11994567
Enhancing Levin's method for computing quadric-surface intersections
Levin's method produces a parameterization of the intersection curve of two quadrics in the form p(u) = a(u) ± d(u) √s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical structural information required by solid modeling applications. We study the theoretical foundation of Levin's method, as well as the parameterization p(u) it produces. The following contributions are presented in this paper: (1) It is shown how the roots of s(u) can be used to classify the morphology of an irreducible intersection curve of two quadric surfaces. (2) An enhanced version of Levin's method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular. (3) A simple geometric proof is given for the existence of a real ruled quadric in any quadric pencil, which is the key result on which Levin's method is based. These results enhance the capability of Levin's method in processing the intersection curve of two general quadrics within its own self-contained framework.
16675497
Revisiting the [mu]-basis of a rational ruled surface
The µ-basis of a rational ruled surface P(s,t) = P0(s) + tP1(s) is defined in Chen et al. (Comput. Aided Geom. Design 18 (2001) 61) to consist of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z. It is shown there that the resultant of p and q with respect to s gives the implicit equation of the rational ruled surface; however, the parametric equation P(s, t) of the rational ruled surface cannot be recovered from p and q. Furthermore, the µ-basis thus defined for a rational ruled surface does not possess many nice properties that hold for the µ-basis of a rational planar curve (Comput. Aided Geom. Design 18 (1998) 803). In this paper, we introduce another polynomial r(x, y, z, s, t) that is linear in x, y, z and t such that p, q, r can be used to recover the parametric equation P(s, t) of the rational ruled surface; hence, we redefine the µ-basis to consist of the three polynomials p, q, r. We present an efficient algorithm for computing the newly-defined µ-basis, and derive some of its properties. In particular, we show that the new µ-basis serves as a basis for both the moving plane module and the moving plane ideal corresponding to the rational ruled surface.
14471402
Computing quadric surface intersections based on an analysis of plane cubic curves
Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve is computed first and the intersection curve of the two quadrics is then found by transforming the cubic curve by a rational quadratic mapping. Topological classification and parameterization of the intersection curve are achieved by invoking results from algebraic geometry on plane cubic curves. 2003 Elsevier Science (USA). All rights reserved.
45794206
Rational Quadratic Parameterizations of Quadrics
Every irreducible quadric in E3 has infinitely many different rational quadratic parameterizations. These parameterizations and the relationships between them are investigated. It is shown that every faithful rational quadratic parameterization of a quadric can be generated by a stereographic projection from a point on the quadric, called the center of projection (COP). Two such parameterizations for the same quadric are related by a rational linear reparameterization if they have the same COP; otherwise they are related by a rational quadratic reparameterization. We also consider unfaithful parameterizations for which, in general, a one-to-one correspondence between points on the surface and parameters in the plane does not exist. It is shown that all unfaithful rational quadratic parameterizations of a properly degenerate quadric can be characterized by a simple canonical form, and there exist no unfaithful rational quadratic parameterizations for a nondegenerate quadric. In addition, given a faithful rational quadratic parameterization of a quadric, a new technique is presented to compute its base points and inversion formula. These results are applied to solve the problems of parameterizing the intersection of two quadrics and reparameterizing a given quadric parameterization with respect to a different COP without implicitization.
2992545
Constrained 3D shape reconstruction using a combination of surface fitting and registration
We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.
7101460
On the Difference Method for Drawing Conic Arcs
Abstract The difference method is an efficient way to generate an inscribed polygon of a conic section. We address the implementation issues of the difference method, that is, how to choose the difference parameter and initial points so that the inscribed polygon has a minimal number of line segments and is within a given tolerance of the conic arc. We also discuss how the difference method can be used to draw conic arcs represented by rational quadratic Bezier curves.
7326824
On the colorings of outerplanar graphs
Abstract In this paper, we have studied seven colorings of outerplanar graphs. Two main conclusions have been proved: if G is an outerplanar graph without cut vertex and Δ(G) ⩾ 6, then (i) χef(G) = Δ(G), and (ii) χvef(G) = Δ(G) + 1, where χef and χvef are the edge-face chromatic number and the entire chromatic number of G, respectively, and Δ(G) is the maximum degree of vertices of G.
17166482
Benchmarking the effectiveness of sequential pattern mining methods
Recently, there is an increasing interest in new intelligent mining methods to find more meaningful and compact results. In intelligent data mining research, accessing the quality and usefulness of the results from different mining methods is essential. However, there is no general benchmarking criteria to evaluate whether these new methods are indeed more effective compared to the traditional methods. Here we propose a novel benchmarking criteria that can systematically evaluate the effectiveness of any sequential pattern mining method under a variety of situations. The benchmark evaluates how well a mining method finds known common patterns in synthetic data. Such an evaluation provides a comprehensive understanding of the resulting patterns generated from any mining method empirically. In this paper, the criteria are applied to conduct a detailed comparison study of the support-based sequential pattern model with an approximate pattern model based on sequence alignment. The study suggests that the alignment model will give a good summary of the sequential data in the form of a set of common patterns in the data. In contrast, the support model generates massive amounts of frequent patterns with much redundancy. This suggests that the results of the support model require more post processing before it can be of actual use in real applications.
17218997
Profiling program behavior for anomaly intrusion detection based on the transition and frequency property of computer audit data
Intrusion detection is an important technique in the defense-in-depth network security framework. In recent years, it has been a widely studied topic in computer network security. In this paper, we present two methods, namely, the Hidden Markov Models (HMM) method and the Self Organizing Maps (SOM) method, to profile normal program behavior for anomaly intrusion detection based on computer audit data. The HMM method utilizes the transition property of events while SOM method relies on the frequency property of events. Two data sets, CERT synthetic Sendmail system call data collected in the University of New Mexico (UNM) and Live FTP system call data collected in the CNSIS lab of Xi'an Jiaotong University, were used to assess the two methods. Testing results show that the HMM method using the transition property of events produces good detection performance while high computational expense is required both for training and detection. The HMM method is better than other two methods reported previously in terms of detection accuracy for the same data set. The SOM method considering the frequency property of events, on the other hand, is suitable for real-time intrusion detection because of its capability of processing a large amount of data with low computational overhead.
11539721
XParent: an efficient RDBMS-Based XML database system
Presents, XParent, an XML document management system built on top of RDBMS. It is based on an efficient, model-mapping-based approach that uses a fixed database schema to store any XML documents without assistance of DTD. The visual query interface of XParent provides both expressive power for professionals and user friendliness for naive users. The proposed multi-level query translation scheme makes it possible to develop a generic XML application that supports multiple XML query languages and mapping schemas.
8102164
XR-tree: indexing XML data for efficient structural joins
XML documents are typically queried with a combination of value search and structure search. While querying by values can leverage traditional database technologies, evaluating structural relationship, specifically parent-child or ancestor-descendant relationship, between XML element sets has imposed a great challenge on efficient XML query processing. We propose XR-tree, namely, XML region tree, which is a dynamic external memory index structure specially designed for strictly nested XML data. The unique feature of XR-tree is that, for a given element, all its ancestors (or descendants) in an element set indexed by an XR-tree can be identified with optimal worst case I/O cost. We then propose a new structural join algorithm that can evaluate the structural relationship between two XR-tree indexed element sets by effectively skipping ancestors and descendants that do not participate in the join. Our extensive performance study shows that the XR-tree based join algorithm significantly outperforms previous algorithms.