This is one of those - how the heck did I stumble onto this website while searching for something else - kind of things. 
It is a 2001 / 2002 patent application by Fuji Hiromichi ( 冨士弘道) & Kabushikigaisha dan, 株式会社ダン. Dan Co., Ltd. If you do a web search with the Japanese name 2 company website show up. dan - international & dan - line. Links to the patent application at the bottom of this page.
It pretty interesting reading. The digital translation into English is pretty odd in some paragraphs, and the translated page also strips off the Fig. # on the many drawings. If you want to take a look at it I recommend opening the web-page in 2 tabs: one in the original Japanese language and the other tab the digitally translated window.
技術情報 ；テンカラ釣り用テーパライン
Technical information: Tapered Line for Tenkara Fishing.
A short summary:
It describes several claims and features for the line. That is is a triple tapered line (a point in the line about 1/4 total line length from the tip is constricted, tapering toward both the rod end and the tippet end, point 11 on the line drawiing)
This feature is said to provide several advantages, The thinner part acts as a hinge, allowing the angler to more easily land the kebari under low brush. It allows the line to remain thicker, therefore stronger than single tapered lines. This also allows softer landing of the kebari on the water, more like how mayflies would land on the water. It is easy for beginners to cast.
It also applies for a multi-color marker section at the tippet end.
And the patent includes the Fuji type loop connection to the Lillian. If you have a Fujino tapered line you know the connection loop is designed with a sliding collar that tightens on the lillian. It is not intended to be used as other tapered line connection loops, where the loop is folded back forming a girth hitch onto the lillian. Here is a drawing from the Plat website for those not familiar with the design:
The sliding collar is called 乳輪, (nyūrin) , in some places it translates as “Isola”, in other places it translates differently. It is item # 13a on fig. 2 (図２ )
It also describes the 捨てバリ効果, Sutebari effect, or discarded hook effect. And how it had been written about in various magazines by that patent applicant.
Next is a link to a drawing of the line 10, the constricted hinge point at 11, & the forward and rearward tapers 11a & 11b (sorry it is a png file and it would not embed ):
Taper line drawing fig. 1 図１
Another claim for the line are that it permits a shorter casting arc. If imagining the casting stroke to be CCW his taper line allows casting over 60 ˚ arc ( 12:00 to 10:00) vs previous lines requiring 90˚ (1:00 to 10:00) The shorter casting arc being an advantage on brushy streams. This, I think, is considered normal today, but apparently not at the time this patent was applied for.
The patent is for lines from 3 meters to 6 meters in length. A 3.6m line is described as tapering from ~ #6 (0.4mm) to ~ #4.5 (0.35mm) and weighting 0.8 grams. With an overall taper (slope) of .0015/100.
Start by scrolling down to the section - Effect of the invention, paragraphs 0031 to 0034, to read the summary overview of the claims for this line.
Anyway, if you’re the technical type you might find it interesting reading. it is basically an essay by Fuji Hiromichi-san on his thought process and goals for a tapered line. I found it interesting to read about this process from a tenkara angler held in high regard in Japan. 
技術情報 ；テンカラ釣り用テーパライン