The Anatomy of a
Jigsaw Puzzle

Act IThe Grid Beneath

You pick up a jigsaw piece and what do you see? A weird little shape — some bumps sticking out, some holes punched in. It looks organic, irregular, designed.

But here's the thing: almost every jigsaw puzzle you've ever touched was born as a grid.

A standard 1000-piece puzzle is typically 38 columns by 27 rows — that's 1,026 pieces, not 1,000, but who's counting. The manufacturer starts with a flat rectangle, lays an invisible grid over it, and every piece gets one cell. The tabs and blanks overflow the cell boundary, sure. But conceptually, each piece lives in exactly one cell of a regular, boring, rectangular grid.

This is the skeleton of every ribbon-cut puzzle in existence. "Ribbon cut" — also called "grid cut" — is the dominant style used by nearly every mass-market manufacturer: Ravensburger, Buffalo Games, Galison. The pieces are arranged in neat rows and columns, and the die that stamps them out follows this grid faithfully.

Some puzzles don't use a grid. Random-cut puzzles have wildly irregular pieces with no underlying rows or columns — gorgeous and challenging, mostly found in artisan wooden puzzles. But the grid is the foundation. It's where we start.

So: jigsaw pieces are monospace? Kind of! Each piece nominally occupies the same rectangular cell. The tabs stick out beyond the boundary and the blanks carve into it, but the footprint — the space each piece "owns" on the board — is uniform. Think of it like characters in a monospace font: the letter "i" and the letter "W" occupy the same cell width, even though their ink spills differently.

But a grid of identical rectangles makes for a terrible puzzle. What makes each piece feel different?

Act IIEdges, Not Pieces

Here is the single most important idea in jigsaw puzzle generation, and it's the thing that makes the whole system click:

You don't design pieces. You design edges.

Every edge in the grid is shared between exactly two pieces. The top edge of piece (2, 3) is the same physical cut as the bottom edge of piece (2, 2). One cut in the cardboard creates both shapes simultaneously.

And here's the contract: if one side of that shared edge gets a tab (a bump sticking out), the other side must get a blank (a matching hole). They're complementary. Lock and key.

This means generating a full puzzle board is a propagation problem. You don't need to think about 1,000 pieces — you think about the ~1,900 shared edges. For each edge, you make two decisions: which direction does the tab point? And what shape does it have?

The algorithm is beautifully simple. Scan left to right, top to bottom. For each piece, you only need to generate two new edges: its right edge and its bottom edge. Why? Because its left edge was already generated as the right edge of its left neighbor. Its top edge was already generated as the bottom edge of the piece above. The edges propagate like dominoes falling across the grid.

Try it: Hit "Step" to advance one piece at a time. Watch how each piece inherits its left and top edges (shown dimly) and only generates its right and bottom edges (shown brightly). The whole board builds itself from the top-left corner outward.

Corner pieces get two flat edges (the border sides), one inherited edge, and one new edge. Edge pieces get one flat side. Interior pieces get two inherited and two new. That's the whole algorithm.

But we glossed over something: the first trick that makes the grid stop looking mechanical. Before generating the tabs, real puzzle generators jiggle the interior corners of the grid — nudging each vertex by a small random offset. This makes every cell a slightly different wonky quadrilateral. The border stays straight, but the interior goes wobbly.

Try it: Drag the jiggle slider from 0% to maximum. Even a small value makes the grid feel dramatically more organic. Hit re-randomize to try a different seed.

Putting it together

Let's combine everything we've built so far: a jiggled grid with procedurally generated tab edges on every shared side. This is what a real puzzle grid looks like before the image is applied.

Try it: This is the full procedural pipeline — jiggled vertices plus Bézier tab edges. Every interior edge has a randomly oriented tab with randomized proportions. Crank the jiggle up to see how the grid goes from mechanical to organic.

Act IIIThe Bézier Tab

Now for the shape of the tab itself. This is where the craft meets the math.

