How to Record a Remembered Hexagonal Tile Puzzle with Smooth Curve Joins

Record the scene in three parts: where the hexagonal tiles sit, how they rotate, and how curves continue across their shared edges. Keep unknown details open rather than completing the puzzle.

The task is to preserve a particular visual relationship: separate, rotatable hexagonal tiles carry curves that join across tile boundaries without sharp angles. A useful record must show both the divisions between tiles and the continuity of the curves. A smooth line alone loses the puzzle’s structure; tile outlines alone lose what the rotations accomplish.

The method below combines a small layout sketch, rotation notes and enlarged views of remembered joins. Its numbering conventions are proposed drawing aids. The linked references explain geometry and curve construction; they do not document this remembered scene.

Establish the remembered layout before drawing the curves

Begin with the portion of the arrangement you can actually recall. Draw only known tile outlines and known shared edges. If the full perimeter or tile count is unclear, leave the sketch open at those places and add a short note such as “arrangement continues; extent unspecified.” A tidy outer boundary would otherwise imply information the record does not contain.

Preserve the viewpoint as well as the shape. If you remember looking obliquely across the tiles, keep that view in the main sketch. You may add a simplified overhead diagram for tracking rotations, but label it as a schematic. Do not let a convenient diagram replace the remembered appearance.

Regular hexagonal grids commonly use either a flat side or a vertex at the top. Red Blob Games distinguishes these orientations in its explanation of hexagon geometry. Use whichever matches the recollection; if neither is clear, mark the orientation as unspecified. Hexagonal Grids (https://www.redblobgames.com/grids/hexagons/)

Give each recorded tile a simple identifier, such as A or B. These letters identify pieces in your notes; they do not imply markings on the original tiles. Keep an identifier with the same tile throughout every drawing so that a changed orientation cannot be mistaken for a different piece.

Separate the information into three kinds:

• Remembered geometry: tile shapes, visible boundaries and which tiles touch.

• Remembered appearance: curves, colors, widths and surface details that can be described.

• Recording conventions: letters, arrows, enlarged details and other additions used to explain the sketch.

This distinction is especially useful for material relations. If you remember whether a curve was a surface marking or a groove, describe that relationship. If you remember only a curve associated with a tile, retain that wording. Linework in a drawing need not become a claim about how the tile was made.

Record rotations against a fixed reference

Rotation needs a reference that stays still. Put a small “page top” mark outside the layout, then describe clockwise or counterclockwise movement as viewed in that drawing. If you also make an overhead schematic, state that its rotation arrows refer to the schematic’s viewpoint.

For a regular hexagon, a 60-degree rotation advances the outline through one symmetry step. Red Blob Games explains hexagonal rotations in these one-sixth-turn increments. That makes 60 degrees a useful notation when the remembered movement clearly follows such steps; it does not establish that this particular puzzle used stops or fixed increments. Hexagonal Grids: Rotation (https://www.redblobgames.com/grids/hexagons/#rotation)

Record only the precision available. “Clockwise; amount unclear” preserves more information than an unsupported angle. Likewise, do not add a clicking mechanism, a central pivot or a hand turning the piece unless it belongs to the recollection.

For a more detailed schematic, number the six stationary edge positions around a tile’s location from 0 through 5, clockwise from a clearly marked reference edge. Keep these position numbers fixed on the page while the tile turns. A remembered feature can then be tracked from one position to another without inventing its internal curve pattern.

As an illustrative notation example, a one-step clockwise turn carries a feature at position 5 to position 0. Two clockwise steps carry it to position 1. These numbers demonstrate the recording convention only; they specify neither a tile design nor an observed movement in the scene.

Distinguish a tile rotating in place from a tile moving to another location. If its center remains fixed, preserve that center in successive sketches. If displacement is recalled, record it separately. If only the ability to rotate is remembered, describe the tiles as rotatable without adding a sequence of turns.

Show why the curves join without a sharp angle

At each remembered connection, examine two separate questions: do the curve ends meet at the same place, and do they continue through that meeting in the same direction? Those are different geometric conditions.

