docs: turning a page by an angle that is not a quarter

content/working-with-a-file/operations.md

@@ -22,7 +22,7 @@ pages and `1,1` gives two copies.
 
 ## The verbs
 
-Merge, select, delete, reverse, move, rotate, crop, resize, split; n-up,
+Merge, select, delete, reverse, move, rotate, turn by any angle, crop, resize, split; n-up,
 booklet, overlay and underlay, blank pages; watermarks, page numbers, Bates
 stamps and free stamps; placing a picture — a signature, a logo, a seal;
 sanitize, flatten, strip; compress, encrypt, decrypt and permissions;
@@ -32,6 +32,27 @@ straightening a scan; and reading a page back as text or as pictures.
 a signature, put where you say. It is not cryptography and does not claim to
 be — a drawn squiggle proves nothing about who drew it.
 
+## Turning a page by any angle
+
+`rotate` writes a number on the page — `/Rotate`, a multiple of ninety — and
+`turn` rewrites the page onto a sheet of its own, for every angle in between.
+
+```sh
+pdfops turn -by 30 tilted.pdf turned.pdf
+pdfops turn -pages 2,5-7 -by -1.5 scan.pdf nudged.pdf
+```
+
+⛔ **The paper grows and nothing is cut off.** The sheet is the turned page's
+bounding box — `w·|cos θ| + h·|sin θ|` across, `w·|sin θ| + h·|cos θ|` down —
+and the page is centred on it. That is the difference from straightening a
+scan, below, which keeps the paper it was given.
+
+An angle that is a multiple of ninety goes through `/Rotate` and nothing else
+happens: no transformation, no new content stream, and text that was selectable
+stays selectable.
+
+**Positive is clockwise**, as ISO 32000-1 Table 30 and `Rotate` already mean it.
+
 ## Straightening a scan
 
 `deskew` measures how far each page is tilted and turns the crooked ones back.

content/working-with-a-file/workbench.md

@@ -145,6 +145,29 @@ Beside the page rather than over it, because nearly every verb changes the
 document and the document is drawn from what would be saved — typing a crop box
 and watching the page come back cropped is the whole point.
 
+### Turning by an angle that is not a quarter
+
+**Turn them by an angle**, beside *Turn them*, takes the angles the cycle
+button cannot say: any number of degrees, clockwise, added to whatever the page
+already carries.
+
+⛔ **The paper grows and nothing is cut off.** A page turned thirty degrees
+comes back on a bigger sheet, because a sheet that stayed the same size would
+have two corners of the page over its edge. The status line says so —
+*"turned 1 by 30 degrees — the paper grew to hold the corners"* — since that is
+the part nobody expects. It is the one difference from **straightening a
+crooked scan**, which keeps the paper it was given: a fraction of a degree on a
+page whose text sits well inside its margins costs nothing.
+
+A quarter, a half or three quarters still go through the page's own `/Rotate`
+and change nothing else about the file, so text that was selectable stays
+selectable.
+
+⛔ The two controls **share a row**, which is not a matter of taste: given a row
+of its own the angle pushed the Pages panel forty-four pixels past the bottom
+of its box, and a last control that can only be scrolled to is a control people
+do not find. The workbench has a test that measures exactly that.
+
 Every verb is one
 [`toolkit.Action`](https://pkg.go.dev/github.com/go-widgets/toolkit#Action),
 so a verb that cannot run greys on every surface showing it: the arrows at the