(The map above is by Arsana and Schofield, 2012. A larger, easier to read version, is here and here).
The Australian Naval Institute carrys an excellent article South China Sea decision explained by Clive Schofield, Professor of Geography at the University of Wollongong, NSW, Australia. He served as an independent expert witness (provided by the Philippines) to the Arbitration Tribunal in the case between the Republic of the Philippines and the People’s Republic of China.
An inconvenient insight: "For example, the US claims 200-nautical-mile EEZs from several remote Pacific island territories that appear remarkably similar to some of the South China Sea features that the tribunal found could not generate extended maritime claims. The US welcomed the ruling, but it will be intriguing to see whether the US and other countries modify their practices in light of it."
Another interesting earlier overhead-slides presentation on how boundaries are measured is Professor Schofield's April 2013 Baselines Issues in the South China Sea: Challenges in Defining the ‘Boundary’ between Land and Sea [PDF, 10 MB].
Here is the Press Release for the Court at the Hague's, July 12, 2016, ruling on Philippines versus China.