Scallops and deckles, and where they come from

Both edges are older than photography and both are borrowed from paper. Knowing what they are in the physical world is most of what you need to set them well on a screen.

Two edges with different ancestors

A scallop is a manufactured edge. It is what you get from a die, a rotary cutter or a pair of shaped shears: a repeat of identical arcs, evenly spaced, cut into or out of a straight line. Victorian carte-de-visite mounts had them, doilies have them, so do the paper cases under a cake and the edges of a great many greeting cards. The eye reads a scallop as something that was made in a factory and made carefully, which is exactly why it flatters a photograph of a child or a wedding.

A deckle is the opposite. It is the untrimmed edge of a sheet of hand-made paper, formed where the pulp thins out against the wooden frame — the deckle — that holds the mould. No two are alike, none is straight, and the irregularity is the whole point. Where a scallop says careful, a deckle says made by hand and left that way. Torn paper is the same family with less politeness: an edge pulled apart rather than formed.

That difference in ancestry is worth holding on to, because it decides which control matters. A scallop is judged on its regularity. A deckle is judged on whether its irregularity looks plausible.

The corner problem, and the arithmetic that solves it

Divide a 1200-pixel side by a 47-pixel arc and you get 25.5 arcs. Software that takes the whole number and moves on draws 25 arcs of 47 pixels and a 25-pixel stub at the end, and because all four sides have different lengths the stub lands in a different place on each — which is how you end up with three tidy corners and one that is obviously wrong. It is the single most common defect in scallop tools and it is entirely avoidable.

The fix is to treat the width you asked for as a target rather than a measurement. Round 25.5 to 26, then recompute the arc as 1200 divided by 26, which is 46.15. Every arc on that side is 46.15 wide, the last one finishes exactly on the corner, and nobody can see the 0.85-pixel difference from what was requested. Each side gets its own count, so a 4:3 picture carries more arcs across the top than down the side — which is correct, because the top is longer.

Arc width: The target repeat, as a multiple of the band. Lower numbers give more, smaller scallops; the count follows from the side length.
Arc depth: How far each bump travels, as a share of the band. At 100% the arcs reach the outer edge of the picture.
Tear depth: How far a deckle or a tear wanders from its baseline, as a share of the band.
Roughness: How much fine detail rides on the large movements. Low is a slow waver; high is a jagged fray.

Where a tear actually comes from

The deckle is not random. It is a sum of sine waves — three of them for the deckle, five for the torn paper — whose frequencies are whole numbers of laps around the outline. That constraint is what makes the edge close: the noise at the end of the lap is the same value as the noise at the start, so the last point meets the first without a step. Scatter random numbers along each side instead and the four corners will never agree.

The amplitudes and the phases come from one seed, printed under the sliders. Change it and you get a different tear from the same controls; leave it and the same tear redraws at any size, which is what makes the preview and the saved file the same shape rather than two similar ones.

Curves or facets

The deckle joins its points with quadratic curves through the midpoints, which rounds the movement into the soft waver of a formed edge. The torn paper joins the same kind of points with straight segments and more of them, which gives the flat facets you see on a sheet pulled against a ruler. Same generator, two personalities.

Setting them well

For a scallop, start with the arc width and leave the depth alone. The proportion that reads as a proper scalloped mount is roughly one and a half band widths per arc, at a depth of about two thirds — deeper than that and the arcs start to look like teeth, shallower and they look like a printing error. If the picture is portrait, check the short sides: that is where a large arc width runs out of room.

For a deckle, the trap is depth. A tear that wanders a full band width looks like damage rather than paper; around half is where it stops reading as a mistake. Push roughness up only if the picture is large — fine facets on a small file simply disappear into the pixel grid.

The corner arithmetic has been checked against ordinary proportions and against a six-to-one panorama, and it holds. What has not been tested is a panorama with a very small target arc width, where the short sides end up with one or two arcs and the rounding has almost nothing to redistribute. If a frame looks uneven there, widening the arc is the fix.
A cut edge removes part of the photograph. On these frames that is the feature, but it means the frame cannot be undone by cropping afterwards — the pixels outside the cut are not in the saved file at all.