Lattice Geometry

Contents

• 20.1 Introduction
• 20.2 Using the graph reader
• 20.3 Graph types
  • 20.3.1 Cylinder data blocks
  • 20.3.2 Cone data blocks
• 20.4 Checking lattices
• 20.5 Creating a blended lattice
  • 20.5.1 Blended lattices with lballs of the same blend size
  • 20.5.2 Blended lattices with lballs of various blend sizes
• 20.6 Creating a lattice structure from a core lattice
  • 20.6.1 Deforming the pattern
• 20.7 Creating a lattice-like mesh body
• 20.8 Creating a facet body from a lattice
• 20.9 Clipping a lattice to fit your model
• 20.10 Lattice specific operations

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20.1 Introduction

Lattices are classified as a geometry type which can be created, enquired of, rendered and attached to parts as construction geometry. Lattices can be used to create mesh geometry as well as solid convergent bodies. Furthermore, you can create a lattice structure from a smaller core lattice. Lattices can be rendered as straight lines, or as solid spheres linked by cylindrical or conical rods (as illustrated in Figure 20-1).

Figure 20-1 Lattice geometry

Lattices are represented as collections of lballs joined by lrods (collectively known as lattice topology or ltopols). The radii of lrods can be different where they meet at a common lball, as illustrated in Figure 20-2.

Figure 20-2 Lattice with lrods of different radii meeting at a common lball

Parasolid provides the function PK_LATTICE_create_by_graph to allow you to create an orphan lattice geometry from data supplied by a user-defined callback function.

The function receives the following arguments:

The function has the following options:

Figure 20-3 Snapping lballs together that lie within a supplied snap_tolerance

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20.2 Using the graph reader

This section describes how the callback function, graph_reader , is used to create lattice geometry from graph data. The graph_reader takes a block of user supplied context information and should return a block of lattice data and a return status. The block of lattice data can be one of two types; cylinder or cone. See Section 20.3, “Graph types” for more information.The return status indicates the state of the operation. The graph_reader is called repeatedly by PK_LATTICE_create_by_graph until it returns the status PK_LATTICE_cb_status_stop_c.

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20.3 Graph types

This section describes the two types of data blocks (cylinder and cone) that can be returned by each call to graph_reader .

20.3.1 Cylinder data blocks

This structure contains the data block for lattices with cylindrical shaped lrods. The lballs are provided by arrays of lball_positions and lball_radii . The lrod_start_indices and lrod_end_indices arrays define an array of lrods by specifying the absolute indices of the pair of lballs that each lrod joins.

Individual blend sizes of the lballs within the data block can be supplied via lball_blend_sizes . If the lattice is to be blended, these sizes together with the value of the lball_blend_type option determine the radii of the blends applied at each of the lballs. See Section 20.5.2, “Blended lattices with lballs of various blend sizes” for more information.

The following pseudo-code example shows the data input when using PK_LATTICE_graph_cyl_t to transmit a block of lattice data.

n_lball_positions = 7

lball_positions = {b0,b1,b2,b3,b4,b5,b6}

lball_radii = {br0,br1,br2,br3,b4r,br5,br6}

lball_blend_sizes = NULL

n_lrod_indices = 12

lrod_start_indices = {0,0,0,0,0,0,1,2,3,4,5,1}

lrod_end_indices = {1,2,3,4,5,6,2,3,4,5,6,6}

lrod_radii = {lr0,lr1,lr2,...,lr11}

status = PK_LATTICE_cb_status_stop_c

20.3.2 Cone data blocks

This structure contains the data block for lattices with cone-shaped lrods. The lballs are provided by arrays of lball_positions and lball_radii .The lrod_start_indices and lrod_end_indices arrays define an array of lrods by specifying the absolute indices of the pair of lballs that each lrod joins.

Individual blend sizes of the lballs within the data block can be supplied via lball_blend_sizes . If the lattice is to be blended, these sizes together with the value of the lball_blend_type option determine the radii of the blends applied at each of the lballs. See Section 20.5.2, “Blended lattices with lballs of various blend sizes” for more information.

