1920147
On the intersection of a set of direction cones
The problem of passing a convex polyhedron through a window is described as: Given a convex polyhedron P = (pr, p2,. . . , p,) and a convex polygon W = (WI, w,, *. ., w,) on a plane h not intersecting P, find all the directions for translating (single translation) P through W. Toussaint [l] proposed an O(nm log nm) algorithm to solve this problem. He first showed that P can pass W with a single translation in direction 8 if, and only if, each vertex of P can be passed through W with a single translation in direction 8. Based on this observation, he posed the algorithm as follows: Consider vertex pi of P. All directions for translating pi from its initial position through window W are defined by all the vectors emanating at pi and intersecting H in W. Therefore the cone determined by the half-lines from pi through wj, j = 1,2,. . . , m specifies all such directions for pi. This cone is named as direction cone of pi and is denoted as CONE(pi, W). Construct a 3D euclidean direction space D and translate all the cones CONE(pi, W), i = 1,2,. . . , n in D such that the pi all overlap with the origin of D. Then the intersection of all the cones in D gives another cone which is the set of directions for simultaneous translation of all the pi, and hence of P. Each cone can be computed in O(m) time and thus all the cones can be found in 0( nm) time. All the cones can be translated to D in O(nm) time. To compute the intersection of the cones, Toussaint views each cone as the intersection of M half spaces determined by the planes coplanar with the M faces of each cone. The interior half space contains the cone. Therefore the solution cone is the intersection of all the interior half spaces determined by all the cones in D. Since the
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.
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.
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.
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.
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.