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.
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.
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.
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.
7726677
Parametric representation of a surface pencil with a common spatial geodesic
In this paper, we study the problem of constructing a family of surfaces from a given spatial geodesic curve. We derive a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve. By utilizing the Frenet trihedron frame along the given geodesic, we express the surface pencil as a linear combination of the components of this local coordinate frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the geodesic and the isoparametric requirements. We illustrate and verify the method by finding exact surface pencil formulations for some simple surfaces, such as surfaces of revolution and ruled surfaces. Finally, we demonstrate the use of this method in a garment design application. q 2003 Elsevier Ltd. All rights reserved.
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.