linesweeper: the left intersection scan in docs/sweep.typ uses alpha^(i+1)

The pseudocode for the intersection scan to the left looped j = i down
to 1 and compared each alpha^j with alpha^i, so its first pass compared
alpha^i with itself. The lemma after it is stated for alpha^(i+1), the
segment being inserted to the right of alpha^i. The loop body now uses
alpha^(i+1), and w^j is the smallest event height between j and i+1.

SOURCE.json records the patch in local_patches and the new sha256 of
docs/sweep.typ. README.craft.md and NOTICE say one file is changed.

NOTICE

@@ -218,10 +218,10 @@ applications retain their own document-font selection and licensing policy.
 linesweeper
 
 linesweeper 0.5.0 (https://crates.io/crates/linesweeper/0.5.0), MIT OR Apache-2.0, is stored in
-vendor/linesweeper with its upstream license files and no file changed. Its manifest names Joe Neeman
-as author, and its LICENSE-MIT reads "Copyright (c) 2018 Raph Levien". See
-vendor/linesweeper/README.craft.md and vendor/linesweeper/SOURCE.json for provenance and the files
-left out.
+vendor/linesweeper with its upstream license files and one local patch, to docs/sweep.typ. Its
+manifest names Joe Neeman as author, and its LICENSE-MIT reads "Copyright (c) 2018 Raph Levien". See
+vendor/linesweeper/README.craft.md and vendor/linesweeper/SOURCE.json for provenance, local changes
+and the files left out.
 
 Platform lifecycle source provenance
 

vendor/linesweeper/README.craft.md

@@ -1,15 +1,19 @@
 # Local linesweeper 0.5.0 copy
 
-This is the crates.io linesweeper 0.5.0 package (MIT OR Apache-2.0) with some files left out and no
+This is the crates.io linesweeper 0.5.0 package (MIT OR Apache-2.0) with some files left out and one
 file changed. `.cargo_vcs_info.json` names the commit it was packaged from,
 `824b0791a750f7b27b8edcbb6c6244d0e629875e`. That commit is not in the GitHub repository the manifest
 names, which is archived; its README says development moved off GitHub.
 
-Every file here except this one and `SOURCE.json` is byte for byte the file in the `.crate` archive.
-`SOURCE.json` records the hash of the `.crate` download (`source_archive_sha256`) and, for every file
-kept, the hash in the package (`source_sha256`) and the hash here (`sha256`). `upstream_repository` is
-null because no public repository this copy can name holds `upstream_revision`. `local_patches` is
-empty.
+Every file here except this one, `SOURCE.json` and `docs/sweep.typ` is byte for byte the file in the
+`.crate` archive. `SOURCE.json` records the hash of the `.crate` download (`source_archive_sha256`)
+and, for every file kept, the hash in the package (`source_sha256`) and the hash here (`sha256`).
+`upstream_repository` is null because no public repository this copy can name holds
+`upstream_revision`. `local_patches` lists each change:
+
+- `docs/sweep.typ`: the intersection scan to the left compares each segment with `alpha^(i+1)`
+  instead of `alpha^i`. With `alpha^i`, its first pass compared `alpha^i` with itself, and the lemma
+  after it is stated for `alpha^(i+1)`.
 
 `omitted_files` lists the 43 files of the package left out here, with their hashes:
 

