VectorPaint sixfold rosettes: audit rotational symmetry around one centre

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

Rotational symmetry requires consistent source, centre and angle, not six roughly circular petals. Use one original petal unit to build a sixfold decorative window, then compare a version changing just one petal. This static vector task assumes no kaleidoscope tool, automatic radial duplication or architectural-window fabrication feature.

Define a common centre and six-sector references

Create a 900 by 900 pixel canvas with a central pivot and circular frame reference, leaving title/margins. Six equal sectors use 360/6=60 degrees; record the calculation before layout. References radiate from one centre, not individual petal centres. Manually drawn references remain artwork to hide as appropriate; check native grids/guides in output. This is original flat decoration without claims of unverified manufacturing-angle precision. Save centre and bounds before a later frame can accidentally shift the axis.

Establish one source motif inside its sector

Draw one closed petal within references 60 degrees apart, near but not crowding the centre and inside the circular frame. Use few clear nodes; the motif itself need not be mirror-symmetric. Inspect tips and concavities in flat colour, avoiding fragile narrow ends. An optional secondary marking must belong to the same source group so copies cannot omit it. Save this master before building six instances; independently reshaping them into six different contours would no longer be strict repetition.

Rotate each copy sixty degrees around the same centre

Copy and rotate in 60-degree increments to positions 0,60,120,180,240,300 degrees from the start. Verify the actual pivot: a selection bounding-box centre is not automatically the rosette centre. Keep circles concentric with the rosette as positioning references: first record the source inner and outer endpoints’ distances from the centre. After copying and rotating, reposition the corresponding endpoint on the next 60-degree reference direction and compare radial distance against the concentric circles, then check the other endpoint and neighbouring gap. Use any precise control only within its actual scope; explicitly label manual approximation instead of inventing a hidden pivot command. Inspect inner/outer radii and neighbour spacing after each addition. Count six including the original; a seventh at 360 would duplicate it. Keep source groups independently selectable.

Inspect neighbour rhythm and central clearance separately

Inspect all six gaps clockwise, including last-to-first rather than only the first five. If the centre crowds, revise source inner ends consistently in all instances instead of moving one petal. Define intentional contact versus clearance and apply the same rule to each, not calling an accidental white seam decoration. Hide the frame to inspect the motif alone; it cannot conceal misalignment to manufacture neatness. Establish geometry in one colour before palette changes, which do not determine sixfold geometric repetition.

Retain full repeats before frame clipping

Add a circular frame through a simple ring or verified mask, recording any tip occlusion. Background-coloured cover shapes only simulate the current backdrop, not real transparent cutouts. Preserve the full six-unit source before clipping so a different frame can return to it. Keep frame and motif coaxial rather than shifting the frame to hide one exposed edge. Window here describes decoration, not designed glass divisions, lead cames, material joints or physical openings. Fabrication requires its own material-appropriate professional workflow.

Change one petal to compare broken symmetry

In a copy, lengthen only petal three’s outer end while leaving five unchanged. Inspect affected gaps and radial extents. This may be deliberate variation but no longer supports an identical-source-shape claim. If strict repetition remains the goal, edit the master and update all six rather than hiding the difference with colour. Compare at equal size and distinguish shape from palette effects. Name the test separately so it cannot replace the final master; identical object names do not automatically restore copied shapes.

Check the count and narrowest gaps in output

Save master unit, six-unit baseline and frame version. Count six in the export, then inspect centre clearance, outer clipping and narrow connections. Simplify through a common source instead of deleting nodes randomly per petal. Test transparent PNG on light/dark backgrounds for solid white fringes; reopen SVG/PDF in the receiving tool without assuming universal mask compatibility. Name sixfold decorative rosette, size and revision and reopen it to exclude reference rays and the petal-three test. Retain editable master and angle explanation for later extensions of the verified structure.

Check pivot and accumulated angles when the circle fails to close

For overlap at closure, check a mistaken seventh unit or confusion between relative rotation and absolute angle. If petals spin individually, inspect actual pivots rather than shrinking the whole pattern to hide eccentricity. One wrong instance points to source/selection or an omitted secondary marking. One-sided frame exposure needs coaxial/source checks before a thicker cover. Recheck six positions, six gaps, centre and export. Explain how the repetition is constructed rather than settling for six roughly circular petals.