11609470
Interpolating Polyhedral Models Using Intrinsic Shape Parameters
Metamorphosis, or morphing, is the gradual transformation of one shape into another. It generally consists of two subproblems: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation problem of transforming one polyhedral model into another. It is an extension of the intrinsic shape interpolation scheme (T. W. Sederberg, P. Gao, G. Wang and H. Mu, ‘2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH ’93, pp. 15–18.) for 2D polygons. Rather than considering a polyhedron as a set of independent points or faces, our solution treats a polyhedron as a graph representing the interrelations between faces. Intrinsic shape parameters, such as dihedral angles and edge lengths that interrelate the vertices and faces in the two graphs, are used for interpolation. This approach produces more satisfactory results than the linear or cubic curve paths would, and is translation and rotation invariant.  1997 by John Wiley & Sons, Ltd.
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.
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.
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.
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.
13974173
An empirical investigation of intelligent agents for e-business customer relationship management: a knowledge management perspective
Izak Benbasat MIS Division, Faculty of Commerce and Business Admin. University of British Columbia 2053 Main Mall, Vancouver, BC, V6T1Z2, Canada Phone: (604)822-8396, Fax: (604)822-0045 Email: benbasat@commerce.ubc.ca Abstract: Using a knowledge management perspective, this paper investigates new and efficient ways of applying intelligent agents to e-business customer relationship management. Intelligent agents, as well as knowledge-based systems or expert systems, as a branch of applied artificial intelligence not only predate the recent surge of interest in knowledge management, but also stand out as a well-established means for implementing certain aspects of knowledge management. Intelligent agent technologies make it easier to codify, store, share, and transfer certain kinds of knowledge. Based on the IS literature on explanations and decisional guidance for knowledge-based systems, this paper argues that transferring appropriate knowledge from an organization’s staff to its partners and customers can facilitate efficient customer relationship management (e.g., improving customer trust). It is suggested that three types of knowledge – “How Explanations”, “Why Explanations”, and “Decisional Guidance” – be embedded in intelligent agents, and transferred to the agent’s users. A laboratory experiment is proposed to test if, in which aspects, and to what extent these types of knowledge will increase customer trust.
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.
41898252
Vertex-pancyclicity of edge-face-total graphs
The edge-face-total graph r(G) of a plane graph G is the graph defined on the vertex set E(G)∪F(G) so that two vertices in r(G) are joined by an edge if and only if they were adjacent or incident in G. In this paper we prove that (1) the edge-face-total graph of a 2-connected plane graph is vertex-pancyclic and there exists a connected plane graph G with cut vertices such that r(G) is non-Hamiltonian; (2) the line graph of a 2-connected plane graph with at most one face of degree ⩾4 is pancyclic.
13354529
Edge-pancyclicity of coupled graphs
The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.
9757380
Algorithmic aspects of communication in ad-hoc networks with smart antennas
Smart antennas have gained significant importance in multi-hop wireless networks in recent years, because of their sophisticated signal processing capabilities that hold the potential for increased data rates and reliability. In this work, we consider the problem of communication in multi-hop wireless networks with smart antennas (specifically digital adaptive arrays). These smart antennas provide degrees of freedom (DOFs) that can be used to suppress co-existing communication links, thereby increasing spatial reuse in the network. Thus, the communication problem comprises of not just determining a channel access mechanism to be used by the communication links, but also involves the determination of the communication pattern (usage of DOFs) to be used by each node during channel access. To the best of our knowledge, our work is the first step towards addressing this problem.We first consider the problem of determining the communication pattern to be used by the nodes and formulate it combinatorially with the goal of optimizing network performance through interference minimization. We present efficient centralized and distributed algorithms that are within a factor of ¾ and ½ of the optimum solution respectively. We then extend the distributed algorithm to incorporate TDMA-based scheduling in a purely localized manner. The distributed algorithms are then evaluated through simulations in ns2 and insights are drawn into the potential performance benefits of smart antennas in multi-hop wireless networks.