On this page:
15.3.1 ???
15.3.2 The Bézier extraction file format
15.3.2.1 bezier_  extraction_  patch
15.3.2.2 control_  points
15.3.2.3 elements
15.3.2.4 element_  blocks
15.3.2.5 cell_  sets
15.3.2.6 extraction_  coefficients
15.3.2.7 dense_  blocks
15.3.3 The Bézier extraction file format
15.3.3.1 Introduction
15.3.3.2 ANSYS LS-DYNA keyword
15.3.3.3 Geometry file formats
15.3.3.3.1 ASCII format
15.3.3.3.2 Binary format
15.3.4 The Exodus Bézier extraction file format
15.3.4.1 Control point information
15.3.4.2 Element information
15.3.4.2.1 Node numbering
15.3.4.3 Coefficient vectors
15.3.4.3.1 Examples
15.3.4.3.1.1 Spline mesh with two elements
15.3.4.3.1.2 Rational spline mesh with four elements
8.5

15.3 File Formats

The following file formats are used to export spline data from Cubit using Bézier extraction. For most applications, the json file format is preffered. The first section describes the current json format exported by Coreform Cubit. Unfortunely, many of the fields in this format were created ad-hoc, and there is a good deal of both repeated and deprecated data. The second section describes a new json format that aims to address these deficiencies. This will eventually completely replace the existing format. The last two sections describe the formats for Bézier extraction files for LS-DYNA and Exodus, respectively.

    15.3.1 ???

    15.3.2 The Bézier extraction file format

      15.3.2.1 bezier_extraction_patch

      15.3.2.2 control_points

      15.3.2.3 elements

      15.3.2.4 element_blocks

      15.3.2.5 cell_sets

      15.3.2.6 extraction_coefficients

      15.3.2.7 dense_blocks

    15.3.3 The Bézier extraction file format

      15.3.3.1 Introduction

      15.3.3.2 ANSYS LS-DYNA keyword

      15.3.3.3 Geometry file formats

        15.3.3.3.1 ASCII format

        15.3.3.3.2 Binary format

    15.3.4 The Exodus Bézier extraction file format

      15.3.4.1 Control point information

      15.3.4.2 Element information

        15.3.4.2.1 Node numbering

      15.3.4.3 Coefficient vectors

        15.3.4.3.1 Examples

          15.3.4.3.1.1 Spline mesh with two elements

          15.3.4.3.1.2 Rational spline mesh with four elements

15.3.1 

15.3.2 The Bézier extraction file format

Changes from the old format:
  • Change node to contol_point throughout.

  • Change to storing an array of degrees.

  • Update dense_coefficient_vectors to just story an array of arrays.

  • Dropped all references to sparse_coefficient vectors, as they are not used. May add in later when they are implemented and documented.

  • Update "coeff" to "coefficient".

  • Update "elem" to "elements".

  • Drop num_coefficient_vectors, as this is only needed in the sparse case.

  • Split into 3 high level objects: control_points, elements, and extraction_coefficients.

  • Rename subdomains to cell_sets.

  • Remove the block_elem_map key, as this information was already stored in the cell_sets.

Design considerations:
  • The goal is to be relatively space efficient while still being human readable. For example, we use element blocks to avoid repeatedly storing element degree and type for every element in the block. However, to maintain readability, some implicit data is also stored explicitly. For example, the number of control points is implicit due to the length of coordinates, but we still store num_control_points.

  • Unless otherwise stated, all indexing is 0-based and internal to the file.

  • Unlike the CellSets in the managers the cell_set filed can only encode dim and dim-1 cells. However, this should be sufficient as an export format.

15.3.2.1 bezier_extraction_patch

A spline object represented in extracted form.

Name

 

Type

 

Description

 

Example

 

Default

patch_id

 

NONNEGATIVE INTEGER

 

A unique patch ID.

 

 

control_points

 

SUB OBJECT

 

See linked documentation

 

 

elements

 

SUB OBJECT

 

See linked documentation

 

 

extraction_coefficients

 

SUB OBJECT

 

See linked documentation

 

 

15.3.2.2 control_points

Name

 

Type

 

Description

 

Example

 

Default

is_rational

 

true|false

 

True if the spline is rational, false if not.

 

 

spatial_dimension

 

NONNEGATIVE INTEGER

 

The spatial dimension.

 

 

num_control_points

 

NONNEGATIVE INTEGER

 

The number of spline control points.

 

 

coordinates

 

[ [ DOUBLE, ... ], ... ]

 

The control point coordiantes. If the spline is rational, these are given in projective space.

