PhD Thesis Defence: Shape Compaction via Stacking and Folding- Honghua Li
Space-saving, or collapsible, objects are ubiquitous in our living and working space. They can adjust configurations to either perform their intended functionality or save space, for example, while storing and shipping. This additional space-saving characteristic of collapsible objects comparing to their non-collapsible counterparts makes them more preferable, especially in environments where space is costly.
This thesis addresses the problem of shape compaction - how to geometrically modify a 3D object such that it can be more compactly stored by changing to a different configuration. The main challenge of shape compaction lies in the desire to modify the geometry of the original object only subtly so that the intended functionality and aesthetic appearance of the object are not significantly affected. With this goal in mind, we present optimization methods to solve two shape compaction problems involving commonly conducted collapsing principles, i.e., stacking and folding.
The first problem is stackabilization - making objects more amenable to stacking. As a group collapsing principle, a collection of shapes can cooperatively occupy less space when stacked than they do individually. Given a 3D object and a stacking direction, a measure of stackability is defined to reflect the space-saving ratio of stacking the given object along the given stacking direction. The stackabilization algorithm deforms the input 3D object to meet a target stackability using energy minimization. This energy accounts for the scales of the deformation parameters as well as the preservation of per-existing geometric and structural properties in the objects.
The second problem is foldabilization - modifying a 3D object such that it can be folded into a flat configuration along a prescribed direction. Folding an object involves rearranging its parts via hinging; the folded part configuration usually occupies less space than the unfolded one. The input 3D object is first abstracted into a scaffold, which consists of a collection of connected planar patches. The foldabilization algorithm minimizes the amount of modifications, e.g. shrinking and split, on these patches such that the modified scaffold can be folded into a flat configuration.
Honghua Li's Personal Webpage: http://honghuali.github.io/