A jigsaw tab has an anatomy. Puzzle enthusiasts use wildly different terminology — tabs, knobs, outies, interjambs — but the shape has four recognizable parts:

The shoulder, where the tab begins to depart from the straight edge. The concavity — a subtle inward dip right at the base, where the piece curves toward its own center before heading outward. The neck, the narrow bridge. And the head, the bulbous round end that locks into the matching socket.

If you squint, it looks like a balloon on a stick. The proportions of these parts — how wide the neck is relative to the head, how round the head is, the depth of the concavity — this is what gives a puzzle its feel. The concavity is subtle but critical: it creates the undercut that locks the head into its socket and prevents pieces from sliding apart. Without it, you'd just have a bump.

Stave Puzzles in Vermont, the most revered hand-cut puzzle maker in the world, describes their signature as "heart-shaped interlocks." Par Puzzles, the legendary mid-century maker, used "earlet" connectors with two-lobed ears. Artifact Puzzles catalogs at least six distinct connector families. The shape of the tab is the personality of the brand.

And mathematically, the tab is defined by cubic Bézier curves.

Try it: Make the neck extremely narrow and the head very wide — see how it becomes a mushroom that would be hard to pull apart? Now make the neck almost as wide as the head — a gentle, easy-to-separate bump. The neck-to-head ratio is a huge part of how "locked" a puzzle feels.

A quick Bézier refresher: a cubic Bézier curve is defined by four points — two endpoints and two control points. The curve starts at the first endpoint, gets "pulled" toward the first control point, then toward the second, and arrives at the second endpoint. By chaining several of these curves together, you draw the entire tab profile.

A typical tab uses 3 chained cubic Bézier curves spanning the entire edge from vertex to vertex — there are no straight segments at all. The first curve covers the left shoulder, curving gently away from the baseline before dipping past it (creating the concavity) and arriving at the neck base. The second curve arcs from the left neck over the round balloon head to the right neck. The third curve mirrors the first: neck base, concavity dip, gentle shoulder curve, and on to the right vertex. The randomization happens in the control points — tab height, neck width, head width, lateral offset, shoulder wave, and small perturbations make every edge unique.

One detail that matters for your game: the blank is not separately designed. It's the absence of the tab. When you trace the outline of piece A, the tab protrudes outward. When you trace piece B (which shares that edge), you follow the exact same curve — but now it's a concavity. Same math, same control points, opposite winding direction. This is why the pieces interlock perfectly: they're carved from the same line.

Act IVFalse Fits

Here's something that might surprise you: most mass-produced puzzles do not guarantee that each piece fits in only one place based on shape alone.

In a standard ribbon-cut puzzle, there are only about six distinct piece types based on their tab/blank pattern: all four tabs, all four blanks, two opposite tabs, two adjacent tabs, three tabs, or one tab. With a thousand pieces sharing just six silhouettes, many pieces can physically interlock in the wrong position. Puzzlers call these "false fits" — and they're one of the most common frustrations with cheaper puzzles.

What prevents false fits? Two things. First, the image. Even if two pieces have the same tab pattern, the printed picture won't line up if they're swapped. Second, Bézier variation. Higher-quality puzzles randomize their control points enough that each tab is subtly different — a piece might almost fit in the wrong spot, but it won't click home cleanly.

For your 3D game, false fits are actually a feature, not a bug. They're part of the challenge. A player places a piece, it seems to fit, but later they realize the image is wrong and need to rearrange. That's authentic puzzling.

Try it: Hit "Randomly Shuffle" — interior pieces swap positions, but they all physically fit because their edges are identical. The image fragments are clearly wrong. Hit "Solve" to restore the correct picture. Toggle "Show Image" off to see shapes only — now there's no way to tell which piece goes where. The image is the real puzzle.

Act VFrom Curve to Mesh

You've got the 2D outline of every piece. Now you need to turn each one into a 3D mesh thick enough to pick up and drag around in your game.

The pipeline has four stages, and they're satisfyingly mechanical.

Stage 1: Flatten the Bézier outline

Your Bézier curves are smooth math, but GPUs eat triangles. Walk along each segment and sample it at regular intervals — maybe 8–12 points per tab curve, fewer for the straight sections. You end up with a polygon of roughly 60–100 vertices that approximates the smooth outline. More vertices means a smoother silhouette but a heavier mesh. For a game rendering dozens of pieces, 80-ish vertices per outline is a solid sweet spot.