 

 

15.3.2.3 elements

Name

 

Type

 

Description

 

Example

 

Default

num_elements

 

NONNEGATIVE INTEGER

 

The total number of Bezier elements.

 

 

num_element_blocks

 

NONNEGATIVE INTEGER

 

The number of element blocks.

 

 

element_blocks

 

LIST

 

An array containing the blocks of elements.

 

 

vertex_connectivity

 

[ [ INTEGER, ... ], ... ]

 

Maps internal cell indexing to internal vertex indexing. Vertex ordering follows the standard s, then t, then u fastest ordering. Note: These vertex ids are not the control point ids. They correspond to vertices in the underlying Bezier mesh.

 

 

cell_sets

 

LIST

 

Encodes cell sets in the patch.

 

 

15.3.2.4 element_blocks

An array containing the blocks of elements.

Name

 

Type

 

Description

 

Example

 

Default

element_type

 

STRING

 

The type of element "Cube", "Simplex", or "Pyramid".

 

 

degree

 

[ NONNEGATIVE INTEGER, ... ]

 

Degree of the Bernstein basis on elements in the block.

 

 

num_elements

 

NONNEGATIVE INTEGER

 

Number of elements in this block.

 

 

num_control_points

 

NONNEGATIVE INTEGER

 

Number of control_points for each element in this block.

 

 

control_point_ids

 

[ [ NONNEGATIVE INTEGER, ... ], ... ]

 

The control point ids that define the elements in this block.

 

 

coefficient_vector_ids

 

[ [ NONNEGATIVE INTEGER, ... ], ... ]

 

The coefficient vector ids that define the elements in this block.

 

 

15.3.2.5 cell_sets

Encodes cell sets in the patch.

Name

 

Type

 

Description

 

Example

 

Default

cell_set_id

 

NONNEGATIVE INTEGER

 

External cell group id.

 

 

cell_set_name

 

STRING

 

Name for this cell set.

 

 

cells

 

[ [ INTEGER, ... ], ... ]

 

An array of pairs. The first entry of each pair is the internal cell id, and the second is the cell side index. For cube-type cells, the sides are indexed as follows: s=1 : 0 , s=0 : 1 , t=1 : 2 , t=0 : 3 , u=1 : 4 , u=0 : 5 , and -1 denotes the cell interior.

 

 

15.3.2.6 extraction_coefficients

Name

 

Type

 

Description

 

Example

 

Default

num_dense_blocks

 

NONNEGATIVE INTEGER

 

The number of dense blocks.

 

 

dense_blocks

 

LIST

 

 

 

15.3.2.7 dense_blocks

Name

 

Type

 

Description

 

Example

 

Default

num_coefficient_vectors

 

NONNEGATIVE INTEGER

 

 

 

vector_length

 

NONNEGATIVE INTEGER

 

The length of each coefficient vector in this block.

 

 

coefficient_vectors

 

[ [ DOUBLE, ... ], ... ]

 

 

 

15.3.3 The Bézier extraction file format

15.3.3.1 Introduction

The support of novel computer-aided geometric descriptions forming a potential future basis of isogeometric analysis in ANSYS LS-DYNA is discussed in the present document. In particular, the design of a new keyword as well as the structure of the geometry input file meant to replace the current method using the *INCLUDE_TRANSFORM keyword is outlined. It is also aimed to generalize the geometric description as well as to focus on compressed storage in order to enable the run of larger and more complex examples.

The remaining part of the document is structured as follows. The new LS-DYNA keyword is introduced in ANSYS LS-DYNA keyword. Supported geometry file formats are discussed in Geometry file formats in greater depth.

15.3.3.2 ANSYS LS-DYNA keyword

The *IGA_INCLUDE_{OPTION1}_{OPTION2} keyword is introduced to import geometry files to LS-DYNA with BEZIER being one of the supported first optional arguments and blank or TRANSFORM as second optional argument, i.e.

Card 1

   

1

   

2

   

3

   

4

   

5

   

6

   

7

   

8

Variable

   

FILENAME

Type

   

C


Card 2

   

1

   

2

   

3

   

4

   

5

   

6

   

7

   

8

Variable

   

TYPE

   

PID

   

DIM

   

Type

   

I

   

I

   

I

   

Default

   

none

   

none

   

none

   


Card 3

   

1

   

2

   

3

   

4

   

5

   

6

   

7

   

8

Variable

   

IDPOFF

   

FCTLEN

   

TRANID

   

Type

   

I

   

F

   

I

   


Variable

   

Description

FILENAME

   

Name of file to be included

TYPE

   

File type
1 – ASCII
2 – LSDA

PID

   

Part ID

DIM

   

Parametric dimensions
1 – Curve
2 – Surface
3 – Volume

DIM

   

Offset patch ID

IDPOFF

   

Length transformation factor

FCTLEN

   

Transformation ID

Remarks:
  1. One file per *IGA_INCLUDE_BEZIER keyword. The file, however, may contain multiple patches with the same part ID and parametric dimension (PID and DIM on Card 2), i.e. section and material. Notably, default section properties may be modified on a patch-by-patch basis; e.g., integration rule, number of interpolation elements.

