Voxel Lattices

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A particular type of large lattice is a voxel lattice. They are large hexahedral (6-sided) lattices with each element filled with a single cell that is larger than the element. They are often used for calculations based on a tomographic scan. The Figure at the left shows an example. Moritz assigns a lattice to the voxel type if the cells filling each element are sufficiently larger than the lattice cell so that only the unit cell surfaces are used for the polygonalization of the cell. This method of filling is most easily accomplished with a single filling cell inside a sphere centered on the lattice unit cell with a radius much larger than the unit cell dimensions.

To be automatically recognized as a voxel lattice, each universe filling the lattice elements must contain only 1 cell. For cases where a voxel lattice filling universe contains more than 1 cell, treatment as a voxel lattice (for lattice cell N) can be forced with the embedded command

c moritz Lattice N Voxel

An exception to the 1 filling cell rule is allowed where the filling universe contains two cells, one inside a cell identical to the unit cell and the other outside of that cell. If the cells are not defined with macrobodies, the surfaces in all three cell definitions must be in the same order.

Because voxel lattices are often very large, the 3D performance can be poor if the usual methods are used for the 3D display. On some computers, the lattice may not appear at all. The items in the Scan Lattice box on the 3D Lattice Style property page enable alternate drawing options for enhanced 3D performance. In addition to the default drawing algorithm used for other lattices, three special drawing modes exist. When Visible Faces Only is checked, only those cells that are bounded by both visible and invisible lattice cells are drawn. This mode is useful for compact objects, such as the head shown on this page. Clip planes will reveal a hollow interior.

In the Draw as Points mode, shown in at the right, the visible cells are represented by points at the cell position. The points are square (rather than rounded). Their size is set on the property page. Some 3D lattice display settings, such as showing and repeating the unit cell, are not available in the special display modes for voxel lattices. The Visible Points mode is a combination of the Points and Visible modes.

The size of each element can be increased by the Resolution factor(s) if Scale with Resolution is checked, thereby preserving the appearance of a solid object. This Figure  shows the above model drawn with Resolution = 2 and the elements scaled by the resolution factor.

The Combine method defines boxes that represent N x N x N blocks of lattice elements where N is the Combine number set on the property page. The color is the average of the lattice elements in the block. Combine cannot be used with the Visible Faces Only and Visible Points styles. The combined box is drawn if one or more of its lattice elements are visible. This Figure  shows the above model drawn with Combine = 2. The result is a better approximation to the original than when using a Resolution = N, but extra processing time is required for averaging the lattice elements over a block.

The cells on the periphery of the lattice may contain an uninteresting material, such as air surrounding a body part. When Edge Material Invisible is checked, after a voxel lattice is read, the material that occupies the greatest number of cells in the exterior layers of the lattice is made invisible. Changing the setting does not affect existing lattices.

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