17800585
Computing planar swept polygons under translation
A translational sweep is the translating of a polygon, called the generatrix G, around another polygon, called the directrix D, under two conditions: (1) G is always in contact with D; and (2) the interiors of G and D do not intersect. Three classes of translational sweep are studied, including the case in which both G and D are convex; the case in which G is convex, D monotone; and the case in which both are monotone. Efficient algorithms for computing the trajectory and the swept area as well as geometric and computational properties are presented for each class. A notion called the inverse generatrix, which reveals a duality between the trajectory and the swept polygon, is introduced to reduce complexity.
33407960
Biconic subdivision of surfaces of revolution and its applications in intersection problems
This paper presents a novel method for the subdivision of surfaces of revolution. We develop a new technique for approximating the genertrix by a series of pairs of conic sections. By using an error estimate based on convex combination, an efficient least-squares approach is proposed that yields near-optimal fitting. The resulting surface approximation is shown to be more efficient than other tessellation methods in terms of the number of fitting segments. This in turn allows us to implement efficient and robust algorithms for such surfaces. In particular, novel intersection techniques based on the proposed subdivision method are introduced for the two most fundamental types of intersections – line/surface and surface/surface intersections. The experimental results show that our method outperforms conventional methods significantly in both computing time and memory cost.
30294701
Multiresolution Shape Modeling and Editing in Reverse Engineering
In this paper we propose a multiresolution framework in reverse engineering for complex free-form object modeling and editing. The proposed framework starts with dense point data scanned from the surface of a physical prototype and produces CAD models ready for downstream applications. Targeting on achieving maximum efficiency in the whole reverse engineering process, the proposed framework adopt a hierarchy of shape representations in a special order, i.e. implicit, piecewise linear and parametric surfaces. Based on the proposed hierarchical shape structure, a set of shape editing operators such as Boolean operators, blending, offset, morphing, free-form deformation and texture mapping, is efficiently integrated into the framework. A great diversity of free-form shape models with various modeling operations is presented to demonstrate the effectiveness and efficiency of the proposed multiresolution framework.
12350684
Computing planar sections of surfaces of revolution with revolute quadric decomposition
Computing the planar sections of objects is a fundamental operation in solid modeling. Subdivision method is commonly used for solving such intersection problems. In this paper, a revolute quadric decomposition is proposed for surfaces of revolution, which are subdivided into a set of coaxial revolute quadrics along the generatrix. This reduces the intersection problem of a plane and a surface of revolution to the intersection problem of a plane and a revolute quadric, which has robust, accurate and efficient geometric solution. Further, the intersection curves can be represented with a group of G (G. Baciu et al., 2001) conic arcs. A new concept, valid intersection interval (VII), is introduced and a new technique, cylindrical bounding shell clipping, is proposed for efficient intersection detection for a plane and a surface of revolution. Finally, a tracing algorithm is presented for recognizing singular points and closed loops of intersection curves. Implemented examples show the robustness and effectiveness of the proposed algorithm.
5214346
Efficient and stable numerical algorithms on equilibrium equations for geometric modeling
In this paper the applications of equilibrium equation to geometric modeling is exploited and efficient numerical algorithms are proposed for solving the equilibrium equation. First we show that from diverse geometric modeling applications the equilibrium system can be extracted as the central framework. Second, by exploiting in-depth the special structures inherent in the geometric applications, we present simplified analytic solutions to the resulting geometric equilibrium equations via system decomposition. Finally, given the observation that the geometric equilibrium systems are extremely sensitive to both perturbations in input data and round off errors, efficient, stable and accurate numerical algorithms are proposed.
29005149
Scallop hull and its offset
Abstract A linear-time algorithm that computes the envelope of the offset of a monotone chain is presented. The scallop hull , an extended notion of the convex hull, of the monotone chain is first computed by using an approach similar to that of the convex-hull construction algorithm. The offset of the scallop hull, which yields the desired envelope, can then be computed in linear time from the scallop hull, giving a tool path.
25475263
A Pattern-Based Design Approach for Subscription Management of Software as a Service
Software as a Service (SaaS) is essentially about delivering a software application as a service over the Web with a usage-based charging plan. Existing Web service subscription models do not consider the complexity of the application and the business environment; for example, multiple service elements with mutual dependencies derived from one application, or various business partnership models for reselling and cross-selling services. Therefore the design of subscription management is critical for a SaaS provider to appropriately decompose its application into service elements and then package them into service offerings for a client or business partner to subscribe according to the nature of the application and the overall business design. In this paper, we propose a pattern-based approach for the subscription management design of SaaS. A subscription model is introduced first to capture the different entities and their relationships involved in SaaS subscription. Then a method supported with service structure patterns and business interaction patterns analysis is presented to empower a SaaS provider to design an appropriate subscription model for its service offering. A case study is made to demonstrate the effectiveness of the method at the end of this paper.
195710929
A Supply Chain Network Design Model for Deteriorating Items
We consider a supply chain network design problem for deteriorating items, involving a single supplier, some potential distribution centers and multiple retailers. This problem is to determine how many distribution centers to set up, where to locate them, how to serve the retailers using these distribution centers, and to determine the optimal inventory policies for the whole supply chain network. The goal is to minimize the total deterioration, inventory, transportation and facilities location cost. We formulate this problem as a nonlinear mix-integer programming model. This model is a NP-Hard problem, so we present a Lagrangian relaxation solution algorithm and a Genetic algorithm to solve our model respectively. Finally, numerical examples are given to illustrate the application of these two algorithms, and our computational results show that Lagrangian relaxation algorithm is more efficient for our problem.