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.
205873026
Control point adjustment for B-spline curve approximation
Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and produces a better approximating B-spline curve than existing methods relying on data point parameterization. However, SDM is sensitive to the initial B-spline curve due to its local nature of optimization. To address this, we integrate SDM with procedures for automatically adjusting both the number and locations of the control points of the active spline curve. This leads to a method that is more robust and applicable than SDM used alone. Furthermore, it is observed that the most time consuming part of SDM is the repeated computation of the foot-point on the target curve of a sample point on the active B-spline curve. In our implementation, we speed up the foot-point computation by pre-computing the distance field of the target curve using the Fast Marching Method. Experimental examples are presented to demonstrate the effectiveness of our method. Problems for further research are discussed. q 2003 Elsevier Ltd. All rights reserved.
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.
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.
14611333
TAR: temporal association rules on evolving numerical attributes
Data mining has been an area of increasing interest. The association rule discovery problem in particular has been widely studied. However, there are still some unresolved problems. For example, research on mining patterns in the evolution of numerical attributes is still lacking. This is both a challenging problem and one with significant practical applications in business, science, and medicine. In this paper we present a temporal association rule model for evolving numerical attributes. Metrics for qualifying a temporal association rule include the familiar measures of support and strength used in traditional association rule mining and a new metric called density. The density metric not only gives us a way to extract the rules that best represent the data, but also provides an effective mechanism to prune the search space. An efficient algorithm is devised for mining temporal association rules, which utilizes all three thresholds (especially the strength) to prune the search space drastically. Moreover, the resulting rules are represented in a concise manner via rule sets to reduce the output size. Experimental results on real and synthetic data sets demonstrate the efficiency of our algorithm.
14677925
Universal IP multicast delivery
A ubiquitous and efficient multicast data delivery service is essential to the success of large-scale group communication applications. The original IP multicast design is to enhance network routers with multicast capability [S. Deering, D. Cheriton, Multicast routing in datagram internetworks and extended LANs, ACM Transactions on Computer Systems 8(2) (1990) 85-110]. This approach can achieve great transmission efficiency and performance but also poses a critical dependency on universal deployment. A different approach, overlay multicast, moves multicast functionality to end hosts, thereby removing the dependency on router deployment, albeit at the cost of noticeable performance penalty compared to IP multicast. In this paper we present the Universal Multicast (UM) framework, along with a set of mechanisms and protocols, to provide ubiquitous multicast delivery service on the Internet. Our design can fully utilize native IP multicast wherever it is available, and automatically build unicast tunnels to connect IP Multicast "islands" to form an overall multicast overlay. The UM design consists of three major components: an overlay multicast protocol (HMTP) for inter-island routing, an intra-island multicast management protocol (HGMP) to glue overlay multicast and native IP multicast together, and a daemon program to implement the functionality at hosts. In addition to performance evaluation through simulations, we have also implemented parts of the UM framework. Our prototype implementation has been used to broadcast several workshops and the ACM SIGCOMM 2004 conference live on the Internet. We present some statistics collected during the live broadcast and describe mechanisms we adopted to support end hosts behind Network Address Translation (NAT) gateways and firewalls.
62615149
Mining Asynchronous Periodic Patterns in Time Series Data
Periodicy detection in time series data is a challenging problem of great importance in many applications. Most previous work focused on mining synchronous periodic patterns and did not recognize the misaligned presence of a pattern due to the intervention of random noise. In this paper, we propose a more flexible model of asynchronous periodic pattern that may be present only within a subsequence and whose occurrences may be shifted due to disturbance. Two parameters min/spl I.bar/rep and max/spl I.bar/dis are employed to specify the minimum number of repetitions that is required within each segment of nondisrupted pattern occurrences and the maximum allowed disturbance between any two successive valid segments. Upon satisfying these two requirements, the longest valid subsequence of a pattern is returned. A two-phase algorithm is devised to first generate potential periods by distance-based pruning followed by an iterative procedure to derive and validate candidate patterns and locate the longest valid subsequence. We also show that this algorithm cannot only provide linear time complexity with respect to the length of the sequence but also achieve space efficiency.
14078437
CLUSEQ: efficient and effective sequence clustering
Analyzing sequence data has become increasingly important recently in the area of biological sequences, text documents, Web access logs, etc. We investigate the problem of clustering sequences based on their sequential features. As a widely recognized technique, clustering has proven to be very useful in detecting unknown object categories and revealing hidden correlations among objects. One difficulty that prevents clustering from being performed extensively on sequence data (in categorical domain) is the lack of an effective yet efficient similarity measure. Therefore, we propose a novel model (CLUSEQ) for sequence cluster by exploring significant statistical properties possessed by the sequences. The conditional probability distribution (CPD) of the next symbol given a preceding segment is derived and used to characterize sequence behavior and to support the similarity measure. A variation of the suffix tree, namely probabilistic suffix tree, is employed to organize (the significant portion of) the CPD in a concise way. A novel algorithm is devised to efficiently discover clusters with high quality and is able to automatically adjust the number of clusters to its optimal range via a unique combination of successive new cluster generation and cluster consolidation. The performance of CLUSEQ has been demonstrated via extensive experiments on several real and synthetic sequence databases.
2548187
Mining asynchronous periodic patterns in time series data
Periodicy detection in time series data is a challenging problem of great importance in many applications. Most previous work focused on mining synchronous periodic patterns and did not recognize the misaligned presence of a pattern due to the intervention of random noise. In this paper, we propose a more flexible model of asynchronous periodic pattern that may be present only within a subsequence and whose occurrences may be shifted due to disturbance. Two parameters min rep and max dis are employed to specify the minimum number of repetitions that is required within each segment of nondisrupted pattern occurrences and the maximum allowed disturbance between any two successive valid segments. Upon satisfying these two requirements, the longest valid subsequence of a pattern is returned. A two-phase algorithm is devised to first generate potential periods by distance-based pruning followed by an iterative procedure to derive and validate candidate patterns and locate the longest valid subsequence. We also show that this algorithm cannot only provide linear time complexity with respect to the length of the sequence but also achieve space