VectorPaint split-flow bands: preserve the width relation twelve equals five plus seven

English translation of the Chinese original, translated on 2026-11-06. Original publication dates, attribution, code and version notes are retained.

When band width encodes quantity, one unit must retain one width. Manually draw an invented split of 12 into 5 and 7 with one input, two outputs and a central node. This represents no real energy, money or population and calculates no conservation automatically; check both numbers and widths yourself.

Define the node and one common quantity unit

Create a 1200 by 800 pixel canvas with input 12 from left into a central node, output 5 upper right and 7 lower right. Record 12=5+7 in one fictional unit, not mixed counts/percentages. The node is a split location, not a third output or extra consumption. Plan with thin centre references and separate output-label space. Define direction/quantity encoding; importance does not justify extra width. Fix the list before graphics instead of inventing numbers for decorative bands.

Establish the unit width on straight sections

Use 10 pixels per unit: input 120, upper output 50, lower output 70. Measure perpendicular to travel, not a diagonal band’s vertical bounding-box height. Prototype three horizontal rectangles and verify 120=50+70. Their lengths may differ for layout and do not encode quantity; state that in the legend. Retain these straight-width references through later bends rather than judging the 5/7 difference by eye. Pixel widths are teaching encodings, not pipe diameters or capacities.

Separate band widths from the node shape

Join straight bands to the central node through closed paths, checking for necking or abrupt widening at entry/exit. For manually adjusted curves, inspect references without claiming exact constant-width offsets. The node may be larger to accommodate joins, but its shape/area does not encode a quantity comparable to band width. Start with opaque flat colours to detect seams/patches. Ordinary paths do not understand flow or update bent boundaries after numerical edits.

Audit arrows and labels independently

Point input toward the node and both outputs away; a reversed arrow after a bend changes interpretation. Put restrained arrows on straight sections and do not let oversized heads be mistaken for encoded width. Label input 12, upper 5 and lower 7 with fictional scope. Colour may identify routes, but words remain for monochrome. Hide numbers to read directions, then restore and compare each label with its straight width, excluding a 5 on the 7 band. Names identify no real organisations or populations and support no real-world conclusion.

Keep input and unit fixed when changing allocation

In a copy, change outputs to 4 and 8 with input 12. Verify their sum, then use 40/80-pixel widths while input stays 120. Update bends and labels, not only straight ends. The node is not a discrepancy reservoir; unequal totals require source review, not an unnamed patch band. Keep canvas and scale fixed so differences reflect allocation rather than zoom. Name 4/8 and 5/7 versions separately and audit every object on restoration; copies do not follow a data list automatically.

Keep scope and the conservation assumption visible

Assume all input is allocated to two outputs, with no loss, storage or additional exit; that is why 5+7 corresponds to 12. Real cases containing those factors need a new relationship rather than hidden unknowns in an attractive image. Width does not establish causes or an app-generated analysis. State that straight width encodes quantity while curve length/node area do not. Even three bands need explicit rules before expansion. Real data requires provenance, time scope and units rather than mechanical number substitution for publication.

Inspect straight widths before bends in output

Save data, straight sources and closed curves. In the actual-size export, compare 120/50/70 first, then inspect bends/seams/occlusion. Enlarge output or reduce decoration rather than independently scaling a route. Test node joins on changed backgrounds; white covers remain opaque objects. Name fictional 12-to-5/7, dimensions and revision and exclude the 4/8 test. Explain widths and nonencoding node semantics for editable delivery so a route edit prompts sum review. A static image contains no automatic data linkage.

Check units and measurement direction for wrong widths

If 5 appears thicker than 7, compare equivalent straight sections rather than diagonal bounds or arrows. Recalculate numbers before widening input to fit an error. Repair node seams through paths/stacking, not blurred gradients. For reversed labels, audit arrows and identity rather than swapping numbers merely to preserve a sum. Recheck 12=5+7, ten pixels per unit, direction and actual output so width conveys quantity instead of merely decorating numbered curves.