Merge collinear overlapping 2D segments

You are given a collection of 2D line segments. Each segment may be represented either as: - two endpoints `(x1, y1)` and `(x2, y2)`, or - a polyline with multiple points, where **all points are guaranteed to be collinear** (so the polyline still lies on a single infinite line). Two segments are mergeable if: 1. They lie on the **same infinite line** (collinear), and 2. Their projections on that line **overlap or touch** (i.e., they intersect or share an endpoint). ## Task Merge all mergeable segments and output the resulting set of **maximal** segments (no two output segments should be further mergeable). ## Notes / edge cases - Handle **vertical lines** correctly (slope is infinite). - Avoid floating-point precision issues when grouping by line if possible. - Segments may be given with endpoints in any order. ## Input/Output - Input: list of segments/polylines with integer coordinates. - Output: list of merged segments, each as two endpoints `(xa, ya)` and `(xb, yb)`. ## Constraints - Up to ~10^5 segments. - Coordinates fit in 32-bit signed integers.