A Shared Polygon Boundary Does Not Choose One AI Region

A polygon relationship and a region label answer different questions

A regional AI input might associate each observation with a region attribute. If its consumer expects one label, the buyer needs to establish which polygon-point relationships count and which single region label reaches that consumer. Membership supplies relationships; assignment supplies the required label.

For a simple closed rectangle, the interior consists of points strictly between its sides. The boundary consists of the sides and corners. The exterior consists of points beyond the rectangle. The closed rectangle includes both its interior and its boundary. Classify a point relative to each polygon separately: a shared edge can be part of both boundaries.

The PostGIS 3.6 geometry definition of ST_Contains requires every point of the candidate geometry to lie in the region and their interiors to intersect. For a single point tested against a polygon, that means the point must lie in the polygon's interior. ST_Covers requires that none of the candidate lie in the region's exterior, so a single point may lie in the interior or on the boundary.

These are two Boolean membership contracts. Neither definition identifies a preferred region when more than one region qualifies.

References: [P1][P2]

REG-62: four exact observations and two closed rectangles

REG-62 is an original fictional example using exact two-dimensional positions in one shared planar coordinate frame. Its coordinates are dimensionless. Both rectangles are valid, simple and closed; the PostGIS references warn that invalid geometries can produce unexpected results. The results below are mathematical derivations from the documented PostGIS 3.6 geometry definitions, with no actual query execution.

Region A spans x from 0 through 10 and y from 0 through 10, including its edges. Region B spans x from 10 through 20 and y from 0 through 10, also including its edges. Their interiors are disjoint. Their shared boundary segment is x = 10 with y from 0 through 10.

The four input records are L = (5,5), C = (10,5), R = (15,5) and O = (25,5). Keep all four records in view while comparing their relationships.

The stipulated AI input requires exactly one region label for each observation in the closed union of A and B. That union is the rectangle spanning x from 0 through 20 and y from 0 through 10, with its edges included. L, C and R belong to it; O lies outside. The required labeled population therefore contains three observations.

References: [P1][P2]

Derive both predicates for every point and region

L = (5,5) lies in A's interior and B's exterior. ST_Contains(A,L) is true and ST_Contains(B,L) is false. ST_Covers(A,L) is true and ST_Covers(B,L) is false. Both predicates give L the single membership A.

C = (10,5) lies on A's right edge and B's left edge. It is in neither polygon's interior. ST_Contains(A,C) and ST_Contains(B,C) are both false. It is also in neither polygon's exterior, so ST_Covers(A,C) and ST_Covers(B,C) are both true. Contains gives C zero memberships; Covers gives it A and B.

R = (15,5) lies in B's interior and A's exterior. ST_Contains(A,R) is false and ST_Contains(B,R) is true. ST_Covers(A,R) is false and ST_Covers(B,R) is true. Both predicates give R the single membership B.

O = (25,5) lies in both exteriors. ST_Contains(A,O), ST_Contains(B,O), ST_Covers(A,O) and ST_Covers(B,O) are all false. Neither predicate gives O a membership.

The difference at C follows from the shared boundary itself. Two valid polygons with disjoint interiors can both cover that point. Boundary-inclusive membership therefore does not establish exclusive ownership.

References: [P1][P2]

Four records, two or four relationships, three required labels

The true Contains relationships are (L,A) and (R,B): two polygon-point pairs involving two distinct observations. C is eligible under the stipulated closed-union requirement, but neither Contains relationship supplies its region label.

The true Covers relationships are (L,A), (C,A), (C,B) and (R,B): four pairs involving three distinct observations. All three eligible observations have membership evidence, but C has two memberships.

The source population still has four point records. A total of four Covers relationships happens to equal that input-record count, even though O contributes no pair and C contributes two. Equal totals would conceal both facts if the buyer counted relationships as observations.

An offered path may package candidate relationships, preserve unmatched observations or return final assignments. The predicate definition alone does not determine that output structure. Nor do these relationship counts demonstrate that a system deleted or duplicated an input record.

For REG-62, the final requirement is three labeled observations with one label each. Contains alone misses the eligible C; Covers alone gives C two candidate regions. Knowing that C belongs somewhere in the closed union establishes eligibility while leaving which region owns its label unresolved.

Ask what reaches the consumer under the agreed policy

Consider a fictional membership offer that names PostGIS 3.6 geometry ST_Covers and supplies the four derived pairs above. It specifies boundary inclusion clearly. If the requested deliverable is candidate memberships, those four pairs answer that request. If the requested deliverable is one region label per eligible observation, the same pairs leave a decision outstanding.

A separate assignment offer needs to identify the application owner's agreed assignment policy and show the final result for C under it. The geometry definitions alone cannot tell the buyer whether that label should be A or B. This article supplies no tie-breaking rule.

Ask the appointed data or software provider to demonstrate the actual receiving path with the same four observation identifiers, the stated region geometries and the agreed eligibility and assignment policies. Does the consumer receive candidate pairs or final labels? What does it receive for C? How is O's outside status accounted for, and can each eligible identifier be reconciled with exactly one final region label?

Keep the region definitions attached to the comparison. A result produced from different boundaries would answer a different membership question. A proposed example also remains proposed until the actual output is available; naming a predicate supplies its documented semantics, not evidence of an installed path's behavior.

This gives the buyer a concrete decision: accept a membership deliverable when relationships are the required input, or require the additional agreed assignment behavior when the consumer needs one label. Resolving that distinction establishes the input contract without asserting any AI performance result.

Scope surrounding equipment cabling through its service owner

If the surrounding storage or compute equipment independently needs physical connections, Leviathan's Structured Cabling & Fiber Installation service is the relevant route for agreed fiber or copper installation, endpoint labels and connection records.

Use the related service and project inquiry to share a nonconfidential outline of the equipment, site, approved endpoints and routes, material responsibilities and required physical handoff. Region-data processing and AI input implementation remain with the appointed data and software providers.

References: [L1]