Class Name: Finite Element Mesh

Superclass - Primitive Geometry

Definition

A Finite Element Mesh is a tesselation of a surface (or a solid) into Mesh Faces (or solid elements). There may be data associated with each vertex and/or Mesh Face (and/or solid element). Knowing which vertices form a mesh face (or solid) is important for interpolation and other computations.

A Finite_Element_Mesh is comprised of an ordered list of Vertices that associates an index number to each vertex and a Mesh Face Table that defines the mesh faces by mesh face index number in terms of Vertex index numbers. Optional Property Tables provide additional data (Table Property Descriptions) by including a vertex number Axis or a Mesh Face number Axis. If a Property Table of type Solid Element Definition Table is included, then other Property Tables having a solid element number Axis Finite Element Mesh components as well.

Topological information may be optionally included in a Mesh Face Table or in a Solid Element Definition Table.

Primary Page in DRM Diagram:

• 5

Secondary Pages in DRM Diagram:

• 18

Example

1. In support of a rain run-off computational model, a ground surface area is triangulated. At each triangle vertex, the gradient, porosity, flow resistance, water capacity, and rain rate are measured. This data set is represented in a Finite Element Mesh object by an ordered list of Vertex objects - one for each triangle vertex, a Mesh Face Table to define the triangles, a Property Table of data_table_type EDCS_CC_MESH_FACE_PROPERTIES_TABLE for the gradient data, and a Property Table of data_table_type EDCS_CC_MESH_VERTEX_PROPERTIES_TABLE for the remaining properties.

FAQs

What are the expected data_table_types of Finite Element Mesh component Property Tables?

Component Property Tables are used to optionally define solid elements and to associate Table Property Description data to Vertices, Mesh Faces, or solid elements. The allowed Property Tables are:

• For Vertex data -
  • data_table_type = EDCS_CC_MESH_VERTEX_PROPERTIES_TABLE
  • First Axis (Regular Axis):
    • axis_type = EDCS_AC_INDEX_TO_MESH_VERTEX, which indexes into the ordered Vertex list.
    • axis_value_count = total number of Vertices
    • axis_unit = SE_UNITS_INDEX
  • Additional Axes - unconstrained
  • Table Property Descriptions - unconstrained

• For Mesh Face data -
  • data_table_type = EDCS_CC_MESH_FACE_PROPERTIES_TABLE
  • First Axis:
    • axis_type = EDCS_AC_INDEX_TO_MESH_FACE, which is the index from the Mesh Face Table
    • axis_value_count = total number of Mesh Faces in the table.
    • axis_unit = SE_UNITS_INDEX
  • Additional Axes - unconstrained
  • Table Property Descriptions - unconstrained

• For solid element data, a solid element definition table is required - This table defines the solid elements in terms of the Mesh Faces that make up each face of a solid element:
  • data_table_type = EDCS_CC_SOLID_ELEMENT_TABLE
  • First Axis:
    • axis_type = EDCS_AC_INDEX_TO_SOLID_ELEMENT that assigns an index value to each solid element.
    • axis_value_count = total number of solid elements in the table.
    • axis_unit = SE_UNITS_INDEX
  • Second Axis:
    • axis_type = EDCS_AC_INDEX_TO_SOLID_FACE
    • axis_value_count = Maximum number of faces on any one solid element.
    • axis_unit = SE_UNITS_INDEX
  • First Table Property Description:
    • Is the Mesh Face number in the component Mesh Face Table that represents the j-th face of the i-th solid (=0 if j>#of last listed face of solid i, in other words zero fill).
    • attribute_code = EDCS_AC_INDEX_TO_MESH_FACE
  • Optional Second Table Property Description:
    Solid topology is optionally defined by the second Table Property Description that gives the index in this table of the solid element that is adjacent on this face (the value for the (i,j)-th cell is k if the j-th face of solid i is also a face of solid k). If the face is not shared, the value is 0.

• To assign data to solid elements a Solid Element Properties Table is required -
  • data_table_type = EDCS_CC_SOLID_ELEMENT_PROPERTIES_TABLE
  • First Axis:
    • axis_type = EDCS_AC_INDEX_TO_SOLID_ELEMENT, which is the index from the EDCS_CC_SOLID_ELEMENT_TABLE Property Table
    • axis_value_count = total number of solids in the table.
    • axis_unit = SE_UNITS_INDEX
  • Additional Axes - unconstrained
  • Table Property Description - unconstrained

What is the difference between a surface and a solid Finite Element Mesh?

Surface mesh does not have either a Solid_Element_Definition_Table or a Solid_Element_Properties_Table, and may have surface topology in its component Mesh Face Table. A solid mesh must have a Solid_Element_Definition_Table and may have a Solid_Element_Properties_Table and does not have surface topology in its component Mesh Face Table.

How does a data producer build a Finite Element Mesh?

This is a multi-stage process.

1. Build the ordered Vertex list.
2. Build the Mesh Face Table.
   1. Add its first Table Property Description.
   2. If surface topology is to be specified, then the second Table Property Description of adjacent Mesh Face numbers are inserted.
3. If the mesh is a solid mesh, build the Solid_Element_Definition_Table.
   1. Add its first Table Property Description.
   2. If solid topology is specified, add the second Table Property Description of adjacent solid numbers.
4. Build the remaining component Property Table (if any).

Constraints

• No Attribute Conflicts
• Non Crossing Aggregations
• Non Cyclic Aggregations
• Precedence of Attribute Set Index
• Color Mapping Restrictions
• Image Mapping Functions and Texture Coordinates
• Nested Primitive Geometry
• Non Nestable Continuous LOD

Composed of (one-way)(inherited)

• optionally, some {ordered} Attribute Set Indices
• optionally, a Classification Data
• optionally, some Property Tables
• optionally, some Property Table References
• optionally, some Property Values
• optionally, some Tack Points
• optionally, some {ordered} Colors
• optionally, a Light Rendering Properties
• optionally, a Rendering Properties
• optionally, some {ordered} Image Mapping Functions
• optionally, a Rendering Priority Level

Composed of (one-way)

• an unbounded set of {ordered} Base Vertices[3...] (notes)

Composed of (two-way)(inherited)

• optionally, a Union of Primitive Geometry

Composed of (two-way)

• one Mesh Face Table (notes)

Composed of (one-way metadata)(inherited)

• optionally, a Time Constraints Data

Component of (two-way)(inherited)

• one or more Union of Primitive Geometries

Notes

Composed of Notes

Base_Vertex

 Since a <Base Vertex> must have a <Location>, this gives us
 an enumerated collection of <Locations>.

Mesh_Face_Table

 a <Polygon> definition <Data Table>