A.3.3.CC:5.3 - A body must fit, not just its reference point

A rigid body occupies the one-dimensional interval [x-r, x+r]; x is its centre and r its half-length. It must lie wholly inside [0,L]. Contact with the endpoints is permitted in this model.

Containment gives x-r >= 0 and x+r <= L, hence r <= x <= L-r. For L = 3 and r = 1, the admissible centres are [1,2]. Centre x = 0.5 lies inside the container but places part of the body outside it, so a point-only test gives the wrong fitting answer.

If clearance is required, include the clearance in the inequalities. If L = 1.5 while r remains 1, the interval for x is empty. That conditional impossibility directs the next decision to the body size, container size or permitted deformation. It was obtained by connecting a physical extent, a mathematical inequality and a calculation; no motion simulation was needed.