  2. The optional Card 3 contains fields from the INCLUDE_TRANSFORM keyword relevant for geometric entities extended with an offset of patch IDs. The capability to offset patch IDs is important if one wants to include the same file and affinely transform its content to define a new part—e.g., four tires of a car—or if standard NURBS and Bézier extraction-based geometries are combined within a model.

15.3.3.3 Geometry file formats

The key differences with respect to the previous format are as follows:

  1. Reduced storage: Bézier extraction operators are not stored in their full form henceforth. In what follows, we distinguish between tensor product, non-tensor-product, and mixed elements. A -dimensional tensor product element is defined by d local knot vectors. A non-tensor-product element is defined by a set of coefficient vectors essentially representing a row in the Bézier extraction operator. Elements with mixed tensor and non-tensor-product structure, e.g. prism cf. ASCII format may be defined using a combination of local knot and coefficient vectors.

  2. Sorted input: Local knot and coefficient vectors are collected into sorted blocks comprised in a library. Element definitions use local knot and/or coefficient vector identifiers, i.e. pointers to the entries of the library. Furthermore, a coefficient vector may be stored using either the dense or sparse storage formats. Noting that the latter may be beneficial as the element dimension increases but complicate the export of the data, the choice to invoke different storage formats is left to the preprocessor. Assuming, for instance, that tensor product elements are used to define most part of the discretization and non-tensor-product elements occur in the vicinity of a few extraordinary points only, it might be easier to export the data in dense format only.

  3. Format and precision: In order to ensure consistency with the binary input, cf. Binary format, a fixed input format is proposed using (due to the relative indexing) short integers, i.e. , and double precision reals of the form 1PE24.16. Consequently, each line may contain up to ten integers or five reals yielding lines of up to 80 or 120 character long, respectively.

For brevity, local knot vectors are also referred to as coefficient vectors henceforth.

15.3.3.3.1 ASCII format

The following structured input has to be written for each patch separately, i.e.

BLOCK 1 - PATCH

PID, NN, NE, NCV, WFL

Total number of lines: 1


BLOCK 2 - NODES

For each node :

Total number of lines: NN


BLOCK 3 - ELEMENTS

For each element subblock :

For each element subblock :

(as many lines as needed

(as many lines as needed

Total number of lines:


BLOCK 4 - COEFFICIENT VECTORS

NDCVB, NSCVB

For each dense subblock :

NCV, NCVC

For each sparse subblock :

NCV, NCVC

For each coefficient vector in dense subblock :

CVC1, CVC2, ...,CVC (as many lines as needed)

For each sparse subblock :

CVI1, CVI2, ...,CVI (as many lines as needed)

CVC1, CVC2, ...,CVC (as many lines as needed)

Total number of lines:


Variable

  

Description

PID

  

Patch ID

NN

  

Number of nodes/control points.

NE

  

Number of elements

NCV

  

Number of coefficient vectors

WFL

  

Control weight flag
0 – Polynomial
1 – Rational

  

Nodal coordinates of the -th node

  

Nodal weights of the -th node

NEB

  

Number of sorted element sub-blocks: i.e., based on the element type, number of nodes, number of coefficient vectors, and polynomial degrees used in their definition, elements are sorted into subblocks

  

Type of elements in the -th subblock
0 – Cube (tensor product)
1 – Cube (non-tensor-product)
2 – Simplex (non-tensor-product)
3 – Prism (tensor product in one direction only)

  

Number of elements in the -th subblock

  

Number of nodes defining an element in the -th subblock

  

Number of coefficient vectors defining an element in the -th subblock

  

Polynomial degree in the r-direction for elements in the -th subblock

  

Polynomial degree in the s-direction for elements in the -th subblock

  

Polynomial degree in the t-direction for elements in the -th subblock

  

Node IDs defining the element connectivity, in the -th subblock

  

Coefficient vector IDs defining the element, in the -th subblock

  

Number of \textit{sorted} coefficient vector blocks using dense storage format, i.e. the coefficient vectors are stored into sub-blocks based on their length.

