Overview
I had the opportunity to try the IIIF Content State API, so this is a memo of the process.
https://iiif.io/api/content-state/1.0/
The IIIF Content State API is described in Current Awareness-R as follows:
“The IIIF Content State API” can generate links that specify in detail how an object should be displayed, including rotation angle and display position on the page image.
https://current.ndl.go.jp/car/45832
Trying It Out
The “Shueitai / Letterpress Printing Digital Library” provides the IIIF Content State API.
https://archives.ichigaya-letterpress.jp/library/
Documentation is available at the following location.
https://archives.ichigaya-letterpress.jp/library/help
Below is an explanation of usage examples.
Item Detail Page
For example, access the following page.
https://archives.ichigaya-letterpress.jp/library/items/084cef1f7ddc
Then click the link to the IIIF Curation Viewer.

Rectangle Selection
Use the IIIF Curation Viewer to select a rectangle.

For instructions on using the IIIF Curation Viewer, please refer to the following.
http://ch-suzuki.com/icpt/index.html
Skipping a few steps, you can obtain the following information.
The above is in the following format:
Base64 Encoding
For example, access the following site.
Then, using the previously obtained information and the manifest URI of the item, encode the following JSON.
As a result, the following string is obtained.
ewogICAgImlkIjogImh0dHBzOi8vYXJjaGl2ZXMuaWNoaWdheWEtbGV0dGVycHJlc3MuanAvYXBpL3ByZXNlbnRhdGlvbi8yLzA4NGNlZjFmN2RkYy9jYW52YXMvMiN4eXdoPTIxNDgsODEzLDMxMiwzMDQiLAogICAgInR5cGUiOiAiQ2FudmFzIiwKICAgICJwYXJ0T2YiOiBbewogICAgICAgICJpZCI6ICJodHRwczovL2FyY2hpdmVzLmljaGlnYXlhLWxldHRlcnByZXNzLmpwL2FwaS9wcmVzZW50YXRpb24vMi8wODRjZWYxZjdkZGMvbWFuaWZlc3QuanNvbiIsCiAgICAgICAgInR5cGUiOiAiTWFuaWZlc3QiCiAgICB9XQp9
Accessing the Endpoint URL
Using the above string, access the following URL.
As a result, you can access the following page.

Summary
As intended by the IIIF Content State API, we were able to create a link that specifies in detail how an object should be displayed.
There may be more efficient ways to create links, but I hope this serves as a helpful reference.