8271
The power crust
The power crust is a construction which takes a sample of points from the surface of a three-dimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.
This idea leads to a simple algorithm with theoretical guarantees comparable to those of other surface reconstruction and medial axis approximation algorithms. It also comes with a guarantee that does not depend in any way on the quality of the input point sample. Any input gives an output surface which is the `watertight' boundary of a three-dimensional polyhedral solid: the solid described by the approximate MAT. This unconditional guarantee makes the algorithm quite robust and eliminates the polygonalization, hole-filling or manifold extraction post-processing steps required in previous surface reconstruction algorithms.
In this paper, we use the theory to develop a power crust implementation which is indeed robust for realistic and even difficult samples. We describe the careful design of a key subroutine which labels parts of the MAT as inside or outside of the object, easy in theory but non-trivial in practice. We find that we can handle areas in which the input sampling is scanty or noisy by simply discarding the unreliable parts of the MAT approximation. We demonstrate good empirical results on inputs including models with sharp corners, sparse and unevenly distributed point samples, holes, and noise, both natural and synthetic.
We also demonstrate some simple extensions: intentionally leaving holes where there is no data, producing approximate offset surfaces, and simplifying the approximate MAT in a principled way to preserve stable features.
47222760
A Simple Algorithm for Homeomorphic Surface Reconstruction
The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm1 using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming that the sample was sufficiently dense. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the first such topological guarantee for this problem.
3185620
A simple algorithm for homeomorphic surface reconstruction
Abstract 1 Introduction The problem of computing a piecewise linear approximation to a surface from a set of sam- ple points on the surface has been a focus of research in solid modeling and graphics due to its many applications. The input to this sur- face reconstruction problem consists of the three dimensional coordinates of the sampled points. The crust algorithm of [1] reconstructs a surface with topological and geometric guarantees using the Voronoi diagram of the input point set. We present new observations that simplify both the algorithm and the proofs for the crust, and we give for the first time a proof that the crust is homeomorphic to the input surface. *Dept. of Computer Science, U. of Texas, Austin TX 78712. e-mail: amenta@cs.utexas.edu tDept, of Computer Science, U. of Texas, Austin, TX 78712. e-mail: sunghee@cs.utexas.edu SDept. of Computer and Information Science, Ohio State U., Columbus, OH 43210. e-mail: t amaldey¢ci s. ohio-state, edu §Dept. of Computer and Information Science, Ohio State U., Columbus, OH 43210. e-mail: leekha@cis, ohio-state, edu
34200542
MJSA: Markov job scheduler based on availability in desktop grid computing environment
In a desktop grid computing environment, voluntary desktops (i.e., resource providers) are free to leave and join independently in the middle of execution. To develop a reliable desktop grid computing system, a scheduling scheme must consider the dynamic nature (i.e., volatility) of volunteers. Existing desktop grid computing systems, however, do not consider volatility in their scheduling procedures. As a result, job execution is often suspended, resulting in delayed completion time and degraded performance and reliability. To solve these limitations, we propose the Markov Job Scheduler based on Availability (MJSA) supporting three advanced scheduling schemes: OPTIMIST, PESSIMIST, and REALIST. These scheduling schemes are based on stochastic modeling of desktop availability. In the OPTIMIST scheme, in which time constraints are relaxed, the MJSA provides reliable resource selection at low cost. In the PESSIMIST scheme, where time constraints are rigid, the MJSA enables stable makespan in strictly time. Finally, in the REALIST scheme, where time constraints are only partially relaxed, the MJSA provides enhanced cost efficiency. In conclusion, the MJSA improves performance and reliability by adapting the appropriate scheduling scheme when selecting volunteers according to the needs of applications.
13644201
A virtual prototyping system for rapid product development
Abstract This paper describes a virtual prototyping (VP) system that integrates virtual reality with rapid prototyping (RP) to create virtual or digital prototypes to facilitate product development. The proposed VP system incorporates two new simulation methodologies, namely the dexel-based and the layer-based fabrication approaches, to simulate the powder-based and the laminated sheet-based RP processes, respectively. The dexel-based approach deposits arrays of solid strips to form a layer, while the layer-based approach directly forms a complete layer by extruding the slice contours. The layer is subsequently stacked up to fabricate a virtual prototype. The simulation approaches resemble the physical fabrication processes of most RP systems, and are therefore capable of accurately representing the geometrical characteristics of prototypes. In addition to numerical quantification of the simulation results, the system also provides stereoscopic visualisation of the product design and its prototype for detailed analyses. Indeed, the original product design may be superimposed on its virtual prototype, so that areas with dimensional errors beyond design limits may be clearly highlighted to facilitate point-to-point analysis of the surface texture and the dimensional accuracy of the prototype. Hence, the key control parameters of an RP process, such as part orientation, layer thickness and hatch space, may be effectively tuned up for optimal fabrication of physical prototypes in subsequent product development. Furthermore, the virtual prototypes can be transmitted via the Internet to customers to facilitate global manufacturing. As a result, both the lead-time and the product development costs can be significantly reduced.
14566323
Semantic Selection for Resolution in Clause Graphs
In this contribution we present a variant of a resolution theorem prover which selects resolution steps based on the proportion of models a newly generated clause satisfies compared to all models given in a reference class. This reference class is generated from a subset of the initial clause set. Since the empty clause does not satisfy any models, preference is given to such clauses which satisfy few models only. Because computing the number of models is computationally expensive on the one hand, but will remain almost unchanged after the application of one single resolution step on the other hand, we adapt Kowalski's connection graph method to store the number of models at each link.
41968338
Group-Based Scheduling Scheme for Result Checking in Global Computing Systems
This paper considers the problem of correctness to fault-tolerance in global computing systems. Global computing system has been shown to be exposed to intentional attacks, where authentication is not relevant, network security techniques are insufficient. To guarantee correctness for computation, fault-tolerance schemes have been used to majority voting and spot-checking but these schemes intend to high computation delay because are not applied scheduling scheme for result checking. In this paper, we propose a new technique called GBSS(Group-Based Scheduling Scheme) which guarantee correctness and reduce computation delay by using fault-tolerant scheduling scheme to the result checking. Additionally, simulation results show increased usable rate of the CPU and increased performance of the system.
5224987
Differential learning algorithms for decorrelation and independent component analysis
Decorrelation and its higher-order generalization, independent component analysis (ICA), are fundamental and important tasks in unsupervised learning, that were studied mainly in the domain of Hebbian learning. In this paper we present a variation of the natural gradient ICA, differential ICA, where the learning relies on the concurrent change of output variables. We interpret the differential learning as the maximum likelihood estimation of parameters with latent variables represented by the random walk model. In such a framework, we derive the differential ICA algorithm and, in addition, we also present the differential decorrelation algorithm that is treated as a special instance of the differential ICA. Algorithm derivation and local stability analysis are given with some numerical experimental results.