A constructive approach to calculate parameter ranges for systems of geometric constraints

Geometric constraints are at the heart of parametric and feature-based CAD systems. Changing values of geometric constraint parameters is one of the most common operations in such systems. However, because allowable parameter values are not known to the user beforehand, this is often a trial-and-error process. We present an approach for automatically determining the allowable range for parameters of geometric constraints. Considered are systems of distance and angle constraints on points in 3D that can be decomposed into triangular and tetrahedral subproblems, by which most practical situations in parametric and feature-based CAD systems can be represented. Our method uses the decomposition to find critical parameter values for which subproblems degenerate. By solving one problem instance for each interval between two subsequent critical values, the exact parameter range is determined for which a solution exists.     

A traceability information model for CNC manufacturing

This paper proposes an information model for tracing CNC manufacturing operations. The objective of the model is to assure that traceability data is comprehensive and available for every CNC machined product, independent of the relationship between the subcontractor and the contractor. The prominent feature of the model is a link between CNC report data for a product instance, the CAD design and the CAM data. This link enables users to browse the traceability data and understand the relationships between the manufacturing process, the CAD design and the CAM data. The link is independent of the systems used to build the CAD and CAM data, and allows the users to be sure the manufactured product contains the required characteristics. Then if a product instance fails, this linkage will make possible to analyze the trace data and identify any exceptions or unusual conditions in the manufacturing process.     

Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics

This paper compares two techniques for the approximation of the offsets to a given planar curve. The two methods are based on approximate conversion of the planar curve into circular splines and Pythagorean hodograph (PH) splines, respectively. The circular splines are obtained using a novel variant of biarc interpolation, while the PH splines are constructed via Hermite interpolation of C¹ boundary data.We analyze the approximation order of both conversion procedures. As a new result, the C¹ Hermite interpolation with PH quintics is shown to have approximation order 4 with respect to the original curve, and 3 with respect to its offsets. In addition, we study the resulting data volume, both for the original curve and for its offsets. It is shown that PH splines outperform the circular splines for increasing accuracy, due to the higher approximation order.     

Interpolating G Bézier surfaces over irregular curve networks for ship hull design

We propose a local method of constructing piecewise G¹ Bézier patches to span an irregular curve network, without modifying the given curves at odd- and 4-valent node points. Topologically irregular regions of the network are approximated by implicit surfaces, which are used to generate split curves, which subdivide the regions into triangular and/or rectangular sub-regions. The subdivided regions are then interpolated with Bézier patches. We analyze various singular cases of the G¹ condition that is to be met by the interpolation and propose a new G¹ continuity condition using linear and quartic scalar weight functions. Using this condition, a curve network can be interpolated without modification at 4-valent nodes with two collinear tangent vectors, even in the presence of singularities. We demonstrate our approach in a ship hull.     

Cone spline approximation via fat conic spline fitting

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fitting. An efficient fitting algorithm is also proposed for fat conic spline fitting with controllable tolerances. Several examples about approximation of general developable surfaces or other types of ruled surfaces by cone spline surfaces are presented.     

A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.     

Writing power into online discussion

This article considers the way in which control of interaction emerges as a function of personal agency and external factors in a group of students engaged in online asynchronous text-based communication in a distance education program. It is structured around the argument that control is partly related to the power that individuals have to give effect to their wishes, but also acknowledges that this sense of agency is always in relation to the powers of others and more structural constraints. A picture emerges of the choices students make in deciding when to initiate discussion and respond to others, and about decisions concerning whose messages they would read and when. The impact of other students, of online groups, and instructors seems to play an important role in determining how participants participate in online interaction. Consideration of broader issues shows how the context in which students engage in interaction impacts the nature and extent of that interaction. The article concludes that being aware, and taking advantage of the socially grounded nature of online interaction provides the basis from which educators can act to ensure that interaction in online learning communities is enabling for the learning of all students.     

Paying attention to adult learners online: The pedagogy and politics of community

Our article profiles the evolution of a fully online writing course designed for adult learners in our university's Prior Learning Assessment Program. Based on our own observations and experiences teaching adult learners online, we question if the virtual learning environment presents different challenges and prospects for the adult learner versus the traditional student learner, along with an extension and complication of the more social metaphors of “virtual community.” Moreover, because of the changing demographic from traditional to adult students, we argue that this change also fosters a change in the relationship between teachers and students. In chronicling this relationship, we note problems when the labor of adult education becomes invisible to those supervising online instructors. Because of these “invisible” labor issues, we argue that successful online instruction must include a range of interactions between students and instructors that extend the more public concept of community to better acknowledge the importance of personal, private interaction. Thus, we conclude with a call to rethink our online writing pedagogies to be more flexible to adult learner needs and learning styles, simultaneously recognizing the impact of adult online education on faculty workload.     

Why Napster matters to writing: Filesharing as a new ethic of digital delivery

This article discusses the Napster phenomenon and its cultural significance, traces some of the threads of the current “copyright crisis,” and connects these cultural and legal dynamics to show how the current filesharing context of digital environments pertains to issues affecting writing teachers. The article (1) urges writing teachers to view the Napster moment—and the writing practice at the center of it, filesharing—in terms of the rhetorical and economic dynamics of digital publishing and in the context of public battles about copyright and intellectual property and (2) argues that digital filesharing forms the basis for an emergent ethic of digital delivery, an ethic that should lead composition teachers to rethink pedagogical approaches and to revise plagiarism policies to recognize the value of filesharing and to acknowledge Fair Use as an ethic for digital composition.