test_project_ortho_scale_100():
+    # Arrange
+    point = (1.0, 2.0, 3.0)
+    expected = (100.0, 200.0)
+
+    # Act
+    result = project_ortho(point, scale=100)
+
+    # Assert
+    assert result == expected
+
+
+def test_project_perspective_default():
+    # Arrange
+    point = (1.0, 2.0, 3.0)
+    expected = (1.0 / 7.0, 2.0 / 7.0)
+
+    # Act
+    result = project_perspective(point)
+
+    # Assert
+    assert result == pytest.approx(expected)
+
+
+def test_project_perspective_focal_length_2_scale_100():
+    # Arrange
+    point = (1.0, 2.0, 3.0)
+    expected = ((1.0 * 2.0 / 7.0) * 100, (2.0 * 2.0 / 7.0) * 100)
+
+    # Act
+    result = project_perspective(point, focal_length=2.0, scale=100)
+
+    # Assert
+    assert result == pytest.approx(expected)

test/test_matrixmania/test_rot.py

@@ -0,0 +1,36 @@
+
+import math
+
+import pytest
+
+from matrixmania.compute import rot_2D, rot_3D
+
+
+def test_rot_2D():
+    # Arrange
+    angle = math.pi / 2
+    expected = [[0.0, -1.0], [1.0, 0.0]]
+
+    # Act
+    result = rot_2D(angle)
+
+    # Assert
+    for row, expected_row in zip(result, expected):
+        assert row == pytest.approx(expected_row)
+
+
+def test_rot_3D():
+    # Arrange
+    angle = math.pi / 2
+    expected = [
+        [0.0, -1.0, 0.0],
+        [1.0, 0.0, 0.0],
+        [0.0, 0.0, 1.0],
+    ]
+
+    # Act
+    result = rot_3D(angle, "z")
+
+    # Assert
+    for row, expected_row in zip(result, expected):
+        assert row == pytest.approx(expected_row)