  

Number of \textit{sorted} coefficient vector blocks using the sparse storage format, .e. the coefficient vectors are stored into sub-blocks based on their length.

  

Number of dense (sparse) coefficient vectors in the -th (-th) sub-block.

  

Number of dense (sparse) coefficient vector components in the -th (-th) sub-block.

  

Coefficient vector components using the dense (sparse) storage format in the -th (-th) sub-block.

  

Coefficient vector index, (sparse format only)

Remarks:
  1. Element and node IDs are local/relative to the patch and therefore are not defined at input. Consequently, there is no need to offset them on the optional Card 3.

  2. A cube may be defined in two and three dimensions (quadrilateral and hexahedron). Simplexes exist in all three dimensions (line, triangle, tetrahedron). A prism is a five-sided polytope defined in three dimensions and bounded by two triangular caps and three rectangular faces.

  3. For the sake of generality, a non-tensor-product cube (ETYPE=1) may also be used to define tensor product cubes (ETYPE=0). This may be useful in case local knot vectors can not be retrieved from Bézier extraction operators in higher dimensions.

15.3.3.3.2 Binary format

In addition to the ASCII format outlined in the previous section, we intend and in most industrial cases prefer to support binary storage of the geometry using the open LSDA format and API developed and maintained by LSTC. Invoking the binary format will further reduce storage requirements, speeding up I/O. The data should be written using the following path: "keyword/[option]/patch[i8.8]/" where "[option]" is either "isoshell" or "isosolid" for two and three-dimensional patches, respectively.

15.3.4 The Exodus Bézier extraction file format

This document describes a standard format for exporting Bézier extraction information in the Exodus-II file format, v8.03 and newer (simply referred to as the Exodus format for the remainder of this document). We leverage the existing attribute capability in Exodus to output the data needed for Bézier extraction, including control point weights, additional element information, and coefficient vector information. In the following sections, we establish a set of common attribute names used to tag this information.

15.3.4.1 Control point information

Control point information in Bézier extraction is always encoded in homogeneous form. Nodal values, such as spatial coordinates, are always transfered to projective space through a multiplication by their respective weights. The spline control points are written to Exodus in homogeneous form as nodal control points using ex_put_coord. The nodal weights are stored as nodal attribute, bex_weight, as described below.

EX_NODAL

bex_weight

   

Description

   

Control weights associated with the control points

   

Attribute type

   

EX_DOUBLE

   

Array size

   

num_nodes

In the table above, the () symbol indicates that the attribute is optional. If all control weights are one, as is the case for non-rational geometry, this attribute may be omitted. If no bex_weight attribute is specified, the weights are implied to be equal to 1.0.

15.3.4.2 Element information

To explicitly denote Bézier elements, they are named according to established Exodus element names with a BEX_ prefix. It is important to note that Bézier elements diverge from classical Exodus elements in a few important regards.

For reference, the corresponding parametric dimension and degree vector length, num_deg, for each element type are given in the table below:

Exodus element name

   

   

num_deg

BEX_CURVE

   

1

   

1

BEX_QUAD

   

2

   

2

BEX_TRIANGLE

   

2

   

1

BEX_HEX

   

3

   

3

BEX_TETRA

   

3

   

1

BEX_WEDGE

   

3

   

2

Note that the Bézier extraction format does not currently support pyramid elements.

15.3.4.2.1 Node numbering

The node numbering for the Exodus Bézier elements follows an , then , then fastest ordering. While this is a departure from the node ordering traditionally used in Exodus, it is necessary for easily supporting elements with arbitrary polynomial degree. Figure 601 through Figure 605 give examples of this node ordering on quadratic elements.

Figure 606 gives an example of this indexing scheme on a Bézier hexahedron with polynomial degree .

Figure 601: Node ordering for a BEX_CURVE element with degree .

Figure 602: At left: Node ordering for a BEX_QUAD element with degree . At right: Node ordering for a BEX_TRIANGLE element with degree

Figure 603: Node ordering for a BEX_HEX element with degree . From left to right, the figures show the nodes corresponding to slices at , , and , respectively.

Figure 604: Node ordering for a BEX_WEDGE element with degree . From left to right, the figures show the nodes corresponding to slices at at , , and , respectively.

Figure 605: Node ordering for a BEX_TETRA element with degree . From left to right, the figures show the nodes corresponding to slices at at at , , and , respectively.

Figure 606: Node ordering for a BEX_HEX element with degree . From left to right, the figures show the nodes corresponding to slices at at at , , and , respectively.

