Engineering topics
Patney, Anjul
Publications and source records attributed to Patney, Anjul.
Recursive k-d Darts for Exploring High-Dimensional Spaces.
Abstract not provided.
Exercises in high-dimensional sampling: maximal poisson-disk sampling and k -d darts
In this paper, we review our recent progress on efficient algorithms for generating well-spaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. Lastly, we summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.
k -d Darts: Sampling by k -dimensional flat searches
In this work, we introduced k-d darts as a particular type of higherdimensional sampling. We described a k-d dart framework for hyperplanes of general dimension k, and then demonstrated efficiency and accuracy over three applications using k = 1, and accuracy for one application using k = 1. In particular, darts produce accurate estimates of the volume of an object regardless of the dimension, orientation, and aspect ratio of the object. Axis-aligned darts are universally preferable to unaligned ones for sampling square domains, and we expect this to extend to hyperrectangles, such as bounding boxes. Darts also produce accurate mean estimates for function integration.
Efficient Maximal Poisson-Disk Sampling - presentation slides.
Abstract not provided.