We explore the optimization of closed space-filling curves under orientation objectives. By solidifying material along curve, solid layers 3D prints can be manufactured in a single continuous extrusion motion. The control over enables deposition to align with specific directions different areas, or produce locally uniform distribution orientations, patterning solidified volume precisely control...

In this paper the problem of sampling from uniform probability distributions is approached by means space-filling curves, a topological concept that has found number important applications in recent years. Departing theoretical fact they are surjective but not necessarily injective, investigation focused upon structure obtained when their domains swept and discrete manner, corresponding values ...

Hilbert’s two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that the properties that make Hilbert’s curve unique in two dimensions, are shared by 10 694 807 structurally different space-filling curves in three dimensions. ...

of the Thesis Optimizing Cache Behavior of Ray-Driven Volume Rendering Using Space-Filling Curves by Oleg Mishchenko Master of Science in Computer Science Stony Brook University 2006 We study the cache behavior of space-filling curves in the context of volume rendering with raycasting. An efficient bit-oriented algorithm for 3D Hilbert curve traversal is also proposed. We find that data organiz...

Partitioning techniques based on space-filling curves have received much recent attention due to their low running time and good load balance characteristics. The basic idea underlying these methods is to order the multidimensional data according to a space-filling curve and partition the resulting onedimensional order. However, space-filling curves are defined for points that lie on a uniform ...