Trace as

“Trace as” decides what the trace becomes on the sheet: one shape holding every outline, with its holes kept as holes, or a few separate shapes you can handle one at a time. It changes nothing about where the edges are, only how they are grouped.

What it does

• “One shape” (the default). Every outline in the trace, the outside of every region and the edge of every hole, goes into one compound shape, filled by the even-odd rule. It flips as one cut: one piece, folded over one edge.
• “Separate shapes”. Each region of front becomes a shape of its own, with its own holes kept inside it. They are sorted by area, largest first, and only the 12 largest are kept. When some are left out, the message after tracing says so, for example “Traced 12 shapes (the 12 largest)”.

The even-odd rule decides what is inside a compound shape without asking which outline is which. From any point, imagine a line running off to infinity and count how many outlines it crosses. An odd number means inside, and filled; an even number means outside. So the middle of a ring, inside two outlines, is empty, and an island in that middle, inside three, is filled again. It works for any depth of nesting, and it does not care which way around each outline was walked.

Either way, every shape is clipped to the art board, joins the waiting shapes and is judged by the paper under it, as After you trace describes. With separate shapes each is judged on its own, so some can be cuts while others put paper back; with one shape there is one judgment for the lot. After the flip, one shape is one cut in the design, and separate shapes are separate cuts, each of which you can select and change on its own later.

The regions are counted the way Detail counts them: front pixels touching only at a corner are one region. An island inside a hole is a region of its own, so with separate shapes it becomes a separate shape.

Why it works this way

One shape is the default because it is the cheapest thing the design can hold, and the truest to what a trace is. Every cut in a design is worked out against the cuts around it whenever something changes, and that work grows roughly with the square of the number of cuts. A trace of a leafy tree can have hundreds of regions. As hundreds of cuts, it would bring every later edit to a crawl. As one compound shape it is one cut, whatever it contains.

Separate shapes are for when the parts mean different things: the letters of a word you may want to move or reshape one at a time, or figures you mean to rearrange. The cap of 12 is where the cost starts to show; past it, every later edit slows down, so the smallest regions are left out. If they matter, lower “Detail” first so the trace has fewer, larger regions, or trace as one shape.

The metaphor

“Trace as” borrows the stencil, and the stencil's oldest problem. Cut the letter O out of a sheet and its middle falls away: an island has nothing to hold it. Stencil makers solve that with bridges, the little ties that give stencil lettering its broken look. Japanese katagami, the paper stencils used to dye kimono cloth, go further: fine designs were stabilized with a net of silk, and in earlier times of human hair, so that islands could float in an open pattern.

One shape is a stencil cut in one piece, its islands held as if by that invisible net. And here the metaphor breaks, in the app's favor: on the screen nothing falls out. Trace a ring as one shape and flip it, and the paper in its middle stays exactly where it was, attached to nothing. If you mean to cut the design from real paper later, look for those islands and give them bridges, or be ready to glue them down.

A history

In art

Matisse's first large cut-out project was the book Jazz, begun in 1943, whose cut-outs were designed to be reproduced as stencil prints. He cut sheets of paper painted with gouache into shapes and arranged them, working, as he put it, by drawing with scissors. The question “Trace as” asks, one piece or many, runs all through that work: some compositions are made of many separate shapes arranged and rearranged until they settle, others of single forms with openings cut through them.

The cut-paper silhouette is the other tradition. It is always one piece: every opening in a profile, the gap under a chin or between fingers, is a hole in the same sheet, and nothing floats.

In printing

The island problem shaped whole printing crafts. Ise katagami are made of three sheets of washi pasted together with tannin-rich persimmon juice, and for kimono dyeing the cut stencil is stabilized on a fine silk net; in the past, human hair did the same work. Stenciled lettering keeps its bridges to this day, and the broken letters have become a style of their own. In the Paris of the 1920s, pochoir studios, André Marty's and Jean Saudé's among them, colored prints and books by hand through sets of stencils, one for each color.

Screen printing all but abolished the problem. A screen stencil is carried on mesh, so an island is held by the mesh itself and needs no bridge. In a sense the even-odd rule is that mesh: it holds every outline in place, whatever it encloses.

In technology

The even-odd rule is geometry before it is graphics. The Jordan curve theorem, stated by Camille Jordan in 1887 and given what is widely taken as its first rigorous proof by Oswald Veblen in 1905, says that a simple closed curve divides the plane into one inside and one outside. Its practical child is the crossing test above: an odd count means inside.

PostScript, the page description language Adobe introduced in the early 1980s, offered two ways to paint a path: fill, which uses the nonzero winding rule and pays attention to the direction of each outline, and eofill, which uses even-odd. SVG and the browser's canvas inherited the same pair, and a “compound path” in a drawing program is the same idea given a name. The trace uses even-odd because it gets holes right however deeply they nest, without depending on which way each outline was walked.

In professional software

Drawing programs call the one-shape result a compound path: several outlines held as one object, with holes where they nest. The skill that transfers is knowing when to keep outlines together and when to split them.

• Adobe Illustrator. ‘Object › Compound Path › Make’, ⌘8 (Ctrl+8), joins selected paths into one, ‘Release’ splits them again, and the ‘Attributes’ panel chooses the fill rule, even-odd or non-zero. An Image Trace becomes ordinary paths with ‘Expand’, and they arrive as a group, so ‘Ungroup’, ⇧⌘G (Shift+Ctrl+G), gives you separate shapes.
• Inkscape. ‘Path › Combine’, ⌘K (Ctrl+K), makes one path from several. ‘Path › Break Apart’, ⇧⌘K (Shift+Ctrl+K), splits off every outline, holes included, so each hole comes out as a filled shape of its own; ‘Path › Split Path’ keeps each hole with its shape, as Separate shapes does here.
• Cricut Design Space. ‘Weld’ merges overlapping shapes into one cut outline. ‘Attach’ keeps shapes in place relative to each other on the cutting mat without merging them, while a plain ‘Group’ only moves them together on the canvas, and at cut time they may be rearranged on the mat.
• Autodesk AutoCAD. HATCH with normal island detection fills nested boundaries alternately, which is the even-odd rule under another name. REGION turns closed outlines into areas, SUBTRACT cuts holes in them, and EXPLODE breaks a combined object back into its parts.
• Autodesk Fusion (formerly Fusion 360). Every closed loop in a sketch makes a profile, and a loop inside another splits it: the ring between them is one profile, the middle another. To extrude, you pick profiles, so a hole is simply a profile left out.

What carries over. One compound shape is light and holds every hole in place; separate shapes can each be moved, recolored or cut on their own. The pitfall is holes when you split: before anything is cut, check that each hole has stayed with its shape and has not become a filled shape of its own.

Try this

• Trace a word with “One shape” and look at it waiting: one shape. Switch to “Separate shapes” and press “Trace” again. The waiting trace is replaced by one shape per letter, and per dot on an i.
• Trace a ring as one shape and flip it. Look at its middle: an island of paper, attached to nothing.
• Trace a busy photo with “Separate shapes” and read the message. If it says “the 12 largest”, lower “Detail” until it does not.

Going further

See After you trace, Detail and Flipping.

• Henri Matisse, Jazz
• Adobe Systems, PostScript Language Reference Manual