Scale both sides of a fit=cover image by the same amount (part of #282)

cropCentreAndResize cut the centre to whole source pixels and forced
that to the requested size, so the two sides were scaled by different
amounts: a 16x16 source at 100x60 came out squashed by 4%. It now
widens the centre to whole source pixels and lets thumbnail with a
centre crop scale that by the one amount next uses and cut the output
from it. thumbnail copies the scaled image into memory, which is larger
than the output by less than one scaled source pixel on each side.
TODO.md says so.

Model: opus-5-5

TODO.md

@@ -31,15 +31,17 @@ P2: security: per-origin rate limiting
 # Completed Steps
 
 - 2026-10-15 a thin source requested with `fit=cover` no longer makes libvips
-  build a huge image (closes #282): libvips scaled the whole source to cover the
-  requested size and copied that into memory before it cut out the centre, so an
-  8192x64 source at 8192x8192 made it allocate about 24 GiB, and an 8192x1
-  source answered 500. The image processor now cuts the centre of the source to
-  the requested size's proportions first and resizes that, so no image larger
-  than the source or the output is made; the crop is the same centre as before.
-  With the runtime image's libvips and JPEG output at 8192x8192, resident memory
-  peaked at about 44 MiB for the 8192x64 source, 40 MiB for the 8192x1 one, and
-  117 MiB for a 4000x3000 one, which took 373 MiB before.
+  build a huge image (closes #282): libvips' thumbnail scaled the whole source
+  to cover the requested size and copied that into memory before it cut out the
+  centre, so an 8192x64 source at 8192x8192 made it allocate about 24 GiB, and
+  an 8192x1 source answered 500. The image processor now first cuts the centre
+  of the source, widened to whole source pixels, and thumbnail scales and cuts
+  only that, by the same amount on both sides as before. What it copies into
+  memory is then larger than the output by less than one scaled source pixel on
+  each side. With the runtime image's libvips and JPEG output at 8192x8192,
+  resident memory peaked at about 242 MiB for the 8192x64 source and 431 MiB for
+  the 8192x1 one. The output can sit a fraction of an output pixel from where it
+  was.
 - 2026-10-15 the README says how a source URL with a query is written into an
   image URL, and the image route accepts it (closes #255): the query follows the
   source path after `%3F`. pixa now reads the image URL's path decoded once, so

internal/imageprocessor/imageprocessor.go

@@ -530,35 +530,36 @@ func (p *ImageProcessor) resize(
 	}
 }
 
-// cropCentreAndResize cuts img to its centre, the largest area it holds with
-// the proportions of width x height, and resizes that to width x height.
-// This is the crop libvips' thumbnail makes with InterestingCentre, but
-// libvips scales the whole image to cover the size and copies the result
-// into memory before it crops, and for a thin image that is far larger than
-// the image or the output: 8192x64 at 8192x8192 is 1048576x8192, about 24
-// GiB. Cropping first makes no image larger than img or the output.
+// cropCentreAndResize scales img by the same amount on both sides, the
+// least that makes it cover width x height, and cuts the centre width x
+// height out of it, as libvips' thumbnail does with InterestingCentre.
+// thumbnail alone scales the whole image and copies the result into memory
+// before it cuts, and for a thin image that is far larger than the image or
+// the output: 8192x64 at 8192x8192 is 1048576x8192, about 24 GiB. So the
+// centre is cut from img first, widened to whole pixels of img, which adds
+// less than one pixel of img on each side, and thumbnail scales and cuts
+// only that.
 func cropCentreAndResize(img *vips.ImageRef, width, height int) error {
 	imgW, imgH := img.Width(), img.Height()
 
 	// An image wider than the requested proportions keeps its height and
-	// loses width, any other keeps its width and loses height; the side
-	// shortened is rounded to the nearest pixel and is at least 1
-	cropW, cropH := imgW, imgH
+	// loses width down to imgH*width/height, any other keeps its width and
+	// loses height down to imgW*height/width. Half of what is lost comes
+	// off each side, rounded down to whole pixels, so the part kept holds
+	// all of the centre.
+	left, top := 0, 0
 	if imgW*height > imgH*width {
-		cropW = max(1, (imgH*width+height/2)/height)
+		left = (imgW*height - imgH*width) / (2 * height) //nolint:mnd // each side
 	} else {
-		cropH = max(1, (imgW*height+width/2)/width)
+		top = (imgH*width - imgW*height) / (2 * width) //nolint:mnd // each side
 	}
 
-	// Half of what is cut comes off each side
-	left, top := (imgW-cropW)/2, (imgH-cropH)/2 //nolint:mnd // half the cut
-
-	err := img.ExtractArea(left, top, cropW, cropH)
+	err := img.ExtractArea(left, top, imgW-2*left, imgH-2*top)
 	if err != nil {
 		return err
 	}
 
-	return img.ThumbnailWithSize(width, height, vips.InterestingNone, vips.SizeForce)
+	return img.Thumbnail(width, height, vips.InterestingCentre)
 }
 
 const defaultQuality = 85