AIF Mesh

A naïve and high-level implementation of the Adjacency and Incidence Framework mesh data-structure.

Original papers by Frutuoso G. M. Silva & Abel J. P. Gomes:

• A B-Rep Data Structure for Polygonal Meshes
• Adjacency and Incidence Framework - A Data Structure for Effecient and Fast Management of Multiresolution meshes.

Platform

The implementation is written in Javascript and uses Maps, Sets, and for-of statements that are part of the ECMAScript version 6 speicification still under development.

However, most modern browsers, and Node.js v0.11 with the --harmony flag, can run these just fine right now.

Transpiled ES5 versions have still been included for the UMD and CommonJS versions regardless. The CommonJS version, or rather, the NPM module, automatically loads the ES5 version if the ES6 one fails to. But the specific UMD version will have to be added to an HTML file manually.

UMD version exports the global namespace aifm.

Brief Outline

All the geometric elements of the mesh only contain references to their adjacent and incident elements.

These elements also have querying functions to retrieve their immediate and extrapolated references: $verts, $edges, $faces all respective return adjoint verts, edges, and faces of any vert, edge, or face.

Furthermore, each of these functions return the results in a special (Es6) Set-like object which has the same querying methods that it runs on all collected elements and return another such Set-like object. Queries can be chained with this.

The adjacency and incidence relations are all that the structure concerns itself with. Any other information, such as coordiantes of the verts, or metadata of a particular face, should go on the arbitrary object of the annotation property. The BasicMesh does exactly that.

The mesh object, however, does expose all its concent verts, edges, and faces as (ES6) Map objects for batch processing required by any algorithm that uses these structures.

Documentation, Tests, etc.

Having written this implementation for a quick prototype, I haven't had the chance to write any of it. If my prototype gets anywhere, I plan on cleaning it up with proper API documentation, tests, and usage examples.

( It'll still be a bit weird what with relying on ES6 features despite not being an ES6 module or using ES6 classes. In particular trying to extend the built-in Set class was an attempt in futility that the ES6 classes promise to fix. )

The source file aifm-es6.js should be sensible enough to infer usage, I think. Please take a look there if you want more!

Roadmap

1. Add a cell element relations and naïve addVolume helpers.
   • Validating potentially degenerate arbitrary valence cells on SimpleMesh is out of the question! Let it focus on being a surface-mesh.
2. Properly document API and usage.
3. Add badges!
4. Figure out why UMD builds cannot be required by other UMD builds. (set-algebra, in this case, when externalized.)
5. Implement a tetra-mesh volume mesh with proper validation.