VectorPaint fictional region colouring: check colours through shared-edge adjacency

English translation of the Chinese original, translated on 2026-11-05. Original publication dates, attribution, code and version notes are retained.

When colours distinguish neighbouring regions, adjacency must be defined first. Invent five regions and count only a shared boundary segment as adjacency; point contact does not count. This is neither a real map nor an automatic map-colouring tool, and one example proves no general colouring theorem.

Draw a four-region baseline and define adjacency

On a 1000 by 800 pixel canvas, divide a central rectangle once horizontally and vertically into A upper left, B upper right, C lower left and D lower right. Retain the central four-corner meeting as a reference. State that adjacency requires a positive-length common edge, excluding point contact and the outer blank area from this exercise. Inspect equal-colour geometry for full coverage without overlaps or gaps. Use no real place names or scale implying a factual map. Fix identities before shape changes so later lists remain traceable.

Separate four shared edges from two diagonal contacts

Externally list adjacent pairs A/B, A/C, B/D and C/D. A/D and B/C touch only at the centre and are nonadjacent under this rule; verify each against the drawing rather than treating nearby colours as conflicts. Do not silently add the exterior as another region. This list describes current geometry and needs rechecking after boundary edits. Trace edges without labels, then restore identities to catch reversed sides. No built-in adjacency analysis is required; the list must match actual common edges.

Colour the four regions with two colours and audit edges

Give A/D colour one and B/C colour two, without gradients. Same-colour diagonal point contacts are allowed, while all four shared edges need different colours on their sides. Retain region/colour text and consider patterns or IDs for monochrome rather than hue alone. If strokes form a central black mass, reduce weight instead of moving regions apart and creating gaps. This establishes a solution for these four regions only, not that all maps need only two colours or that an unexplained theorem replaces edge checks.

Add an enclave and update adjacency

Place closed E wholly inside A with visible clearance from outer boundaries. E shares its entire perimeter with A, adding E/A adjacency but no edges with B/C/D. Colour two distinguishes it from A; proximity to B does not create adjacency. This layered drawing assigns E’s interior to E rather than A, as the legend should state. Area computation or actual topological files require suitable separate data; overlays alone are not geographic analysis. Update the five-region list before checking all boundaries.

Move the enclave to test changed boundaries

In a copy, extend E to the A/B boundary and distinguish point contact from a shared segment with B. A positive-length E/B boundary adds adjacency, so their original common colour two conflicts and needs another colour or recolouring. Do not add adjacency from impression alone or retain an obsolete list. Check that A remains continuous as intended rather than silently splitting it. Preserve the original and distinguish geometry changes from colour fixes so the conflict has an accountable cause.

Audit colours through region IDs, not overall appearance

Read every region’s neighbours and check the list in both directions: A naming E requires E naming A. Inspect both sides of every shared edge, including the enclave perimeter. Hide colour and identify ownership from labels and boundaries, then restore it to find conflicts. In monochrome, keep patterns inside regions and clear of boundaries, with internal labels or short leaders. Establish the rule before aesthetics or higher contrast; every palette change needs the shared-edge check again.

Retain the rule and fictional scope in output

Save four-region baseline, final five-region map and test copies. Inspect centre contact, E’s perimeter and narrow gaps after export. Retain shared-edge-only adjacency and fictional scope in title/legend instead of cropping it into an apparently factual administrative map. Test transparency against another background; white backing objects remain until handled. Name five-region exercise, revision and size and reopen it to exclude extended-E tests. A classroom version may include the list and a separate answer image; it offers no clickable regions, automatic checking or real boundary dataset.

Determine actual shared edges before fixing colour conflicts

If A/D sharing a colour is challenged, return to the point-contact rule rather than changing the task to make every touch different. For E/B, inspect actual contact length and source paths, not heavy strokes alone. A missing region calls for stacking/identity checks, not duplicate fills to restore a count. Resolve geometry identities before recolouring when drawing and list disagree. Recheck five regions, adjacent pairs, colour differences and the stated rule. Explain why particular pairs may or may not share colour instead of merely filling five shapes randomly.