What a 2×2 does to a court
A pickleball court, 13.41 by 6.10 m, pushed through a 2×2 matrix you set with four sliders. The readout reads the matrix live: its columns are where the two axes land, its determinant is the area scale, its SVD is rotate, stretch, rotate.
Try this
Try every preset, then watch the one number that never changes: the angle between the two sidelines stays at 0°, which is why no 2×2 can map a court seen in perspective.
Where this lab comes from
Rotate, Scale, Shear: Images as 2×2 MatricesLesson 1 of Image Alignment. A 2×2 matrix is where it sends the two axes; its determinant is how much it scales area and its SVD is rotate, stretch, rotate. The one thing it cannot do is make parallel lines meet. On a pickleball court, the sidelines are 20.35° apart in the photograph, so the best 2×2 misses every corner by 60 px.
More in cameras and geometry
- Focus, aperture and depth of field — Move the subject and watch the focus plane and the blur follow.
- Four ways a fisheye maps angle to radius — Plot r(θ) for the classical designs against a fitted curve.
- The scene, and what the camera sees — Orbit a 3-D scene on the left; the pinhole view updates on the right.