Compute point-to-segment minimum distance

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.