The following pseudo-code example shows the data input when using PK_LATTICE_graph_cone_t to transmit a block of lattice data.

n_lball_positions = 7

lball_positions = {b0,b1,b2,b3,b4,b5,b6}

lball_radii = {br0,br1,br2,br3,b4r,br5,br6}

lball_blend_sizes = NULL

lball_lrod_radii = NULL

n_lrod_indices = 12

lrod_start_indices ={0,0,0,0,0,0,1,2,3,4,5,1}

lrod_end_indices = {1,2,3,4,5,6,2,3,4,5,6,6}

lrod_start_radii = {lsr0,lsr1,lsr2,...,lsr11}

lrod_end_radii = {ler0,ler1,ler2,...,ler11}

status = PK_LATTICE_cb_status_stop_c

Figure 20-4 shows an example of a lattice structure

Figure 20-4 Example of lattice structure

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20.4 Checking lattices

You can use PK_GEOM_check to check lattice structures for invalidities. See PK_check_fault_t, for a list of faults that may be returned.

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20.5 Creating a blended lattice

You can optionally choose to create a blended lattice using a number of options in PK_LATTICE_create_by_graph. Blending a lattice allows you to increase the stiffness of the lattice thereby improving its structural strength.

Lattices can be blended in the following ways:

• Create a blended lattice where the blend size applies globally to all lballs in the lattice. See Section 20.5.1, “Blended lattices with lballs of the same blend size”, for more information.
• Create a blended lattice where the blend size applies locally to lballs in the lattice. See Section 20.5.2, “Blended lattices with lballs of various blend sizes”, for more information.

20.5.1 Blended lattices with lballs of the same blend size

Using the lball_blend_type and the lball_blend_size options, you can create a blended lattice whose lballs have the same blend size, where each lball’s blend radius is either a constant or a constant multiple of the lball’s radius. The lball_blend_type option has the following values:

Figure 20-5 Blended lattices whose lballs have the same blend size

20.5.2 Blended lattices with lballs of various blend sizes

Alternatively you can vary the blend size of lballs within the lattice by using the lball_blend_sizes option in the graph_reader callback. In this case, each lball’s blend radius is the corresponding value in lball_blend_sizes , optionally multiplied by the lball’s radius depending on the value of the lball_blend_type option (see table in Section 20.5.1, “Blended lattices with lballs of the same blend size” for a list of these values). Figure 20-6, illustrates where the blends are applied locally with smaller blend radii applied at the larger lballs. See Section 20.3, “Graph types” for more information on the graph reader callback function.

Figure 20-6 Blended lattice whose lballs have different blend sizes

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20.6 Creating a lattice structure from a core lattice

You can create a new lattice from patterned repetitions of a supplied core lattice using PK_LATTICE_make_patterned.

It has the following options:

The cell , which contains the core input lattice that is to be repeated, tessellates to create a pattern of cells which come together to form a new lattice. This is illustrated in Figure 20-7, with the bound option set to (-2 2) in all three directions.

Figure 20-7 Creating a new lattice from a patterned repetition of a supplied lattice

20.6.1 Deforming the pattern

Optionally, you can use the form option and/or the callback option to relocate and deform the supplied pattern. The form option specifies the type of pattern supplied along with the data of the pattern. The type can be one of the following values:

The callback option can be also be used to geometrically deform the supplied pattern. The option takes user supplied information to deform patterned positions. Figure 20-8 shows a core lattice being deformed using the callback to create a patterned lattice, with the bound option set to (0 4) in two directions and (0 0) in the other direction. See the PK Interface Programming Reference Manual for more information on the callback option.

Figure 20-8 Creating a lattice by relocating and deforming a pattern using the callback option

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20.7 Creating a lattice-like mesh body

You can use PK_BODY_make_patterned to create a lattice-like mesh body by patterning a facet body as illustrated in Figure 20-9 with the bound option set to (-2 2) in all three directions. If you supply a sheet body then it must be open such that its laminar edges match neighbouring repetitions.This function has the same options as PK_LATTICE_make_patterned. For more information on these options, see Section 20.6, “Creating a lattice structure from a core lattice”.

Figure 20-9 Creating a lattice-like mesh body

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20.8 Creating a facet body from a lattice

You can create a solid body from lattice geometry using PK_LATTICE_make_bodies. The solid body can have one or more closed mesh faces. See the PK Interface Programming Reference Manual for more information on this function.

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20.9 Clipping a lattice to fit your model

The process of trimming or cutting down a lattice to fit a model, or a sub-set of a model, is referred to as clipping. You can clip a lattice with one or more clip entities using PK_LATTICE_clip. See Section 55.6, “Clipping Lattices”, for more information.

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20.10 Lattice specific operations

Parasolid provides the following functions for enquiring about lattices and their substructures:

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