Background

A lattice configurator declares the referenced volume region to be restricted according to the lattice cell pattern. As a consequence, the optimizer can only change the structural topology within the lattice thickness limits imposed by the configurator.

Note that in ProTOp the term lattice cell has a generalized meaning in the sense that a lattice cell can be either of a

• line-based type
or of a
• surface-based type.

Line-based cells are defined by a set of straight center lines with a separately specified thickness. On the other hand, surface-based cells are defined by a midsurface with a separately specified thickness in its normal direction. Consequently, geometrically seen, a

• line-based cell is a set of straight bars, while a
• surface-based cell is a curved shell.

█ Input data

The following obligatory or optional data has to be provided.

Volume region
Defines the volume region to be configured by this configurator.

Coordinate system
Defines the coordinate system used in computing the lattice cell geometry and positions.

Configurator range
These parameters define the range within the referenced volume region where the configurator will enforce the lattice structure. If skipped, the lattice structure is enforced within the whole referenced volume region. Note that the interpretation of the range parameters (from lower limit; to upper limit) depends on the chosen coordinate system type. For example, in a cylindrical coordinate system the Range X applies to the radius parameter.
NOTE. If the lower and upper range limits for a certain direction are the same, the corresponding range limitation in the same direction is ignored.

Thickness limits
Range Min: [0.0, ~]
Range Max: [>Min, ~]
These parameters define the minimal and maximal allowed thickness of either individual cell bars or cell shell. Note that the Max parameter must be greater than the Min parameter.

Initial thickness
Range: [-1.0, +1.0]
This parameter defines the initial relative thickness of cell bars or shell. A value of -1.0 corresponds to minimal thickness and a value of +1.0 corresponds to maximal thickness.

Cell type and rotation
Defines the cell type (see tables below) used in generating the lattice structure and its rotation. Three 90-degrees rotations (around A, B, and C edges) of the cell are possible in order to orient the cell as desired.

Table. The following line-type cells are currently available

Cell	Parameters
	A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA * Sqrt(3) B = CellSizeB C = CellSizeC d = Thickness
	A = CellSizeA * Sqrt(3) B = CellSizeB C = CellSizeC d = Thickness

Table. The following surface-type cells are currently available

Cell	Surface type and parameters
	Surface type = Gyroid A = CellSizeA B = CellSizeB C = CellSizeC d = Thickness

Cell line subdivisions
Range: [0, 5]
This parameter defines the number of subdivisions when computing the geometry of an individual cell bar. An individual cell bar is in general a straight line. In a curvilinear coordinate system, however, it can also become curvilinear, if it is subdivided and running along a curvilinear axis.
NOTE. The subdivision option is only available for line-based lattice cells. Surface-based lattice cells do not support this option.

Cell dimensions and translations
These parameters define the dimensions of the cell and its translations when computing the lattice structure. Note that the interpretation of these parameters depends on the chosen coordinate system type (see table below).
NOTE. By setting a particular dimension to ZERO, a line-based cell is effectively extruded in the same direction. For a surface-based cell, setting a particular dimension to ZERO is not allowed.

█ Examples

Below are shown a few examples of a solid domain of a part being configured as a lattice structure.

Figure. Free region is configured with a honeycomb cell.

Figure. Free region is configured with a honeycomb cell extruded into Z direction.

Figure. Only a limited range of the free region is configured with a honeycomb cell.