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.
12484776
Revolute Quadric Decomposition of Canal Surfaces and Its Applications
Surfaces subdivision is an important means for geometric computing of surfaces in CAD. This paper proposes a new quadric subdivision for canal surfaces in this paper, RQ-sphere decomposition, that subdivides canal surfaces as a set of truncated revolute quadric with joint spheres. Experimental results show that the RQ-sphere decomposition is better than existing methods.
125731656
Congruent partition and certain computational geometry problems.
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.
5683427
Developability-preserved free-form deformation of assembled patches
A novel and practical approach is presented in this paper that solves a constrained free-form deformation (FFD) problem where the developability of the tessellated embedded surface patches is preserved during the lattice deformation. The formulated constrained FFD problem has direct application in areas of product design where the surface developability is required, such as clothing, ship hulls, automobile parts, etc. In the proposed approach, the developability-preserved FFD problem is formulated as a constrained optimization problem. Different from other contained FFD approaches, the positions of lattice control points are not modified in our algorithm -- as their control is insufficient in regards to the developability of all the nodes in the mesh. Moreover, the optimization is performed on the parameters of the mesh nodes rather than directly modifying their 3D coordinates, which avoids the time-consuming inverse calculation of the parameters of every node in a non-parallelepiped control lattice when further deformations are required.
24231103
Biorthogonal wavelet construction for hybrid quad/triangle meshes
Ever since its introduction by Stam and Loop, the quad/triangle subdivision scheme, which is a generalization of the well-known Catmull–Clark subdivision and Loop subdivision, has attracted a great deal of interest due to its flexibility of allowing both quads and triangles in the same model. In this paper, we present a novel biorthogonal wavelet—constructed through the lifting scheme—that accommodates the quad/triangle subdivision. The introduced wavelet smoothly unifies the Catmull–Clark subdivision wavelet (for quadrilateral meshes) and the Loop subdivision wavelet (for triangular meshes) in a single framework. It can be used to flexibly and efficiently process any complicated semi-regular hybrid meshes containing both quadrilateral and triangular regions. Because the analysis and synthesis algorithms of the wavelet are composed of only local lifting operations allowing fully in-place calculations, they can be performed in linear time. The experiments demonstrate sufficient stability and fine fitting quality of the presented wavelet, which are similar to those of the Catmull–Clark subdivision wavelet and the Loop subdivision wavelet. The wavelet analysis can be used in various applications, such as shape approximation, progressive transmission, data compression and multiresolution edit of complex models.
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.