Convert each point to polar angle via atan2(dy, dx) relative to viewpoint. Points coincident with viewpoint are always visible — count them separately and remove.

Duplicate sorted angle array with +2π for circular wrap-around. Sliding window finds max count within the field-of-view angle. Each point has a single valid angle range.

Use small epsilon for angle boundary checks (point exactly at angle boundary is visible, use ≤). For large n, O(n log n) from sorting dominates — sliding window is O(n).