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FML Concept

<b>FML Concept Document</b><br><br>Hi, this is David from UNSW working of Field Representation Language. I thought I’d share some of the basic concepts and requirements of my work. After speaking to Prof Nielsen at the CellML workshop, I’ll probably incrementally add more features as my PhD progress. Any feedback or suggestion will be greatly appreciated.<br><br><b>Current Requirements for FML:</b><br><ul><li>Boundary representation scheme for spatial field objects</li><ul><li>Topological data structure</li></ul><li>Frame/Field hierarchy support</li><ul><li>Mapping</li><li>Transformation</li><li>Embedding etc</li></ul><li>Field Function Description (Analytical, numeric fields etc)</li><ul><li>Basis Functions</li><li>Parameters, inputs</li><li>Default support for Bezier, Bspline, Nurbs, hermite etc</li><li>Non-Spatial fields?<br></li></ul></ul><br><i>&nbsp;Note 1: Originally FML contains both model relational data (i.e. CellML ref etc) and field &amp; geometrical information. After attending the CellML workshop 2007, it was decided to split the content into ModelML like language for (relational and model&nbsp; data) and FML (field &amp; geometries).<br><br></i><b>Basic Concepts<br><br></b>1)&nbsp; Frame<br><br>A frame declares a perspective with regards to dimension, region etc. A frame encapsulates field information that is dependent on the dimension of that particular perspective.<br><br>2) Frame Hierarchy<br><br>This elements allows a frame tree hierarchy to be constructed. This allows frames to be mapped (mapping, transformation etc) onto other frames. This could be possibly used for both scale or simplify complex model geometries into simpler objects<br><br>3) Fields <br><br>&nbsp;A field is usually contained in a frame container as it contains dimension dependent parameters. It contains field function reference, parameter inputs (control points, weights, dx etc).<br><br>&nbsp;&nbsp;&nbsp; a) Parameters : (control points, weights, dx etc), <br>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; Allow fields to be embedded into other fields through here. <br><br>4) Field Function<br>&nbsp;&nbsp;&nbsp; - Contains Basis Function<br>&nbsp;&nbsp;&nbsp; - Contains Input Declaration<br>&nbsp;&nbsp;&nbsp; - A Field Function declares the mathematical construct. <br>&nbsp;&nbsp;&nbsp; - Bezier, BSpline, Hermite, NURBS. Default Support<br><br>5)&nbsp; Spatial Geometries <br><br>&nbsp;&nbsp;&nbsp; Boundary Representation Scheme, Geometrical and Topological data. The spatial information are encapsulated within the frame container<br><br>&nbsp;&nbsp;&nbsp; 5a)&nbsp; Geometrical Data<br>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; Generally field data (point, curves, surfaces etc)<br>&nbsp;&nbsp;&nbsp; 5b) Topological Data<br>&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; Topological data describes the relational information between geometrical objects.<br><ul><li>Vertex, Edge, Faces are abstract objects that refrences field objects. Geometrical objects describes an object in reference to its local space </li><li>Vertex-Edge Topology</li><li>Edge-Face Topology</li><li>Subdomain, regions topology<br></li></ul>