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This paper makes three observations: 1) that preference is a partial ordering in one-dimension; 2) that a product, or a service, may be high-dimensional; consequently, and 3) transitivity, or its lack, results from choice of the direction for projection from high to low dimensions. The mass customization of cellular telephone designs gives this paper a context. The dimensions of the product space are: function, size, styling, color, etc. The medium for presentation (i.e., screen or paper), however, is necessarily two-dimensional (2-D). A criterion for projection is to preserve the information (such as, the similarity between the products, manifested as clusters, and the market opportunities, manifested as voids) from the high dimension. Drawing upon an analogy from the deformation mechanics of materials, the equilibrium conditions are formulated as distance and curvature. Distances give the clustering information; curvature gives the shape information. Projection is then seen as the process that minimizes the deformation in the projected geometry. The findings then become apparent. There are infinitely many ways to project. In most projections, intransitivity of preference results. Index Terms--Design methodology, distance measurement, geometry, human factors, optimization methods, perception.

In this paper we consider two manufacturing-related problems: 3D part disassemblability and surface machinability. The former is to find a feasible direction along which a part can be separated from a given 3D assembly, and the latter is to find a feasible direction in which an NC machining tool can approach a given surface. We present a unified formulation of these problems by using a system of linear inequalities. We also show that a feasible direction can be found in O(n) time by transforming the formulation into the 2D linear separability problem, where n is the number of faces. All feasible directions can also be found in O(n log n) time. Furthermore, by transforming the formulation into the smallest enclosing sphere problem, an O(n) time algorithm is proposed to find the optimal direction, i.e., the direction minimizing the maximum angle to the normal vectors of 3D surfaces., 1. Introduction This paper considers two geometric problems that arise in manufacturing: three-dimensional (3D) part disassemblability and surface machinability. The first problem is encountered in automatic generation of an assembly [...]

Automatic assignment of tolerances to dimensional mechanical assemblies is studied as an optimization problem; the objective of which is to minimize the (manufacturing) cost, subject to the constraints of (design) functionality and (assembly) interchangeability. By associating a nominal dimension and a tolerance to the variance, a probabilistic approach is adopted.Trigonometric functions relating the component geometries give rise to the nonlinearity in the system. Estimating an n-dimensional nonlinear integral by a polytope converts the probabilistic optimization formulation to a deterministic one. It also allows rapid evaluation of tolerance analysis embedded in tolerance synthesis.Local optimality is ensured by analysis of convexity and quasi-concavity of the objective function and some of the constraints. Sensitivity analysis is performed to provide search directions for global optimality. An implementation is reported with an example.

The visibility of a surface has wide applications in manufacturing, where accessibility of the workpiece to the processing agent is of critical importance. A surface is visible to a direction d if for every point on the surface a line-of-sight can be established along d. Important applications, such as die-face design, arise in manufacturing where surfaces must be constructed visible to a given direction. In this paper we present a family of swept surfaces with built-in visibility. In particular, methods are laid out to build translational, rotational and spined sweeps visible to a given direction by sweeping monotone section curves. In these methods, minimal limitations are imposed besides those needed to avoid surface singularities. To increase modeling flexibility, the methods are extended to sweeps with distinct end sections and nonuniform scaling functions. [S1087-1357(00)00103-9]

As data can be compressed, we inquire if time can also be compressed. In the context of manufacturing systems, time compression adopts such names as "concurrency" or "simultaneity." While it may be intuitively appealing that scaling (halving the size of a task, for example) should be linear (halving the time), such is not quite the case, as we have discovered. We report a quantitative explanation for the nonlinear behavior of time, as a function of the size of a task and the number of agents performing the task. Index Terms--Concurrency, cycle minimization, time compression, time density.

Studies whether time can be compressed in manufacturing systems. Quantitative explanation for the nonlinear behavior of time; Algebraical view of manufacturing operations; Model of concurrency; Processing and idleness.

In this paper we consider two manufacturing-related problems: 3D part disassemblability and surface machinability. The former is to find a feasible direction along which a part can be separated from a given 3D assembly, and the latter is to find a feasible direction in which an NC machining tool can approach a given surface. We present a unified formulation of these problems by using a system of linear inequalities. We also show that a feasible direction can be found in O(n) time by transforming the formulation into the 2D linear separability problem, where n is the number of faces. All feasible directions can also be found in O(n log n) time. Furthermore, by transforming the formulation into the smallest enclosing sphere problem, an O(n) time algorithm is proposed to find the optimal direction, i.e., the direction minimizing the maximum angle to the normal vectors of 3D surfaces. [ABSTRACT FROM AUTHOR]

As preprocessing for the two-dimensional cutting stock problem or pallet loading problem, we compute the minimum area convex hull. Given two polygons P and Q, we find their relative positions such that the convex hull encasing them is minimum in area. Let N be the total number of vertices in P and Q. We determine the minimum area convex hull in O(N) time. Q is allowed to translate by any amount relative to P, while assuming a constant number of orientations. Instead of recomputing the convex hull after every translation, we update the computed area at certain critical points. Linearity follows by showing that there are O(N) such critical points. [ABSTRACT FROM AUTHOR]

Purpose: Recent reports demonstrate a dramatically increased rate of secondary leukemia for breast cancer patients receiving adjuvant high-dose anthracycline and radiotherapy, and that radiation is an independent factor for the development of leukemia. This study aimed to evaluate the radiation body exposure during breast radiotherapy and to characterize the factors associated with an increased exposure., Patients and Methods: In a prospective cohort of 120 women, radiation measurements were taken from four sites on the body at the time of adjuvant breast radiotherapy. Multiple regression analysis was performed to analyze patient and treatment factors associated with the amount of scattered radiation., Results: For standard 50 Gy breast radiotherapy, the minimal dose received by abdominal organs is on average 0.45 Gy, ranging from 0.06 to 1.55 Gy. The use of physical wedges as a compensation technique was the most significant factor associated with increased scattered dose (p < 0.001), resulting in approximately three times more exposure compared with breast intensity-modulated radiation therapy (IMRT) and dynamic wedge., Conclusions: The amount of radiation that is scattered to a patient's body is consistent with exposure reported to be associated with excess of leukemia. In accordance with the As Low As Reasonably Achievable (ALARA) principle, we recommend using breast IMRT or virtual wedging for the radiotherapy of breast cancer receiving high-dose anthracycline chemotherapy.

With the emergence of new imaging and implant techniques, prostate brachytherapy has become increasingly popular over the last decade. Brachytherapy promises to deliver twice the biologically effective dose as conventional external beam treatments without increasing the dose to tissues surrounding the prostate. However, there are few or no published Australian series of its efficacy in the clinic. We present the experience of one of the first centres in Australia to offer this service to its patients: a series from Sir Charles Gairdner Hospital in Western Australia. We present data on the efficacy of brachytherapy in maintaining prostate specific antigen levels, as well as the rate of urinary, rectal and sexual complications. Our results compare favourably with other brachytherapy and external beam treatment series. We believe that with the increasing trend towards dose escalation and novel therapies, standardized measurements of success and failure need to be better defined, and that randomized trials comparing modalities are needed to improve the management of prostate cancer.