Autodesk’s curve-continuity documentation calls a shared endpoint positional continuity, or G0. Tangent continuity, or G1, also matches the curve directions at that endpoint. Its next level, G2, additionally matches curvature. For this recording task, the first two distinctions help explain a join without a corner; the phrase “without sharp angles” alone does not establish matching curvature. Continuity G0 G1 G2 G3 (https://help.autodesk.com/cloudhelp/2026/ENU/Alias-Video-Tutorials/files/essential-concepts/continuity-g0-g1-g2-g3.html)

Make an enlarged detail of a remembered shared edge. Include enough of both neighboring tiles to show the curve approaching from one side and leaving on the other. Keep the boundary visible, with a label if necessary, so the detail records a curve continuing across two pieces.

Use this three-part check:

• Position: mark where the curve reaches the shared edge. Do not assume the crossing is at the midpoint.

• Direction: compare the curve immediately before and after the crossing. Look for a corner, offset or reversal introduced by the sketch.

• Bend: preserve the remembered tightness or openness of the curve on either side, without imposing an identical arc on both tiles.

A lightly drawn tangent guide can help explain direction. Place it through the crossing to indicate the local direction of travel, and label it as a construction aid. It should clarify the remembered join rather than dictate an otherwise unknown curve.

If the crossing position is uncertain but the absence of a corner is clear, write both facts: “crossing location unspecified; continuation remembered as smooth.” That is enough to preserve the essential relation. There is no need to choose an exact point merely to finish the drawing.

For a digital drawing, Bézier curves offer a way to control the approach and departure. The W3C path specification defines cubic Bézier segments using endpoints and two control points; its smooth continuation command reflects the preceding control point across the join. This supplies a concrete construction example for a smooth connection. Treat any such construction as an approximation unless the curve’s exact geometry is known. Paths — SVG 1.1, cubic Bézier curve commands (https://www.w3.org/TR/SVG11/paths.html#PathDataCubicBezierCommands)

Preserve every remembered change in order

When actual turns are recalled, make a separate state sketch for each distinguishable stage. Reuse the tile identifiers, viewpoint and stationary reference marks. Show the starting arrangement, each remembered change and the last remembered arrangement, including any intermediate misalignment that is part of the sequence.

Beside each transition, record the moving tile, the direction and amount of rotation if known, and the resulting change at the relevant edges. Keep the distinction between observation and inference explicit: seeing a curve aligned afterward does not by itself reveal how far the tile turned.

If the beginning and ending states are remembered but the intervening movement is missing, place “intermediate rotation unspecified” between them. Do not insert the shortest possible turn as though it were recalled. Similarly, when several pieces change but their order is unclear, group those changes under an order-unspecified note.

Keep internal tile geometry consistent across states. When a curve is remembered as belonging to a rigid tile, its drawn shape should rotate with that tile. Redrawing it differently in each panel could accidentally depict the curve changing shape. Where the internal shape itself is uncertain, label that uncertainty rather than adjusting the pattern to make neighboring lines connect.

Do not extend a local connection into an invented solution. Several smooth joins do not supply the remainder of a route, a closed loop or a completed board. Stop a traced curve at the last remembered portion and state that its continuation is unspecified.

Check the record without completing the puzzle

Review the manuscript and sketches together. First compare tile locations and identifiers across states. Next inspect each recorded rotation against the fixed reference. Finally, follow each remembered curve across its shared edges, checking that the drawing preserves both the crossing position and the absence of a corner where those details are known.

Resolve a drawing problem according to what is actually recalled:

• If two curve ends miss but their meeting point is known, correct the endpoint placement.

• If they meet with an unintended corner and their directions are known, correct the local approach and departure.

• If the required shape is unknown, retain the uncertainty instead of inventing a connecting segment.

• If a smooth join is remembered but cannot be drawn precisely, preserve it in an adjacent written note.

The finished record should let a reader distinguish the tile boundaries, the recorded rotations and the curves continuing across them. It is complete when it preserves every available spatial relationship and change, with gaps identified. An unfinished arrangement can be a faithful record; it does not need a solved puzzle to make the remembered geometry clear.

Sources

• Hexagonal Grids — Red Blob Games (https://www.redblobgames.com/grids/hexagons/)

• Continuity G0 G1 G2 G3 — Autodesk Alias (https://help.autodesk.com/cloudhelp/2026/ENU/Alias-Video-Tutorials/files/essential-concepts/continuity-g0-g1-g2-g3.html)

• Paths — SVG 1.1 (Second Edition) — W3C (https://www.w3.org/TR/SVG11/paths.html)