orthogonale Projektion

src/matrixmania/compute.py

@@ -220,6 +220,40 @@ def rot_3D(angle: float, axis: str) -> list[list[float]]:
     return [[c, -s, 0.0], [s, c, 0.0], [0.0, 0.0, 1.0]]
 
 
+def project_ortho(
+    point: tuple[float, float, float], scale: float = 1
+) -> tuple[float, float]:
+    """Orthogonally projects a 3D point onto the 2D plane.
+
+    The viewer looks head‑on onto the plane spanned by the x‑ and
+    y‑axis, so the z‑coordinate (the distance of the point) is simply
+    ignored. The remaining coordinates are multiplied with ``scale``,
+    e.g. to map model coordinates onto screen pixels::
+
+        project_ortho((0.5, -0.5, 10), scale=200)  # -> (100, -100)
+
+    Parameters
+    ----------
+    point : tuple[float, float, float]
+        3D point ``(x, y, z)`` in model coordinates.
+    scale : float, optional
+        Factor the projected x‑ and y‑coordinates are multiplied with
+        (default ``1``, i.e. no scaling).
+
+    Returns
+    -------
+    tuple[float, float]
+        2D point ``(x * scale, y * scale)`` without the z‑coordinate.
+
+    Notes
+    -----
+    * Orthogonal projection means there is no perspective foreshortening:
+      distant points have the same size as nearby ones.
+    """
+    x, y, _z = point
+    return (x * scale, y * scale)
+
+
 if __name__ == "__main__":
     # Beispiel 1: 2x3 × 3x2
     a = [[1, 2, 3], [4, 5, 6]]
@@ -265,6 +299,10 @@ if __name__ == "__main__":
     for row in matmul(r3, [[1.0], [0.0], [0.0]]):
         print([round(v, 10) for v in row])
 
+    # Beispiel 6: Orthogonale Projektion eines 3D-Punktes auf 2D
+    print("\nBeispiel 6 Projektion (0.5, -0.5, 10) mit scale=200:")
+    print(project_ortho((0.5, -0.5, 10), scale=200))
+
 # Docstring und Type Hints sind vorhanden und stimmen mit dem Code überein.
 # Fehlerfälle werden behandelt
 # Namen sind Aussagekräftig