Class Name: Finite Element Mesh

Superclass - <Primitive Geometry>

Subclasses

Definition

An instance of this DRM class specifies a tesselation of a surface into mesh faces, or of a solid into solid elements. Additional data may be associated with each vertex, mesh face, and / or solid element.

More specifically, a <Finite Element Mesh> instance is comprised of

1. an ordered list of <Vertex> instances, which thus associates an index number to each <Vertex> instance,



2. a <Mesh Face Table> instance, which defines the mesh faces in terms of <Vertex> index numbers,



3. optionally, <Property Table> instances providing additional data (details given below).

Knowledge of which vertices form a mesh face (or solid) is important for various computations, such as interpolation.

Component <Property Table> instances are optional; when present, they are used to define solid elements and to associate data with <Vertex> instances, mesh faces, or solid elements.

Topological information may be optionally included in the <Mesh Face Table>, or in an ECC_MESH_SOLID_SET <Property Table>, depending on whether the <Finite Element Mesh> instance is a surface or a solid. Surface mesh does not have any <Property Table> instances classified as either ECC_MESH_SOLID_SET or ECC_MESH_SOLID_PROPERTY_SET, but may have surface topology in its component <Mesh Face Table>.

A solid mesh shall have a ECC_MESH_SOLID_SET <Property Table>, may have a ECC_MESH_SOLID_PROPERTY_SET <Property Table>, and does not have surface topology in its component <Mesh Face Table>.

The permitted <Property Table> instances are the following.

1. To define solid elements in terms of the mesh faces making up each face of a solid element, a <Property Table> instance with the following constraints.

   <Classification Data>'s tag = ECC_MESH_SOLID_SET

   First <Axis> (a <Regular Axis>):

   Field	Value
   axis_type	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_SOLID_ELEMENT}} assigns an index value to each solid element.
   axis_value_count	total number of solid elements in the table.
   value_unit	EUC_UNITLESS
   value_scale	ESC_UNI

   Second <Axis> (a <Regular Axis>):

   Field	Value
   axis_type	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_SOLID_FACE}}
   axis_value_count	Maximum number of faces on any one solid element.
   value_unit	EUC_UNITLESS
   value_scale	ESC_UNI

   First <Table Property Description>:

   Field	Value
   meaning	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_MESH_FACE}} This is an index into the <Mesh Face Table>, the (i,j)-th cell of which represents the j-th face of the i-th solid. If j is greater than the number of the last face of solid i, the (i,j)-th cell contains zero (0).

   Optional Second <Table Property Description>: Solid topology can be defined by providing a second <Table Property Description>, which 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.

   Note that the presence or absence of this particular component <Property Table> instance determines whether the <Finite Element Mesh> instance is a solid or a surface.

2. To associate data with <Vertex> instances, a <Property Table> instance with

   <Classification Data>'s tag = ECC_MESH_NODE_PROPERTY_SET

   First <Axis> (<Regular Axis>):

   Field	Value
   axis_type	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_MESH_VERTEX}} an index into the ordered <Vertex> list, identifying the <Vertex> instance for which data is being provided
   axis_value_count	total number of <Vertex> instances
   value_unit	EUC_UNITLESS
   value_scale	ESC_UNI

   Additional <Axes> - unconstrained

   <Table Property Descriptions> - unconstrained

3. To associate data with mesh faces, a <Property Table> instance with

   <Classification Data>'s tag = ECC_MESH_FACE_PROPERTY_SET

   First <Axis> (<Regular Axis>):

   Field	Value
   axis_type	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_MESH_FACE}} the index from the <Mesh Face Table>
   axis_value_count	total number of mesh faces in the table
   value_unit	EUC_UNITLESS
   value_scale	ESC_UNI

   Additional <Axes> - unconstrained

   <Table Property Descriptions> - unconstrained

4. To associate data with solid elements (given that a <Property Table> instance ECC_MESH_SOLID_SET has been provided), a <Property Table> instance with

   <Classification Data>'s tag = ECC_MESH_SOLID_PROPERTY_SET

   First <Axis> (<Regular Axis>):

   Field	Value
   axis_type	{ SE_ELEM_CODE_TYP_INDEX, { SE_INDEX_CODE_SOLID_ELEMENT}} the index from the ECC_MESH_SOLID_SET <Property Table>
   axis_value_count	total number of solids in the table
   value_unit	EUC_UNITLESS
   value_scale	ESC_UNI

   Additional <Axes> - unconstrained

   <Table Property Descriptions> - unconstrained

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> instance by

   1. an ordered list of <Vertex> instances (one for each triangle vertex),
   2. a <Mesh Face Table> to define the triangles, an ECC_MESH_FACE_PROPERTY_SET <Property Table> for the gradient data, and
   3. an ECC_MESH_NODE_PROPERTY_SET <Property Table> for the remaining properties.

FAQs

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

Surface mesh does not have any <Property Table> instances classified as either ECC_MESH_SOLID_SET or ECC_MESH_SOLID_PROPERTY_SET, but may have surface topology in its component <Mesh Face Table>.

A solid mesh shall have a ECC_MESH_SOLID_SET <Property Table>, may have a ECC_MESH_SOLID_PROPERTY_SET <Property Table>, and does not have surface topology in its component <Mesh Face Table>.

As a user, where can users obtain further information about <Finite Element Mesh> and its associated <Data Table> instances?

See Part 4 Volume 6, Data Tables Technical Guide, of the SEDRIS Documentation Set.

Constraints

• <<No Attribute Conflicts>>
• <<Non Crossing Aggregations>>
• <<Non Cyclic Aggregations>>
• <<Precedence of Attribute Set Index>>
• <<Colour Mapping Restrictions>>
• <<Continuous LOD Restrictions>>
• <<Image Mapping Functions and Texture Coordinates>>
• <<Nested Primitive Geometry>>
• <<Finite Element Mesh Structure>>

Composed of (two-way)(inherited)

• zero or more {ordered} <Attribute Set Index> instances
• zero or one <Classification Data> instance
• zero or more <Property Table> instances
• zero or more <Property Table Reference> instances
• zero or more <Property Value> instances
• zero or more <Colour> instances
• zero or more {ordered} <Image Mapping Function> instances
• zero or one <Light Rendering Properties> instance
• zero or one <Presentation Domain> instance
• zero or one <Rendering Priority Level> instance
• zero or one <Rendering Properties> instance
• zero or more <Tack Point> instances
• zero or one <Union Of Primitive Geometry> instance (notes)

Composed of (two-way)

• 3 or more {ordered} <Base Vertex> instances (notes)
• one <Mesh Face Table> instance (notes)

Composed of (two-way metadata)(inherited)

• zero or one <Time Constraints Data> instance

Component of (two-way)(inherited)

• one or more <Union Of Primitive Geometry> instances

Inherited Field Elements

Notes

Composed of Notes

Union_Of_Primitive_Geometry

 A <Primitive Geometry> contains a <Union Of Primitive Geometry>
 instance as a component only when that <Primitive Geometry>
 can be decomposed into nested <Primitive Geometry>, as (for
 example) a <Polygon> can be decomposed into subfaces.

Base_Vertex

 Since a <Base Vertex> shall have a <Location>, this provides
 an enumerated collection of <Location> instances.

Mesh_Face_Table

 This is an ECC_MESH_FACE_SET <Data Table>.