15.3.4.3 Coefficient vectors

The final set of attributes that must be stored are the extraction operator coefficient vectors. Many Bézier extraction file formats allow for both dense and sparse storage of coefficient vectors. Dense storage entails storing every coefficient vector entry for the extraction operators on multivariate () elements. Sparse storage is an optimization scheme for tensor-product elements, wherein only the coefficient vectors for univariate extraction operators are stored. The coefficient vectors for tensor product elements can then be computed from the tensor product of these univariate coefficient vectors. As an example, the coefficient vector for a degree BEX_QUAD element

can be computed as the Kronecker product of two univariate coefficient vectors

Currently, only dense coefficient vector storage has been specified for Exodus, but sparse storage will be added in the future. The coefficient vector is stored as an EX_BLOB with name bex_cv_blob Let NDCVB denote the number of dense coefficient vector blocks in the file. The attributes and variables stored on the blob are given in the table below.

EX_BLOB

bex_dense_cv_info

   

Description

   

Array containing the number of coefficient vectors and coefficient vector lengths for each dense block.

   

Attribute Type

   

EX_INTEGER

   

Array size

   

2 * NDCVB

bex_dense_cv_blocks

   

Description

   

Array containing the coefficient vector values

   

Variable Type

   

EX_DOUBLE

   

Array Size

   

bex_dense_cv_info

In the case of an Exodus file with transient data, the bex_dense_cv_blocks variable will always be stored at the first time step time_step=1.

15.3.4.3.1 Examples

In this final section, we supply three simple examples to illustrate how Bézier extraction information is encoded in the Exodus format.

15.3.4.3.1.1 Spline mesh with two elements

In this first example, we save a simple two element U-spline to an Exodus file. The mesh is a simple rectangle composed of two biquadratic elements, and the interelement continuity is one. Using Coreform Cubit, the Exodus file can be generated with the following commands:

reset create surf rect width 2 height 1 move surf 1 x 1 y 0.5 surf 1 size 1 mesh surf 1 uspline surf 1 export uspline 1 exodus ’two_elem_example’

The resulting U-spline surface is shown in figure 607.

Figure 607: Schematic of the simple U-spline surface created by the Coreform Cubit commands shown above. The surface is composed of two biquadratic Bézier elements, and , with continuity between elements. The global control points are shown in red.

Attribute or variable name

   

Value

xcoord

   

{ 2.0, 2.0, 2.0, 1.5, 1.5, 1.5, 0.5, 0.5, 0.5, 0.0, 0.0, 0.0 }

ycoord

   

{ 1.0, 0.5, 0.0, 1.0, 0.5, 0.0, 1.0, 0.5, 0.0, 1.0, 0.5, 0.0 }

zcoord

   

{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

Attribute or variable name

   

Value

elem_type

   

BEX_QUAD

num_elem_blk

   

2

num_entries_per_elem

   

18

bex_elem_degrees

   

{ 2, 2 }

connect

   

{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 12, 6, 15, 9, 3, 13, 7, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 10, 4, 17, 11, 5, 14, 8, 2 }

Attribute or variable name

   

Value

bex_dense_cv_info

   

{18, 9}

bex_dense_cv_blocks

   

{ 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

15.3.4.3.1.2 Rational spline mesh with four elements

This example shows just the data entries for a four element mesh of a quarter section of a plate with a hole.

Figure 608: Quarter segment of a plate with a hole.

Attribute or variable name

   

Value

xcoord

   

{1,1.25,1.75,0.92388,1.25,1.75,0.382684,0.56066,0.853553,2,2,2,0,0,0,1,0}

ycoord

   

{0,0,0,0.382684,0.56066,0.853553,0.92388,1.25,1.75,0,1,2,1,1.25,1.75,2,2}

zcoord

   

{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }

bex_weight

   

{ 1, 1, 1, 0.92388, 1, 1, 0.92388, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

Attribute or variable name

   

Value

elem_type

   

BEX_QUAD

num_elem_blk

   

4

num_entries_per_elem

   

18

bex_elem_degrees

   

{ 2, 2 }

connect

   

{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 31, 23, 19, 16, 13, 11, 8, 4, 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 28, 30, 14, 15, 6, 7, 20, 12, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 28, 21, 17, 29, 22, 18, 10, 5, 2, 5, 6, 8, 9, 12, 14, 15, 16, 17, 24, 26, 25, 27, 20, 8, 9, 12, 3 }

Attribute or variable name

   

Value

bex_dense_cv_info

   

{31, 9}

bex_dense_cv_blocks

   

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