Compute point-to-segment minimum distance

Q: Compute point-to-segment minimum distance

This question evaluates understanding of computational geometry and numerical robustness, testing the ability to compute Euclidean distances between a point and a line segment using analytic geometry concepts.

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Question

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Problem

Given a 2D point P(x, y) and a line segment with endpoints A(x1, y1) and B(x2, y2), compute the minimum Euclidean distance from point P to the segment AB.

Input

Real numbers (or integers) representing coordinates of P , A , and B .

Output

A single floating-point number: the minimum distance from P to segment AB .

Notes / Edge cases

If the perpendicular projection of P onto the infinite line AB falls within the segment, the answer is the perpendicular distance.
Otherwise, the answer is min(dist(P, A), dist(P, B)) .
Handle degenerate segments where A == B (distance is dist(P, A) ).

Constraints (assume)

Coordinates are within a reasonable range (e.g., [-1e9, 1e9] ).
Use double precision.