Stage 2: Tessellate the top face

You have a 2D polygon. You need to fill it with triangles. This is the classic polygon triangulation problem, and the standard solution is the ear clipping algorithm: find an "ear" (a triangle formed by three consecutive vertices that doesn't cross the polygon boundary), clip it off, repeat. The result: a triangle mesh for the top face.

Stage 3: Extrude

Duplicate the top face, offset it downward by the piece thickness — maybe 3–5mm in world units. Connect corresponding vertices on the top and bottom outlines with quads (or triangle pairs). This creates the side walls. You now have a solid piece: flat top, flat bottom, vertical walls.

Stage 4: Bevel

Real puzzle pieces don't have knife-sharp edges where the top meets the sides. They have a subtle rounding — a fillet. This is what makes them feel good to pick up. Insert a ring of vertices near the top edge, slightly inset and slightly lowered, creating a chamfer strip. Even a single-segment chamfer makes a huge visual difference. The normals on these transitional faces catch light beautifully and sell the "real object" illusion.

Try it: Step through the four stages. In "Outline" you see the 2D Bézier contour. "Tessellate" fills it with triangles. "Extrude" gives it depth. "Bevel" rounds the top edge. Toggle wireframe to see the mesh topology. Drag to orbit and inspect from any angle.

UV Mapping

One critical detail: the top face needs to display the correct fragment of the source image. Since each piece occupies one grid cell, the UV coordinates map directly to that cell's position. A piece at grid position (3, 5) in a 10×8 puzzle maps its UVs to the rectangle from (0.3, 0.625) to (0.4, 0.75) in normalized texture coordinates. The tabs that protrude beyond the cell boundary? Their UVs extend into the neighbor's image region — which is correct, because in the solved puzzle, those tabs sit on top of the neighbor's area.

Act VIThe Craft

Everything we've built so far is the engineering of jigsaw puzzles. But there's a whole world of craft that procedural generators usually miss — and understanding it will make your game feel alive.

Color-line cutting

Color-line cutting is the technique that separates a good puzzle from a great one. Stave Puzzles artisans — who hand-cut every piece with a scroll saw, no computers, no lasers — obsess over cutting along the boundaries in the image. If the painting shows a red barn against a blue sky, the cut follows the roofline exactly. The piece boundary reinforces the image content instead of arbitrarily slicing through it.

One Stave artisan described how elements like a ceramic pot or a bowl of fruit are "begging to be color-line cut." Another said she'd "cut the water in her curlicue style to really drive you nuts."

For your game, this suggests an advanced feature: analyze the source image for strong edges (Canny edge detection, perhaps?) and bias your grid perturbation and cut lines to follow them. It's hard to automate well, but even a rough implementation adds enormous personality.

Whimsy pieces

Victorian-era wooden puzzles — and their modern descendants from Stave, Liberty, and Artifact Puzzles — include "whimsies" or "figurals": pieces shaped like recognizable objects. A butterfly. A sailing ship. A cat. A seahorse (Par Puzzles' signature piece). These break the grid entirely for a few special locations, and they add delight. Puzzlers hunt for them eagerly — they're landmarks in the sea of similar shapes.

The devious arts

Stave's founder Steve Richardson earned the title "Chief Tormentor" for inventing trick puzzles — jigsaws that assemble in multiple ways, with only one correct solution. Their puzzle "Champ" has 44 blue pieces that fit together 32 different ways. Teasers have intentional negative spaces in the center. Tormentors have no interlocking at all — like tangrams that happen to be disguised as jigsaws.

Connector styles as personality

Beyond the standard mushroom-shaped knob, the world of wooden puzzles features a startling variety of connector designs — each with a different tactile and aesthetic character.

The lesson for your game: the tab shape is not just a functional interlock. It's a design parameter — a dial you can turn to give your puzzles personality. A children's puzzle might use chunky, wide-necked tabs. A difficult adult puzzle might use narrow, mushroom-shaped ones that resist separation. The shape speaks.