Pre-Defined Structures

This section covers the different techniques for manipulating a base model to obtain a complex structure. Users are advised to read the Modeling Techniques section first.

Although a general Boolean mask allows for a highly customized structure, some processes or algorithms are so common and useful that they have been implemented in VCAMS as part of the mask module.

These pre-defined structures are boolean masks that are widely used and have been added to the library so they can be created using very little input. This allows for a degree of standardization, eases creation of fairly complex structures based on common patterns, and reduces the risk of bugs. As discussed in the Modeling Techniques section, the masks can then be combined in various ways and applied to a VoxelPart object.

Currently, the following groups of pre-defined structures can be used:

Geometric Shapes

Triply Periodic Minimal Surfaces

Image-Based Structures

Level-Set Functions

A number of these structures are modeled using level-set functions. The main idea behind this method is that an implicit function $\Phi$ describes a closed curve. $\Phi(x,y,z)$ can then be evaluated for each point $P$ in space, and:

\[\begin{split}\Phi(x,y,z)= \begin{cases} < 0, & \text{$P$ is inside the surface}\\ = 0, & \text{$P$ is on the surface boundary}\\ > 0, & \text{$P$ is outside the surface} \end{cases}\end{split}\]

Many different functions can be derived for modeling simple or complex shapes, as listed above. For more information, see the famous book by Osher and Fedkiw [1].