import math
import pytest

from matrixmania import project_perspective


def approx_equal(a: float, b: float, rel_tol: float = 1e-9) -> bool:
    """Utility to compare two floats with a relative tolerance."""
    return math.isclose(a, b, rel_tol=rel_tol)


@pytest.mark.parametrize(
    "point,focal_length,scale,expected",
    [
        # Case 1 – no scaling, unit focal length
        (
            (1.0, 2.0, 3.0),
            1.0,  # focal_length
            1.0,  # scale
            (
                1.0 / (4.0 + 3.0),  # x projected
                2.0 / (4.0 + 3.0),  # y projected
            ),
        ),
        # Case 2 – scale 100, focal length 2
        (
            (1.0, 2.0, 3.0),
            2.0,  # focal_length
            100.0,  # scale
            (
                2.0 * 100.0 / (4.0 + 3.0),  # x projected
                2.0 * 100.0 * 2.0 / (4.0 + 3.0),  # y projected
            ),
        ),
    ],
)
def test_project_perspective(point, focal_length, scale, expected):
    """Test that project_perspective returns the correct 2‑D projection."""
    # Call the function under test
    result = project_perspective(point, focal_length=focal_length, scale=scale)

    # Basic sanity checks
    assert isinstance(result, tuple), "Result should be a tuple"
    assert len(result) == 2, "Result should contain two coordinates"

    # Confirm values are close to expected (within tiny tolerance)
    assert approx_equal(result[0], expected[0]), f"X coordinate mismatch: {result[0]} != {expected[0]}"
    assert approx_equal(result[1], expected[1]), f"Y coordinate mismatch: {result[1]} != {expected[1]}"