Joshua A. Levine

State of the Art in Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations -- not necessarily the explicit geometry. This state-of-the-art report surveys the field of surface reconstruction, providing a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, this report provides a detailed characterization of the field, highlights similarities between diverse reconstruction techniques, and provides directions for future work in surface reconstruction.

A Practical Delaunay Meshing Algorithm for aLarge Class of Domains

Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all non-manifolds. In contrast to previous approaches, the algorithm does not impose any restriction on the input angles. Although this algorithm has a provable guarantee about topology, certain steps are too expensive to make it practical.

A benchmark for surface reconstruction

We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

RRTs for nonlinear, discrete, and hybrid planning and control

In this paper, we describe a planning and control approach in terms of sampling using Rapidly-exploring Random Trees (RRTs), which were introduced by LaValle. We review RRTs for motion planning and show how to use them to solve standard nonlinear control problems. We extend them to the case of hybrid systems and describe our modifications to LaValles Motion Strategy Library to allow for hybrid motion planning. Finally, we extend them to purely discrete spaces (using heuristic evaluation as a distance metric) and provide computational experiments comparing them to conventional methods, such as A.

Analysis of large-scale scalar data using hixels

One of the greatest challenges for todays visualization and analysis communities is the massive amounts of data generated from state of the art simulations. Traditionally, the increase in spatial resolution has driven most of the data explosion, but more recently ensembles of simulations with multiple results per data point and stochastic simulations storing individual probability distributions are increasingly common. This paper introduces a new data representation for scalar data, called hixels, that stores a histogram of values for each sample point of a domain. The histograms may be created by spatial down-sampling, binning ensemble values, or polling values from a given distribution. In this manner, hixels form a compact yet information rich approximation of large scale data. In essence, hixels trade off data size and complexity for scalar-value “uncertainty”. Based on this new representation we propose new feature detection algorithms using a combination of topological and statistical methods. In particular, we show how to approximate topological structures from hixel data, extract structures from multi-modal distributions, and render uncertain isosurfaces. In all three cases we demonstrate how using hixels compares to traditional techniques and provide new capabilities to recover prominent features that would otherwise be either infeasible to compute or ambiguous to infer. We use a collection of computer tomography data and large scale combustion simulations to illustrate our techniques.

A Survey of Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

Visualizing Network Traffic to Understand the Performance of Massively Parallel Simulations

The performance of massively parallel applications is often heavily impacted by the cost of communication among compute nodes. However, determining how to best use the network is a formidable task, made challenging by the ever increasing size and complexity of modern supercomputers. This paper applies visualization techniques to aid parallel application developers in understanding the network activity by enabling a detailed exploration of the flow of packets through the hardware interconnect. In order to visualize this large and complex data, we employ two linked views of the hardware network. The first is a 2D view, that represents the network structure as one of several simplified planar projections. This view is designed to allow a user to easily identify trends and patterns in the network traffic. The second is a 3D view that augments the 2D view by preserving the physical network topology and providing a context that is familiar to the application developers. Using the massively parallel multi-physics code pF3D as a case study, we demonstrate that our tool provides valuable insight that we use to explain and optimize pF3Ds performance on an IBM Blue Gene/P system.

Mapping applications with collectives over sub-communicators on torus networks

The placement of tasks in a parallel application on specific nodes of a supercomputer can significantly impact performance. Traditionally, this task mapping has focused on reducing the distance between communicating tasks on the physical network. This minimizes the number of hops that point-to-point messages travel and thus reduces link sharing between messages and contention. However, for applications that use collectives over sub-communicators, this heuristic may not be optimal. Many collectives can benefit from an increase in bandwidth even at the cost of an increase in hop count, especially when sending large messages. For example, placing communicating tasks in a cube configuration rather than a plane or a line on a torus network increases the number of possible paths messages might take. This increases the available bandwidth which can lead to significant performance gains. We have developed Rubik, a tool that provides a simple and intuitive interface to create a wide variety of mappings for structured communication patterns. Rubik supports a number of elementary operations such as splits, tilts, or shifts, that can be combined into a large number of unique patterns. Each operation can be applied to disjoint groups of processes involved in collectives to increase the effective bandwidth. We demonstrate the use of Rubik for improving performance of two parallel codes, pF3D and Qbox, which use collectives over sub-communicators.

Delaunay Meshing of Piecewise Smooth Complexes without Expensive Predicates

Recently a Delaunay refinement algorithm has been proposed that can mesh piecewise smooth complexes which include polyhedra, smooth and piecewise smooth surfaces, and non-manifolds. However, this algorithm employs domain dependent numerical predicates, some of which could be computationally expensive and hard to implement. In this paper we develop a refinement strategy that eliminates these complicated domain dependent predicates. As a result we obtain a meshing algorithm that is practical and implementation-friendly.

Delaunay Meshing of Isosurfaces

We present an isosurface meshing algorithm, DelIso, based on the Delaunay refinement paradigm. This paradigm has been successfully applied to mesh a variety of domains with guarantees for topology, geometry, mesh gradedness, and triangle shape. A restricted Delaunay tri- angulation, dual of the intersection between the surface and the three dimensional Voronoi diagram, is often the main ingredient in Delaunay refinement. Computing and storing three dimensional Voronoi/Delaunay diagrams become bottlenecks for Delaunay refinement techniques since isosurface computations generally have large input datasets and output meshes. A highlight of our algorithm is that we find a simple way to recover the restricted Delaunay triangulation of the surface without computing the full 3D structure. We employ techniques for efficient ray tracing of isosurfaces to generate surface sample points, and demonstrate the effectiveness of our implementation using a variety of volume datasets.