vendor/linesweeper/SOURCE.json

@@ -7,7 +7,9 @@
   "upstream_repository": null,
   "upstream_revision": "824b0791a750f7b27b8edcbb6c6244d0e629875e",
   "upstream_directory": "",
-  "local_patches": [],
+  "local_patches": [
+    "In `docs/sweep.typ`, the intersection scan to the left compares each segment with `alpha^(i+1)`, the segment the lemma after it is stated for, instead of `alpha^i`."
+  ],
   "files": [
     { "path": ".cargo_vcs_info.json", "source_sha256": "47fba6a9dbdf445a5c97f783c9be62093035f9d5e5cdc2cf3216ad8259bcd8fc", "source_git_blob": null, "sha256": "47fba6a9dbdf445a5c97f783c9be62093035f9d5e5cdc2cf3216ad8259bcd8fc" },
     { "path": ".gitignore", "source_sha256": "88b59092499ae05234330eb7d0b01e953e969caf05261530e3765eef02536cf0", "source_git_blob": null, "sha256": "88b59092499ae05234330eb7d0b01e953e969caf05261530e3765eef02536cf0" },
@@ -21,7 +23,7 @@
     { "path": "benches/linebender_logo.rs", "source_sha256": "d10867f43439d37f0e1da5d30eaed9ab3bfbe655ed47212f65dc20ab4db65cb3", "source_git_blob": null, "sha256": "d10867f43439d37f0e1da5d30eaed9ab3bfbe655ed47212f65dc20ab4db65cb3" },
     { "path": "benches/painted_dreams.rs", "source_sha256": "073008db93840d380710e13ed3ae38e08cb823f10c12e5f838dac1ccf37eaecf", "source_git_blob": null, "sha256": "073008db93840d380710e13ed3ae38e08cb823f10c12e5f838dac1ccf37eaecf" },
     { "path": "benches/synthetic.rs", "source_sha256": "7ce59bef2e1c4f28b00cb89feb15bc71ca4b098a8d27e7b02ea699aca9bcc810", "source_git_blob": null, "sha256": "7ce59bef2e1c4f28b00cb89feb15bc71ca4b098a8d27e7b02ea699aca9bcc810" },
-    { "path": "docs/sweep.typ", "source_sha256": "4766082c8672a7bb4356b5581043489c13b4e3fb8931ba3a5f0a473fab0172f3", "source_git_blob": null, "sha256": "4766082c8672a7bb4356b5581043489c13b4e3fb8931ba3a5f0a473fab0172f3" },
+    { "path": "docs/sweep.typ", "source_sha256": "4766082c8672a7bb4356b5581043489c13b4e3fb8931ba3a5f0a473fab0172f3", "source_git_blob": null, "sha256": "571f227f4b43eaba8060c48344e26b639a4fea8787e5c63bd3f826836c5e4806" },
     { "path": "examples/boolean_op.rs", "source_sha256": "3b38a1ccda7e736cce4b191a3a45ab4824c4c365190e3eb637b2fb39b5996c9f", "source_git_blob": null, "sha256": "3b38a1ccda7e736cce4b191a3a45ab4824c4c365190e3eb637b2fb39b5996c9f" },
     { "path": "examples/bus.rs", "source_sha256": "e206a08be73899f564188052c8ecc15526b54606e52ee2935a64ce6b5723da33", "source_git_blob": null, "sha256": "e206a08be73899f564188052c8ecc15526b54606e52ee2935a64ce6b5723da33" },
     { "path": "examples/curve_metrics.rs", "source_sha256": "0db6a5327fd2119a03a9a66624fea3e04b6bbb519655667ad30487aee6c787d2", "source_git_blob": null, "sha256": "0db6a5327fd2119a03a9a66624fea3e04b6bbb519655667ad30487aee6c787d2" },

vendor/linesweeper/docs/sweep.typ

@@ -368,13 +368,13 @@ of the other one.
 #figure(
   pseudocode-list([
     + *for* $j = i$ down to $1$
-      + let $w^j$ be the smallest height of any event between $j$ and $i$
+      + let $w^j$ be the smallest height of any event between $j$ and $i+1$
 
-      + *if* $(alpha^j_(-,epsilon), alpha^i)$ cross by $w^j$
-        + choose $z$ before the crossing, such that $alpha^j approx_(z,epsilon) alpha^i$
-        + insert an intersection event for $(alpha^j, alpha^i)$ at $z$
+      + *if* $(alpha^j_(-,epsilon), alpha^(i+1))$ cross by $w^j$
+        + choose $z$ before the crossing, such that $alpha^j approx_(z,epsilon) alpha^(i+1)$
+        + insert an intersection event for $(alpha^j, alpha^(i+1))$ at $z$
 
-      + *if* $alpha^j_+ (z) <= alpha^i (z)$ for all $z in [y, w^j]$
+      + *if* $alpha^j_+ (z) <= alpha^(i+1) (z)$ for all $z in [y, w^j]$
         + *break*
   ]),
   caption: "Intersection scan to the left"