A circle that resembles most selected points can still exclude another point. Containment is an explicit geometric requirement.
Retain the containment requirement
A minimum enclosing circle contains the selected point set with the smallest circle area. A circle chosen by a separate fitting criterion need not enforce the same containment constraint. The point selection and requested objective therefore belong beside the center and radius before their meaning is compared. Primary reference: OpenCV minimum enclosing circle.
For an original worksheet, keep each selected point and its distance from the proposed center. State whether every distance must be at most the radius. Do not describe a visually plausible circle as an enclosure merely because most displayed boundary points lie near it.
Check fictional points explicitly
Use the invented points (−1,0), (1,0), (0,−1), (0,1) and (3,0). A candidate circle centered at (0,0) with radius 1 passes through four points but excludes (3,0). This is an illustrative candidate, not a computed least-squares solution.
The minimum enclosing circle is centered at (1,0) with radius 2. The extreme horizontal points are four units apart, requiring radius at least 2; that circle also contains the remaining points, whose distances are zero or √2. The diameter bound establishes minimality for this constructed set.
Review selection and objective
Prepare an original distance table for every retained point, including the extreme observation. If a point is excluded before fitting, preserve that selection explicitly. A different objective or point set may produce a useful result, but its center and radius should not inherit an untested all-points containment claim.
No example here supplies an HM inspection radius or physical roundness acceptance. It separates the objective of enclosing selected coordinates from another fitting task. The reader decision is whether containment was required and actually checked, rather than inferred from the appearance of a circle overlay.
Customer Questions
Does the radius-one candidate contain every fictional point?
No. It excludes the point at (3,0).
What is the enclosing radius?
Two coordinate units.
Is the candidate a claimed least-squares output?
No. It is an explicitly illustrative candidate.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
Discuss Your Machine Requirement
Share your product, container, required output and the evidence needed for your technical review.
Request a Technical Review