API: Spatial Surfaces

[jstoobysmith]

Details

Key data structure

This API is not directed around a single key data structure, instead it is centred around the concept of a surface in space. For each type of surface is defined around an embedding into Space d.

Need

This API is needed for a number of reasons, common examples involve any system where distributions in space are important for example in Electromagnetism.

Requirements

For each of the following surface we require that the API has the following requirements:

• The API shall contain a map corresponding to the embedding of the surface into Space d.
• The API shall contain a measure on Space d corresponding to integration over the surface.
• The API shall contain a proof that the above measure has tempered growth.
• The API shall contain a distribution corresponding to the surface.
• The API shall where applicable contain a proof that the surface is of measure zero.

The surfaces these apply to are:

• The spherical shell
• The line
• The solid sphere
• The spherical cylinder
• The solid cylinder
• The thin ring
• The half-plane

Example PRs

Example PRs in this direction include #942.

Corresponding file system

There is as of yet no file system for this API, but we see it sitting in ./SpaceAndTime/Space/Surfaces/

Parent APIs

#854