The AuthaGraph projection (Narukawa 2017) has less area distortion. It also evenly distributes the distortion. And this map projection has a rectangular outline. AuthaGraph projection fits a sphere into a rectangle by projecting it onto a regular tetrahedron. It uses a projection plane so called “curved tetrahedron” named by the author. 96 faces form a “curved regular tetrahedron”. The method by using the projection plane reduces distortion. Most of the world maps so far have concentrated distortions in high latitude areas. Therefore, these maps have had difficulty in viewing the high latitude area. AuthaGraph projection improves this challenge. From different viewpoint, most of the world maps so far have the earth's axis as the axis of projection. That is, these maps follow latitude and longitude. Cylindrical projection and conic projection are typical examples of these.

On the other hand, the AuthaGraph projection uses a regular tetrahedron. The regular tetrahedron has a closed surface. By utilizing the characteristics of regular tetrahedron, the projection improves the visibility of polar regions. It was created with the aim of creating a world map that does not use this latitude and longitude line as a guideline. And it is made with the aim of giving an equal overview of the whole world. However, it pays a trade-off for this purpose. AuthaGraph projection has not been able to link latitude and longitude to map coordinates x and y. That has been a challenge to make the formula of it.

As a result, the world map by AuthaGraph projection has been created by making full use of computational power. In addition, the author operated a 3D modeling software to create a map of the world by AuthaGraph projection. Without the above manual work, the AuthaGraph projection could not be practiced. From another academic point of view, it is necessary to formulate the AuthaGraph projection. The formula allows map projection researchers to quantitatively verify the distortion of the projection. Based on the above viewpoints, this paper practices the following three ideas and comparative verification.

1. Formulate the AuthaGraph projection.

2. The formula quantitatively evaluates the distortion.

3. The evaluation of the distortion compares the existing rectangular area-equal world map with the AuthaGraph projection.

The earth shapes a spheroid. Its flattening is approximately equal to 1/300. However, in discussing the projection, the shape of the earth may be simplified as a sphere. This paper as well, set the earth as a sphere for the map projection’s formula.

For the Taiwan expedition (1874) and military action to suppress local resistance after the SinoJapanese War (1894-5), Japanese navy prepared nautical charts re-engraving from British Admiralty charts. Concerning place names, Japanese Hydrographical Office tried to transcribe those on British charts into Chinese characters locally used. However, it was not easy to infer exact Chinese characters on the basis of transliterated alphabetical local place names on British charts. Although a Chinese nautical chart titled Da Qing yi tong hai dao zong tu 大清一統海道總圖 (General map of the Chinese coast and sea-routes) re-engraved from a British chart was consulted, even place names of major ports of Taiwan on it were not always correct, because it transliterated many local place names phonetically into Chinese characters. After a process of trial and error up to 1905, place names in Chinese characters conformed to local use were put on Japanese charts of Taiwan.

Loxodromes (rhumb lines) are plotted as straight lines on maps in Mercator projection. The angle the loxodrome makes with the meridian, i.e. bearing or azimuth, has been called “dakaku” in the field of cartography and geography in Japan. “Dakaku”, if translated literally, is the steering angle or helm and the same word is used in the field of navigation in this meaning. Therefore, this wording is confusing and not appropriate.

This word has been used more than ninety years in cartographic literature in Japan. The author, however, argues that we should cease using this word as meaning bearings of loxodromes and just use “houi” which means bearing instead.

It is unknown why this wording “dakaku” occurred, but the author conjectures that the word “houi” has been solely used as meaning the direction from point A to point B in cartography and geography in Japan and that has prohibited the use of the word “houi” for the direction of loxodrome. But this is not proper usage of Japanese language. “Houi” can be used in this meaning of course but is also used at one point on the Earth to express bearings. There is no problem to use “houi” as meaning bearings of loxodromes.

Therefore, we should cease using “houi” in a very limited sense but freely use this word in the meanings of original Japanese language also in the field of cartography and geography

We have some methods to lead ships to their destinations safely, and among them, the main tool for the purpose is a chart. The modern nautical charts have accepted the demand of voyagers to secure voyage for more than 500 years. Charts started with only description of slight depth and shoreline, and then been refined to become modern nautical charts.

With the appearance of ENC, the Electronic Navigational Chart, the demand of paper charts has decreased. And now ENCs take over the leading role of charts. The main reason for this trend is that the SOLAS Convention imposes the obligation of ECDIS carriage on the ocean liners.　For those equipping ECDIS onboard, paper charts become unnecessary under a certain condition.

I hope that still developing ENCs would inherit DNA of the modern paper charts refined during their history.

This paper is a report of the “Future of Nautical Charts” reported at the symposium in Nov. 2021, with some revisions and some considerations.